Polytope 0
Image of polytope 0 PALP id: 0
grdb id: 547386
Integer points: [ 1 0 0 -1 0]
[ 0 1 0 -1 0]
[ 0 0 1 -1 0]
Degree: 64
Hilbert function: 1 + 35 t + 165 t2 + 455 t3 + 969 t4 + 1771 t5 + 2925 t6 + 4495 t7 + 6545 t8 + 9139 t9 + 12341 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
12 rank 1, P3 x + y + z + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Polytope 1
Image of polytope 1 PALP id: 1
grdb id: 547378
Integer points: [ 1 0 0 -2 -1 0]
[ 0 1 0 -2 -1 0]
[ 0 0 1 -1 0 0]
Degree: 54
Hilbert function: 1 + 30 t + 140 t2 + 385 t3 + 819 t4 + 1496 t5 + 2470 t6 + 3795 t7 + 5525 t8 + 7714 t9 + 10416 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
4 rank 1, Q3 x + y + z + 2*x-1*y-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Polytope 2
Image of polytope 2 PALP id: 2
grdb id: 547377
Integer points: [ 1 0 0 -3 -1 0]
[ 0 1 0 -1 0 0]
[ 0 0 1 -1 0 0]
Degree: 72
Hilbert function: 1 + 39 t + 185 t2 + 511 t3 + 1089 t4 + 1991 t5 + 3289 t6 + 5055 t7 + 7361 t8 + 10279 t9 + 13881 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 2 1 none
Polytope 3
Image of polytope 3 PALP id: 3
grdb id: 544395
Integer points: [ 1 0 -1 0 -1 0]
[ 0 1 -1 0 0 0]
[ 0 0 0 1 -1 0]
Degree: 54
Hilbert function: 1 + 30 t + 140 t2 + 385 t3 + 819 t4 + 1496 t5 + 2470 t6 + 3795 t7 + 5525 t8 + 7714 t9 + 10416 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
4 rank 1, Q3 x + y + z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 4
Image of polytope 4 PALP id: 4
grdb id: 544392
Integer points: [ 1 -1 0 0 0 0]
[ 0 0 1 0 -1 0]
[ 0 0 0 1 -1 0]
Degree: 54
Hilbert function: 1 + 30 t + 140 t2 + 385 t3 + 819 t4 + 1496 t5 + 2470 t6 + 3795 t7 + 5525 t8 + 7714 t9 + 10416 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
44 rank 2, number 34 x + y + z + x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Polytope 5
Image of polytope 5 PALP id: 5
grdb id: 544391
Integer points: [ 1 -1 0 0 1 0]
[ 0 0 1 0 -1 0]
[ 0 0 0 1 -1 0]
Degree: 56
Hilbert function: 1 + 31 t + 145 t2 + 399 t3 + 849 t4 + 1551 t5 + 2561 t6 + 3935 t7 + 5729 t8 + 7999 t9 + 10801 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
30 rank 2, number 35 x + y + z + x*y-1*z-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Polytope 6
Image of polytope 6 PALP id: 6
grdb id: 544390
Integer points: [ 1 0 -1 0 1 0]
[ 0 1 -1 0 0 0]
[ 0 0 0 1 -1 0]
Degree: 54
Hilbert function: 1 + 30 t + 140 t2 + 385 t3 + 819 t4 + 1496 t5 + 2470 t6 + 3795 t7 + 5525 t8 + 7714 t9 + 10416 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
54 rank 2, number 33 x + y + z + x*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Polytope 7
Image of polytope 7 PALP id: 7
grdb id: 544387
Integer points: [ 1 -1 0 0 2 0]
[ 0 0 1 0 -1 0]
[ 0 0 0 1 -1 0]
Degree: 62
Hilbert function: 1 + 34 t + 160 t2 + 441 t3 + 939 t4 + 1716 t5 + 2834 t6 + 4355 t7 + 6341 t8 + 8854 t9 + 11956 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
58 rank 2, number 36 x + y + z + x2*y-1*z-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Polytope 8
Image of polytope 8 PALP id: 8
grdb id: 547367
Integer points: [ 1 0 0 -1 0 0 0]
[ 0 1 1 -2 -1 0 1]
[ 0 0 2 -2 -1 0 1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
2 rank 1, B4 y*z2 + 2*y*z + x + y + 2*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Polytope 9
Image of polytope 9 PALP id: 9
grdb id: 547363
Integer points: [ 1 0 0 -4 -2 -1 0]
[ 0 1 0 -2 -1 0 0]
[ 0 0 1 -1 0 0 0]
Degree: 64
Hilbert function: 1 + 35 t + 165 t2 + 455 t3 + 969 t4 + 1771 t5 + 2925 t6 + 4495 t7 + 6545 t8 + 9139 t9 + 12341 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 4 1 none
Polytope 10
Image of polytope 10 PALP id: 10
grdb id: 544357
Integer points: [ 1 0 -2 0 -2 -1 0]
[ 0 1 -1 0 0 0 0]
[ 0 0 0 1 -1 0 0]
Degree: 64
Hilbert function: 1 + 35 t + 165 t2 + 455 t3 + 969 t4 + 1771 t5 + 2925 t6 + 4495 t7 + 6545 t8 + 9139 t9 + 12341 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 5 1 none
Polytope 11
Image of polytope 11 PALP id: 11
grdb id: 544354
Integer points: [ 1 0 -2 0 -1 -1 0]
[ 0 1 -1 0 1 0 0]
[ 0 0 0 1 -1 0 0]
Degree: 64
Hilbert function: 1 + 35 t + 165 t2 + 455 t3 + 969 t4 + 1771 t5 + 2925 t6 + 4495 t7 + 6545 t8 + 9139 t9 + 12341 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 6 1 none
Polytope 12
Image of polytope 12 PALP id: 12
grdb id: 544356
Integer points: [ 1 0 0 -1 -2 -1 0]
[ 0 1 0 -1 -1 0 0]
[ 0 0 1 -1 0 0 0]
Degree: 48
Hilbert function: 1 + 27 t + 125 t2 + 343 t3 + 729 t4 + 1331 t5 + 2197 t6 + 3375 t7 + 4913 t8 + 6859 t9 + 9261 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
6 rank 2, number 32 x + y + z + 2*x-1 + x-1*y-1*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 13
Image of polytope 13 PALP id: 13
grdb id: 544343
Integer points: [ 1 0 0 -1 -1 -1 0]
[ 0 1 0 -1 -1 -1 0]
[ 0 0 1 -1 1 0 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
70 rank 2, number 30 x + y + z + x-1*y-1*z + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Polytope 14
Image of polytope 14 PALP id: 14
grdb id: 544345
Integer points: [ 1 0 -2 0 0 -1 0]
[ 0 1 -1 0 1 0 0]
[ 0 0 0 1 -1 0 0]
Degree: 56
Hilbert function: 1 + 31 t + 145 t2 + 399 t3 + 849 t4 + 1551 t5 + 2561 t6 + 3935 t7 + 5729 t8 + 7999 t9 + 10801 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
137 ? x + y + z + y*z-1 + 2*x-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Polytope 15
Image of polytope 15 PALP id: 15
grdb id: 544341
Integer points: [ 1 0 -1 0 -2 -1 0]
[ 0 1 -1 0 0 0 0]
[ 0 0 0 1 -1 0 0]
Degree: 56
Hilbert function: 1 + 31 t + 145 t2 + 399 t3 + 849 t4 + 1551 t5 + 2561 t6 + 3935 t7 + 5729 t8 + 7999 t9 + 10801 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
78 ? x + y + z + 2*x-1 + x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Polytope 16
Image of polytope 16 PALP id: 16
grdb id: 544337
Integer points: [ 1 0 0 -2 -1 -1 0]
[ 0 1 0 -1 1 0 0]
[ 0 0 1 -1 0 0 0]
Degree: 58
Hilbert function: 1 + 32 t + 150 t2 + 413 t3 + 879 t4 + 1606 t5 + 2652 t6 + 4075 t7 + 5933 t8 + 8284 t9 + 11186 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 2 1 none
Polytope 17
Image of polytope 17 PALP id: 17
grdb id: 544342
Integer points: [ 1 0 0 0 -2 -1 0]
[ 0 1 -1 0 0 0 0]
[ 0 0 0 1 -1 0 0]
Degree: 48
Hilbert function: 1 + 27 t + 125 t2 + 343 t3 + 729 t4 + 1331 t5 + 2197 t6 + 3375 t7 + 4913 t8 + 6859 t9 + 9261 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
21 rank 3, number 27 x + y + z + y-1 + 2*x-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Polytope 18
Image of polytope 18 PALP id: 18
grdb id: 544339
Integer points: [ 1 0 1 0 -2 -1 0]
[ 0 1 -1 0 0 0 0]
[ 0 0 0 1 -1 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
42 rank 2, number 29 x + y + z + x*y-1 + 2*x-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Polytope 19
Image of polytope 19 PALP id: 19
grdb id: 544340
Integer points: [ 1 -1 0 0 2 1 0]
[ 0 0 1 0 -2 -1 0]
[ 0 0 0 1 -1 0 0]
Degree: 52
Hilbert function: 1 + 29 t + 135 t2 + 371 t3 + 789 t4 + 1441 t5 + 2379 t6 + 3655 t7 + 5321 t8 + 7429 t9 + 10031 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
53 ? x + y + z + 2*x*y-1 + x2*y-2*z-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Polytope 20
Image of polytope 20 PALP id: 20
grdb id: 520159
Integer points: [ 1 -1 0 1 0 0 0]
[ 0 0 1 -1 0 -1 0]
[ 0 0 0 0 1 -1 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
48 rank 2, number 31 x + y + z + x*y-1 + x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 21
Image of polytope 21 PALP id: 21
grdb id: 520158
Integer points: [ 1 0 -1 0 0 -1 0]
[ 0 1 0 -1 0 -1 0]
[ 0 0 0 0 1 -1 0]
Degree: 48
Hilbert function: 1 + 27 t + 125 t2 + 343 t3 + 729 t4 + 1331 t5 + 2197 t6 + 3375 t7 + 4913 t8 + 6859 t9 + 9261 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
6 rank 2, number 32 x + y + z + y-1 + x-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 22
Image of polytope 22 PALP id: 22
grdb id: 520157
Integer points: [ 1 0 0 -1 -1 1 0]
[ 0 1 0 0 -1 1 0]
[ 0 0 1 -1 0 1 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
70 rank 2, number 30 x*y*z + x + y + z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 23
Image of polytope 23 PALP id: 23
grdb id: 520154
Integer points: [ 1 -1 0 -1 0 -2 0]
[ 0 0 1 -1 0 -1 0]
[ 0 0 0 0 1 -1 0]
Degree: 54
Hilbert function: 1 + 30 t + 140 t2 + 385 t3 + 819 t4 + 1496 t5 + 2470 t6 + 3795 t7 + 5525 t8 + 7714 t9 + 10416 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
44 rank 2, number 34 x + y + z + x-1 + x-1*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 24
Image of polytope 24 PALP id: 24
grdb id: 520135
Integer points: [ 1 -1 0 -1 0 1 0]
[ 0 0 1 -1 0 0 0]
[ 0 0 0 0 1 -1 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
41 ? x + y + z + x*z-1 + x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Polytope 25
Image of polytope 25 PALP id: 25
grdb id: 520137
Integer points: [ 1 -1 0 0 0 1 0]
[ 0 0 1 0 -1 1 0]
[ 0 0 0 1 -1 0 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
113 rank 3, number 26 x*y + x + y + z + x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Polytope 26
Image of polytope 26 PALP id: 26
grdb id: 520127
Integer points: [ 1 -1 0 0 1 1 0]
[ 0 0 1 0 -1 1 0]
[ 0 0 0 1 -1 0 0]
Degree: 50
Hilbert function: 1 + 28 t + 130 t2 + 357 t3 + 759 t4 + 1386 t5 + 2288 t6 + 3515 t7 + 5117 t8 + 7144 t9 + 9646 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
163 ? x*y + x + y + z + x*y-1*z-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Polytope 27
Image of polytope 27 PALP id: 27
grdb id: 520139
Integer points: [ 1 -1 0 0 1 1 0]
[ 0 0 1 0 0 -1 0]
[ 0 0 0 1 -1 0 0]
Degree: 52
Hilbert function: 1 + 29 t + 135 t2 + 371 t3 + 789 t4 + 1441 t5 + 2379 t6 + 3655 t7 + 5321 t8 + 7429 t9 + 10031 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
53 ? x + y + z + x*z-1 + x*y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Polytope 28
Image of polytope 28 PALP id: 28
grdb id: 520136
Integer points: [ 1 -1 0 1 0 0 0]
[ 0 0 1 -1 0 1 0]
[ 0 0 0 0 1 -1 0]
Degree: 50
Hilbert function: 1 + 28 t + 130 t2 + 357 t3 + 759 t4 + 1386 t5 + 2288 t6 + 3515 t7 + 5117 t8 + 7144 t9 + 9646 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
84 ? x + y + z + y*z-1 + x*y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Polytope 29
Image of polytope 29 PALP id: 29
grdb id: 520138
Integer points: [ 1 0 0 -1 0 1 0]
[ 0 1 -1 0 0 0 0]
[ 0 0 0 0 1 -1 0]
Degree: 48
Hilbert function: 1 + 27 t + 125 t2 + 343 t3 + 729 t4 + 1331 t5 + 2197 t6 + 3375 t7 + 4913 t8 + 6859 t9 + 9261 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
90 rank 3, number 28 x + y + z + x*z-1 + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Polytope 30
Image of polytope 30 PALP id: 30
grdb id: 520140
Integer points: [ 1 0 0 0 0 -1 0]
[ 0 1 0 0 -1 0 0]
[ 0 0 1 -1 0 0 0]
Degree: 48
Hilbert function: 1 + 27 t + 125 t2 + 343 t3 + 729 t4 + 1331 t5 + 2197 t6 + 3375 t7 + 4913 t8 + 6859 t9 + 9261 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
21 rank 3, number 27 x + y + z + z-1 + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Polytope 31
Image of polytope 31 PALP id: 31
grdb id: 547347
Integer points: [ 1 0 0 -5 -3 -1 -2 0]
[ 0 1 0 -2 -1 0 -1 0]
[ 0 0 1 -2 -1 0 -1 0]
Degree: 50
Hilbert function: 1 + 28 t + 130 t2 + 357 t3 + 759 t4 + 1386 t5 + 2288 t6 + 3515 t7 + 5117 t8 + 7144 t9 + 9646 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 7 1 none
Polytope 32
Image of polytope 32 PALP id: 32
grdb id: 544246
Integer points: [ 1 0 0 -3 -1 -2 -1 0]
[ 0 1 0 -1 -1 -1 0 0]
[ 0 0 1 -1 1 0 0 0]
Degree: 56
Hilbert function: 1 + 31 t + 145 t2 + 399 t3 + 849 t4 + 1551 t5 + 2561 t6 + 3935 t7 + 5729 t8 + 7999 t9 + 10801 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 8 1 none
Polytope 33
Image of polytope 33 PALP id: 33
grdb id: 544228
Integer points: [ 1 0 0 -1 -1 -1 -1 0]
[ 0 1 0 -1 -1 -1 -1 0]
[ 0 0 1 -1 2 1 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
33 rank 2, number 28 x + y + z + x-1*y-1*z2 + 3*x-1*y-1*z + 3*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Polytope 34
Image of polytope 34 PALP id: 34
grdb id: 544232
Integer points: [ 1 -1 0 0 1 1 0 0]
[ 0 0 1 0 -2 -1 -1 0]
[ 0 0 0 1 -2 -1 -1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
57 ? x + y + z + 2*x*y-1*z-1 + x-1 + 2*y-1*z-1 + x*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Polytope 35
Image of polytope 35 PALP id: 35
grdb id: 544230
Integer points: [ 1 0 -2 0 -2 -1 -1 0]
[ 0 1 -1 0 -2 -1 0 0]
[ 0 0 0 1 -1 0 0 0]
Degree: 50
Hilbert function: 1 + 28 t + 130 t2 + 357 t3 + 759 t4 + 1386 t5 + 2288 t6 + 3515 t7 + 5117 t8 + 7144 t9 + 9646 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
73 ? x + y + z + 2*x-1 + 2*x-1*y-1 + x-2*y-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Polytope 36
Image of polytope 36 PALP id: 36
grdb id: 544205
Integer points: [ 1 0 -1 0 -2 -1 -1 0]
[ 0 1 1 0 -2 -1 0 0]
[ 0 0 0 1 -1 0 0 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 4 1 none
Polytope 37
Image of polytope 37 PALP id: 37
grdb id: 544227
Integer points: [ 1 0 0 -1 -2 -1 -1 0]
[ 0 1 0 -1 1 0 1 0]
[ 0 0 1 -1 0 0 0 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 2 1 none
Polytope 38
Image of polytope 38 PALP id: 38
grdb id: 544212
Integer points: [ 1 0 -1 0 -2 -1 -1 0]
[ 0 1 -1 0 2 1 0 0]
[ 0 0 0 1 -1 0 0 0]
Degree: 62
Hilbert function: 1 + 34 t + 160 t2 + 441 t3 + 939 t4 + 1716 t5 + 2834 t6 + 4355 t7 + 6341 t8 + 8854 t9 + 11956 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 4 1 none
Polytope 39
Image of polytope 39 PALP id: 39
grdb id: 544231
Integer points: [ 1 0 2 0 -2 -1 0 1]
[ 0 1 1 0 -2 -1 0 1]
[ 0 0 0 1 -1 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
29 rank 2, number 23 x2*y + 2*x*y + x + y + z + 2*x-1*y-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Polytope 40
Image of polytope 40 PALP id: 40
grdb id: 544218
Integer points: [ 1 -1 0 0 3 2 0 1]
[ 0 0 1 0 -2 -1 0 -1]
[ 0 0 0 1 -2 -1 0 -1]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
74 ? x + y + z + 2*x2*y-1*z-1 + x3*y-2*z-2 + 2*x*y-1*z-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Polytope 41
Image of polytope 41 PALP id: 41
grdb id: 520061
Integer points: [ 1 0 0 -2 -2 1 -1 0]
[ 0 1 0 0 -1 1 0 0]
[ 0 0 1 -1 0 1 0 0]
Degree: 56
Hilbert function: 1 + 31 t + 145 t2 + 399 t3 + 849 t4 + 1551 t5 + 2561 t6 + 3935 t7 + 5729 t8 + 7999 t9 + 10801 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
30 rank 2, number 35 x*y*z + x + y + z + x-1 + x-2*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Polytope 42
Image of polytope 42 PALP id: 42
grdb id: 520063
Integer points: [ 1 0 0 0 -1 -2 -1 0]
[ 0 1 -1 0 1 0 0 0]
[ 0 0 0 1 -1 -1 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
14 rank 1, B5 x + y + z + x-1*y*z-1 + y-1 + 2*x-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 43
Image of polytope 43 PALP id: 43
grdb id: 520049
Integer points: [ 1 0 0 0 -1 -1 -1 0]
[ 0 1 0 -1 -1 1 0 0]
[ 0 0 1 -1 0 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
63 ? x + y + z + x-1*y + 2*x-1 + y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 44
Image of polytope 44 PALP id: 44
grdb id: 520041
Integer points: [ 1 0 -1 -1 0 -1 -1 0]
[ 0 1 -1 1 0 2 0 0]
[ 0 0 0 0 1 -1 0 0]
Degree: 56
Hilbert function: 1 + 31 t + 145 t2 + 399 t3 + 849 t4 + 1551 t5 + 2561 t6 + 3935 t7 + 5729 t8 + 7999 t9 + 10801 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
78 ? x + y + z + x-1*y2*z-1 + x-1*y + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 45
Image of polytope 45 PALP id: 45
grdb id: 520058
Integer points: [ 1 -1 0 0 -2 0 -1 0]
[ 0 0 1 0 -1 -1 -1 0]
[ 0 0 0 1 -1 1 0 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
48 rank 2, number 31 x + y + z + y-1*z + x-1 + 2*x-1*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 46
Image of polytope 46 PALP id: 46
grdb id: 520051
Integer points: [ 1 -1 0 0 -1 -2 -1 0]
[ 0 0 1 0 -1 -2 -1 0]
[ 0 0 0 1 -1 -1 0 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
41 ? x + y + z + x-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 47
Image of polytope 47 PALP id: 47
grdb id: 520020
Integer points: [ 1 0 -2 0 0 -1 -1 0]
[ 0 1 -1 0 1 0 0 0]
[ 0 0 0 1 -1 1 0 0]
Degree: 54
Hilbert function: 1 + 30 t + 140 t2 + 385 t3 + 819 t4 + 1496 t5 + 2470 t6 + 3795 t7 + 5525 t8 + 7714 t9 + 10416 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 6 1 none
Polytope 48
Image of polytope 48 PALP id: 48
grdb id: 520026
Integer points: [ 1 0 -1 -1 0 -2 -1 0]
[ 0 1 -1 1 0 -1 0 0]
[ 0 0 0 0 1 -1 0 0]
Degree: 50
Hilbert function: 1 + 28 t + 130 t2 + 357 t3 + 759 t4 + 1386 t5 + 2288 t6 + 3515 t7 + 5117 t8 + 7144 t9 + 9646 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 6 1 none
Polytope 49
Image of polytope 49 PALP id: 49
grdb id: 520044
Integer points: [ 1 0 -1 -1 0 -2 -1 0]
[ 0 1 -1 1 0 0 0 0]
[ 0 0 0 0 1 -1 0 0]
Degree: 54
Hilbert function: 1 + 30 t + 140 t2 + 385 t3 + 819 t4 + 1496 t5 + 2470 t6 + 3795 t7 + 5525 t8 + 7714 t9 + 10416 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 5 1 none
Polytope 50
Image of polytope 50 PALP id: 50
grdb id: 520019
Integer points: [ 1 0 -1 -1 0 -2 -1 0]
[ 0 1 -1 1 0 1 0 0]
[ 0 0 0 0 1 -1 0 0]
Degree: 58
Hilbert function: 1 + 32 t + 150 t2 + 413 t3 + 879 t4 + 1606 t5 + 2652 t6 + 4075 t7 + 5933 t8 + 8284 t9 + 11186 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 6 1 none
Polytope 51
Image of polytope 51 PALP id: 51
grdb id: 520057
Integer points: [ 1 0 -1 0 -2 0 -1 0]
[ 0 1 -1 0 0 -1 0 0]
[ 0 0 0 1 -1 1 0 0]
Degree: 48
Hilbert function: 1 + 27 t + 125 t2 + 343 t3 + 729 t4 + 1331 t5 + 2197 t6 + 3375 t7 + 4913 t8 + 6859 t9 + 9261 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
90 rank 3, number 28 x + y + z + y-1*z + 2*x-1 + x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 52
Image of polytope 52 PALP id: 52
grdb id: 520054
Integer points: [ 1 0 0 -1 -2 -1 -1 0]
[ 0 1 0 -1 -1 0 0 0]
[ 0 0 1 -1 0 1 0 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
108 ? x + y + z + x-1*z + 2*x-1 + x-1*y-1*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 53
Image of polytope 53 PALP id: 53
grdb id: 520027
Integer points: [ 1 0 0 -1 -1 -2 -1 0]
[ 0 1 0 -1 0 -1 0 0]
[ 0 0 1 -1 1 -1 0 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 2 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 54
Image of polytope 54 PALP id: 54
grdb id: 520050
Integer points: [ 1 0 0 -1 0 -1 -1 0]
[ 0 1 0 -1 1 1 0 0]
[ 0 0 1 0 -1 -2 -1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
33 rank 2, number 28 x + y + z + y*z-1 + x-1*y*z-2 + 2*x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 55
Image of polytope 55 PALP id: 55
grdb id: 520047
Integer points: [ 1 0 0 0 -1 -2 -1 0]
[ 0 1 0 -1 1 1 0 0]
[ 0 0 1 -1 1 1 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
42 rank 2, number 29 x + y + z + x-1*y*z + x-2*y*z + 2*x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 56
Image of polytope 56 PALP id: 56
grdb id: 519917
Integer points: [ 1 -1 0 0 1 -1 0 0]
[ 0 0 1 0 -1 -1 -1 0]
[ 0 0 0 1 -1 -1 -1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
57 ? x + y + z + x*y-1*z-1 + x-1 + 2*y-1*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Polytope 57
Image of polytope 57 PALP id: 57
grdb id: 519925
Integer points: [ 1 0 -1 -1 0 -1 -1 0]
[ 0 1 -1 1 0 1 0 0]
[ 0 0 0 0 1 -1 0 0]
Degree: 52
Hilbert function: 1 + 29 t + 135 t2 + 371 t3 + 789 t4 + 1441 t5 + 2379 t6 + 3655 t7 + 5321 t8 + 7429 t9 + 10031 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
120 ? x + y + z + x-1*y + x-1*y*z-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Polytope 58
Image of polytope 58 PALP id: 58
grdb id: 519921
Integer points: [ 1 0 -1 0 -1 -1 -1 0]
[ 0 1 -1 0 -1 1 0 0]
[ 0 0 0 1 -1 0 0 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
130 rank 3, number 24 x + y + z + x-1*y + 2*x-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Polytope 59
Image of polytope 59 PALP id: 59
grdb id: 519920
Integer points: [ 1 0 -1 0 0 -1 -1 0]
[ 0 1 -1 0 1 1 0 0]
[ 0 0 0 1 -1 0 0 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
150 ? x + y + z + y*z-1 + x-1*y + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Polytope 60
Image of polytope 60 PALP id: 60
grdb id: 519932
Integer points: [ 1 0 0 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 0 0]
[ 0 0 1 -1 0 0 0 0]
Degree: 48
Hilbert function: 1 + 27 t + 125 t2 + 343 t3 + 729 t4 + 1331 t5 + 2197 t6 + 3375 t7 + 4913 t8 + 6859 t9 + 9261 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
117 ? x + y + z + x-1*y + 2*x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Polytope 61
Image of polytope 61 PALP id: 61
grdb id: 519916
Integer points: [ 1 0 0 0 -1 -1 -1 0]
[ 0 1 -1 0 0 0 0 0]
[ 0 0 0 1 -1 1 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
142 ? x + y + z + x-1*z + y-1 + 2*x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Polytope 62
Image of polytope 62 PALP id: 62
grdb id: 519918
Integer points: [ 1 0 1 0 -1 -1 -1 0]
[ 0 1 -1 0 0 0 0 0]
[ 0 0 0 1 -1 1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
160 ? x + y + z + x*y-1 + x-1*z + 2*x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Polytope 63
Image of polytope 63 PALP id: 63
grdb id: 519928
Integer points: [ 1 -1 0 0 0 2 1 0]
[ 0 0 1 0 -1 -1 -1 0]
[ 0 0 0 1 -1 -1 -1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
152 rank 3, number 22 x + y + z + x2*y-1*z-1 + 2*x*y-1*z-1 + x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Polytope 64
Image of polytope 64 PALP id: 64
grdb id: 519913
Integer points: [ 1 0 -1 0 0 -2 -1 0]
[ 0 1 0 -1 0 -2 -1 0]
[ 0 0 0 0 1 -1 0 0]
Degree: 50
Hilbert function: 1 + 28 t + 130 t2 + 357 t3 + 759 t4 + 1386 t5 + 2288 t6 + 3515 t7 + 5117 t8 + 7144 t9 + 9646 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
73 ? x + y + z + y-1 + x-1 + 2*x-1*y-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Polytope 65
Image of polytope 65 PALP id: 65
grdb id: 519911
Integer points: [ 1 0 0 -1 0 -2 -1 0]
[ 0 1 -1 1 0 0 0 0]
[ 0 0 0 0 1 -1 0 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
133 ? x + y + z + x-1*y + y-1 + 2*x-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Polytope 66
Image of polytope 66 PALP id: 66
grdb id: 519912
Integer points: [ 1 0 0 1 0 -2 -1 0]
[ 0 1 -1 1 0 0 0 0]
[ 0 0 0 0 1 -1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
105 ? x*y + x + y + z + y-1 + 2*x-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Polytope 67
Image of polytope 67 PALP id: 67
grdb id: 430442
Integer points: [ 1 0 0 -1 0 0 -1 0]
[ 0 1 0 0 0 -1 -1 0]
[ 0 0 1 0 -1 0 -1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
14 rank 1, B5 x + y + z + z-1 + y-1 + x-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Polytope 68
Image of polytope 68 PALP id: 68
grdb id: 430441
Integer points: [ 1 0 1 0 -1 0 1 0]
[ 0 1 1 -1 0 0 1 0]
[ 0 0 2 -1 -1 1 1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
33 rank 2, number 28 x*y*z2 + x*y*z + x + y + z + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Polytope 69
Image of polytope 69 PALP id: 69
grdb id: 430433
Integer points: [ 1 -1 0 0 -1 -1 0 0]
[ 0 0 1 0 -1 0 1 0]
[ 0 0 0 1 0 -1 1 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
48 rank 2, number 31 y*z + x + y + z + x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 70
Image of polytope 70 PALP id: 70
grdb id: 430438
Integer points: [ 1 -1 0 0 1 -1 0 0]
[ 0 0 1 0 0 -1 -1 0]
[ 0 0 0 1 -1 0 -1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
61 rank 2, number 27 x + y + z + x*z-1 + x-1 + y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 71
Image of polytope 71 PALP id: 71
grdb id: 430439
Integer points: [ 1 0 0 -1 0 1 0 0]
[ 0 1 -1 0 0 0 1 0]
[ 0 0 0 0 1 -1 -1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
42 rank 2, number 29 x + y + z + x*z-1 + y*z-1 + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 72
Image of polytope 72 PALP id: 72
grdb id: 430418
Integer points: [ 1 -1 0 -1 0 -1 -1 0]
[ 0 0 1 -1 0 -1 0 0]
[ 0 0 0 0 1 -1 1 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
113 rank 3, number 26 x + y + z + x-1*z + x-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 73
Image of polytope 73 PALP id: 73
grdb id: 430422
Integer points: [ 1 -1 0 0 -1 -1 -1 0]
[ 0 0 1 0 -1 0 -1 0]
[ 0 0 0 1 0 -1 -1 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
41 ? x + y + z + x-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 74
Image of polytope 74 PALP id: 74
grdb id: 430426
Integer points: [ 1 -1 0 0 0 -1 1 0]
[ 0 0 1 0 -1 -1 0 0]
[ 0 0 0 1 -1 -1 1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
57 ? x*z + x + y + z + x-1 + y-1*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 75
Image of polytope 75 PALP id: 75
grdb id: 430417
Integer points: [ 1 -1 0 0 0 1 1 0]
[ 0 0 1 0 -1 -1 0 0]
[ 0 0 0 1 -1 -1 1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
152 rank 3, number 22 x*z + x + y + z + x*y-1*z-1 + x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 76
Image of polytope 76 PALP id: 76
grdb id: 430423
Integer points: [ 1 -1 0 0 1 0 1 0]
[ 0 0 1 0 -1 -1 0 0]
[ 0 0 0 1 0 -1 1 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
158 ? x*z + x + y + z + x*y-1 + x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 77
Image of polytope 77 PALP id: 77
grdb id: 430420
Integer points: [ 1 0 -1 0 -1 0 -1 0]
[ 0 1 0 -1 1 0 -1 0]
[ 0 0 0 0 0 1 -1 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
86 ? x + y + z + x-1*y + y-1 + x-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 78
Image of polytope 78 PALP id: 78
grdb id: 430425
Integer points: [ 1 0 0 -1 0 0 -1 0]
[ 0 1 -1 0 0 -1 0 0]
[ 0 0 0 0 1 -1 1 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
86 ? x + y + z + x-1*z + y-1 + x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 79
Image of polytope 79 PALP id: 79
grdb id: 430424
Integer points: [ 1 0 0 -1 1 0 -1 0]
[ 0 1 -1 0 1 0 -1 0]
[ 0 0 0 0 0 1 -1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
63 ? x*y + x + y + z + y-1 + x-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 80
Image of polytope 80 PALP id: 80
grdb id: 430411
Integer points: [ 1 0 0 -1 -1 0 -2 0]
[ 0 1 -1 0 1 0 1 0]
[ 0 0 0 0 0 1 -1 0]
Degree: 48
Hilbert function: 1 + 27 t + 125 t2 + 343 t3 + 729 t4 + 1331 t5 + 2197 t6 + 3375 t7 + 4913 t8 + 6859 t9 + 9261 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
90 rank 3, number 28 x + y + z + x-1*y + y-1 + x-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 81
Image of polytope 81 PALP id: 81
grdb id: 430515
Integer points: [ 1 0 0 -1 0 1 0 0]
[ 0 1 -1 0 0 1 -1 0]
[ 0 0 0 0 1 0 -1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
102 ? x*y + x + y + z + y-1 + x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 10 irreducible and admissible
Polytope 82
Image of polytope 82 PALP id: 82
grdb id: 430513
Integer points: [ 1 0 0 -1 0 1 1 0]
[ 0 1 -1 0 0 1 0 0]
[ 0 0 0 0 1 0 -1 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
93 ? x*y + x + y + z + x*z-1 + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 10 irreducible and admissible
Polytope 83
Image of polytope 83 PALP id: 83
grdb id: 430516
Integer points: [ 1 0 0 -1 1 0 1 0]
[ 0 1 -1 0 1 0 1 0]
[ 0 0 0 0 0 1 -1 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
150 ? x*y + x*y*z-1 + x + y + z + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 10 irreducible and admissible
Polytope 84
Image of polytope 84 PALP id: 84
grdb id: 430514
Integer points: [ 1 0 0 0 0 -1 1 0]
[ 0 1 0 0 -1 0 1 0]
[ 0 0 1 -1 0 0 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
142 ? x*y + x + y + z + z-1 + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 10 irreducible and admissible
Polytope 85
Image of polytope 85 PALP id: 85
grdb id: 547330
Integer points: [ 1 0 0 -3 -2 -1 0 -1 0]
[ 0 1 1 -2 -1 0 1 -1 0]
[ 0 0 2 -2 -1 0 1 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 12 1 none
Polytope 86
Image of polytope 86 PALP id: 86
grdb id: 547336
Integer points: [ 1 0 0 -2 -1 0 -1 0 0]
[ 0 1 1 -3 -1 1 -2 0 -1]
[ 0 0 2 -3 -1 1 -2 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 4 1 none
Image of facet 9 2 irreducible and admissible
Polytope 87
Image of polytope 87 PALP id: 87
grdb id: 547337
Integer points: [ 1 0 0 -4 -3 -2 -1 -1 0]
[ 0 1 0 -4 -3 -2 -1 -1 0]
[ 0 0 1 -3 -2 -1 0 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 2 1 none
Image of facet 13 2 irreducible and admissible
Polytope 88
Image of polytope 88 PALP id: 88
grdb id: 547334
Integer points: [ 1 0 0 -6 -3 -2 -1 -1 0]
[ 0 1 0 -4 -2 -1 0 -1 0]
[ 0 0 1 -1 0 0 0 0 0]
Degree: 72
Hilbert function: 1 + 39 t + 185 t2 + 511 t3 + 1089 t4 + 1991 t5 + 3289 t6 + 5055 t7 + 7361 t8 + 10279 t9 + 13881 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 4 1 none
Image of facet 12 1 none
Polytope 89
Image of polytope 89 PALP id: 89
grdb id: 547331
Integer points: [ 1 0 0 -6 -4 -2 -3 -1 0]
[ 0 1 0 -3 -2 -1 -1 0 0]
[ 0 0 1 -2 -1 0 -1 0 0]
Degree: 48
Hilbert function: 1 + 27 t + 125 t2 + 343 t3 + 729 t4 + 1331 t5 + 2197 t6 + 3375 t7 + 4913 t8 + 6859 t9 + 9261 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 14 1 none
Image of facet 9 1 irreducible and admissible
Polytope 90
Image of polytope 90 PALP id: 90
grdb id: 544072
Integer points: [ 1 0 0 -2 -2 -1 -1 -1 0]
[ 0 1 0 -2 -1 -1 -1 0 0]
[ 0 0 1 -1 -2 -1 0 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 2 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 91
Image of polytope 91 PALP id: 91
grdb id: 544065
Integer points: [ 1 0 0 -2 0 0 -1 -1 0]
[ 0 1 0 0 -2 -1 0 -1 0]
[ 0 0 1 -1 -1 0 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
2 rank 1, B4 x + y + z + 2*y-1 + 2*x-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 92
Image of polytope 92 PALP id: 92
grdb id: 544075
Integer points: [ 1 0 0 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -2 -1 0 -1 0]
[ 0 0 1 1 -2 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + x-1*y*z + 3*x-1 + 2*y-1*z-1 + 3*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 2 irreducible and admissible
Polytope 93
Image of polytope 93 PALP id: 93
grdb id: 544059
Integer points: [ 1 0 -2 0 -1 -1 -1 0 0]
[ 0 1 -1 0 2 1 0 1 0]
[ 0 0 0 1 -2 -1 0 -1 0]
Degree: 48
Hilbert function: 1 + 27 t + 125 t2 + 343 t3 + 729 t4 + 1331 t5 + 2197 t6 + 3375 t7 + 4913 t8 + 6859 t9 + 9261 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 17 1 none
Polytope 94
Image of polytope 94 PALP id: 94
grdb id: 544070
Integer points: [ 1 0 0 -3 -3 -2 -1 -1 0]
[ 0 1 0 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 0 0 0 0 0]
Degree: 54
Hilbert function: 1 + 30 t + 140 t2 + 385 t3 + 819 t4 + 1496 t5 + 2470 t6 + 3795 t7 + 5525 t8 + 7714 t9 + 10416 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 18 1 none
Polytope 95
Image of polytope 95 PALP id: 95
grdb id: 544071
Integer points: [ 1 0 0 -2 -3 -2 -1 -1 0]
[ 0 1 0 -2 -2 -1 0 -1 0]
[ 0 0 1 -1 0 0 0 0 0]
Degree: 48
Hilbert function: 1 + 27 t + 125 t2 + 343 t3 + 729 t4 + 1331 t5 + 2197 t6 + 3375 t7 + 4913 t8 + 6859 t9 + 9261 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Image of facet 5 1 none
Polytope 96
Image of polytope 96 PALP id: 96
grdb id: 544068
Integer points: [ 1 0 0 -2 -3 -1 -2 0 -1]
[ 0 1 0 -1 -2 0 -1 0 -1]
[ 0 0 1 0 -2 0 -1 0 -1]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 4 1 none
Polytope 97
Image of polytope 97 PALP id: 97
grdb id: 544066
Integer points: [ 1 0 0 -2 -3 -2 -1 -1 0]
[ 0 1 0 0 -2 -1 0 -1 0]
[ 0 0 1 -1 0 0 0 0 0]
Degree: 48
Hilbert function: 1 + 27 t + 125 t2 + 343 t3 + 729 t4 + 1331 t5 + 2197 t6 + 3375 t7 + 4913 t8 + 6859 t9 + 9261 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 19 1 none
Polytope 98
Image of polytope 98 PALP id: 98
grdb id: 544073
Integer points: [ 1 0 0 -1 -3 -2 -1 -1 0]
[ 0 1 0 0 -3 -2 -1 -1 0]
[ 0 0 1 -1 -2 -1 0 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 2 1 none
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Polytope 99
Image of polytope 99 PALP id: 99
grdb id: 544054
Integer points: [ 1 0 0 -1 -3 -2 -1 -1 0]
[ 0 1 0 1 -2 -1 0 -1 0]
[ 0 0 1 -1 0 0 0 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 21 1 none
Polytope 100
Image of polytope 100 PALP id: 100
grdb id: 544074
Integer points: [ 1 0 0 0 -3 -1 -2 0 -1]
[ 0 1 0 -1 -2 -1 -1 0 0]
[ 0 0 1 -1 0 0 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Image of facet 6 1 none
Polytope 101
Image of polytope 101 PALP id: 101
grdb id: 544069
Integer points: [ 1 0 -3 0 -4 -2 -1 -1 0]
[ 0 1 -2 0 -3 -1 0 -1 0]
[ 0 0 0 1 -1 0 0 0 0]
Degree: 60
Hilbert function: 1 + 33 t + 155 t2 + 427 t3 + 909 t4 + 1661 t5 + 2743 t6 + 4215 t7 + 6137 t8 + 8569 t9 + 11571 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Image of facet 6 1 none
Polytope 102
Image of polytope 102 PALP id: 102
grdb id: 544062
Integer points: [ 1 0 -3 0 -4 -2 -1 -1 0]
[ 0 1 -2 0 -2 -1 0 -1 0]
[ 0 0 0 1 -1 0 0 0 0]
Degree: 60
Hilbert function: 1 + 33 t + 155 t2 + 427 t3 + 909 t4 + 1661 t5 + 2743 t6 + 4215 t7 + 6137 t8 + 8569 t9 + 11571 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 19 1 none
Polytope 103
Image of polytope 103 PALP id: 103
grdb id: 544063
Integer points: [ 1 0 0 -2 -4 -2 -3 -1 0]
[ 0 1 0 0 -2 -1 -1 0 0]
[ 0 0 1 -1 -1 0 -1 0 0]
Degree: 48
Hilbert function: 1 + 27 t + 125 t2 + 343 t3 + 729 t4 + 1331 t5 + 2197 t6 + 3375 t7 + 4913 t8 + 6859 t9 + 9261 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
6 rank 2, number 32 x + y + z + 2*x-1 + x-2*z-1 + 2*x-2*y-1 + 2*x-3*y-1*z-1 + x-4*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 104
Image of polytope 104 PALP id: 104
grdb id: 544061
Integer points: [ 1 0 -3 0 -5 -2 -1 -1 0]
[ 0 1 -2 0 -3 -1 0 -1 0]
[ 0 0 0 1 -1 0 0 0 0]
Degree: 66
Hilbert function: 1 + 36 t + 170 t2 + 469 t3 + 999 t4 + 1826 t5 + 3016 t6 + 4635 t7 + 6749 t8 + 9424 t9 + 12726 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 21 1 none
Polytope 105
Image of polytope 105 PALP id: 105
grdb id: 544019
Integer points: [ 1 0 0 -2 -2 -1 -1 -2 0]
[ 0 1 0 0 -2 0 -1 -1 0]
[ 0 0 1 -1 -1 0 0 -1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
42 rank 2, number 29 x + y + z + 2*x-1 + 2*x-1*y-1 + x-2*z-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 106
Image of polytope 106 PALP id: 106
grdb id: 543995
Integer points: [ 1 0 0 -2 -1 -1 -1 0 0]
[ 0 1 0 0 -2 0 -1 0 -1]
[ 0 0 1 -1 0 0 0 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 4 1 none
Polytope 107
Image of polytope 107 PALP id: 107
grdb id: 543998
Integer points: [ 1 0 0 -2 0 0 -1 0 -1]
[ 0 1 0 1 -2 -1 0 0 1]
[ 0 0 1 0 -1 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 4 1 none
Polytope 108
Image of polytope 108 PALP id: 108
grdb id: 544035
Integer points: [ 1 -1 0 0 1 1 0 0 0]
[ 0 0 1 1 -2 -1 1 0 -1]
[ 0 0 0 2 -2 -1 1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
32 ? y*z2 + 2*y*z + x + y + 2*x*y-1*z-1 + x-1 + 2*y-1*z-1 + x*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 6 irreducible and admissible
Polytope 109
Image of polytope 109 PALP id: 109
grdb id: 544032
Integer points: [ 1 0 -3 0 -3 -2 -1 -1 0]
[ 0 1 -2 0 -2 -1 0 -1 0]
[ 0 0 0 1 -1 0 0 0 0]
Degree: 54
Hilbert function: 1 + 30 t + 140 t2 + 385 t3 + 819 t4 + 1496 t5 + 2470 t6 + 3795 t7 + 5525 t8 + 7714 t9 + 10416 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
89 ? x + y + z + 3*x-1 + 2*x-1*y-1 + 3*x-2*y-1 + x-3*y-2 + x-3*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Polytope 110
Image of polytope 110 PALP id: 110
grdb id: 544033
Integer points: [ 1 0 0 -2 -3 -2 -1 -1 0]
[ 0 1 0 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 0 0 0 0 0]
Degree: 48
Hilbert function: 1 + 27 t + 125 t2 + 343 t3 + 729 t4 + 1331 t5 + 2197 t6 + 3375 t7 + 4913 t8 + 6859 t9 + 9261 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
115 ? x + y + z + 3*x-1 + 2*x-1*y-1 + 3*x-2*y-1 + x-2*y-1*z-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Polytope 111
Image of polytope 111 PALP id: 111
grdb id: 544034
Integer points: [ 1 0 0 -1 -3 -2 -1 -1 0]
[ 0 1 0 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 0 0 0 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
139 ? x + y + z + 3*x-1 + 2*x-1*y-1 + x-1*y-1*z-1 + 3*x-2*y-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Polytope 112
Image of polytope 112 PALP id: 112
grdb id: 544024
Integer points: [ 1 0 0 -1 -3 -2 -1 -1 0]
[ 0 1 0 0 -2 -1 0 -1 0]
[ 0 0 1 -1 0 0 0 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
118 ? x + y + z + 3*x-1 + x-1*z-1 + 2*x-1*y-1 + 3*x-2*y-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Polytope 113
Image of polytope 113 PALP id: 113
grdb id: 544028
Integer points: [ 1 0 0 0 -3 -2 -1 -1 0]
[ 0 1 -1 0 0 0 0 0 0]
[ 0 0 0 1 -2 -1 0 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
43 ? x + y + z + y-1 + 3*x-1 + 2*x-1*z-1 + 3*x-2*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Polytope 114
Image of polytope 114 PALP id: 114
grdb id: 544027
Integer points: [ 1 0 0 0 -3 -1 0 -2 -1]
[ 0 1 0 -1 1 0 0 1 1]
[ 0 0 1 -1 0 0 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Image of facet 2 1 none
Polytope 115
Image of polytope 115 PALP id: 115
grdb id: 544025
Integer points: [ 1 0 0 0 -3 -2 -1 -1 0]
[ 0 1 0 1 -2 -1 0 -1 0]
[ 0 0 1 -1 0 0 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
138 ? x + y + z + y*z-1 + 3*x-1 + 2*x-1*y-1 + 3*x-2*y-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Polytope 116
Image of polytope 116 PALP id: 116
grdb id: 544026
Integer points: [ 1 0 1 0 -3 -2 -1 -1 0]
[ 0 1 -1 0 0 0 0 0 0]
[ 0 0 0 1 -2 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
77 ? x + y + z + x*y-1 + 3*x-1 + 2*x-1*z-1 + 3*x-2*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Polytope 117
Image of polytope 117 PALP id: 117
grdb id: 543994
Integer points: [ 1 0 0 0 -4 -2 -1 -1 0]
[ 0 1 -1 0 2 1 0 1 0]
[ 0 0 0 1 -1 0 0 0 0]
Degree: 56
Hilbert function: 1 + 31 t + 145 t2 + 399 t3 + 849 t4 + 1551 t5 + 2561 t6 + 3935 t7 + 5729 t8 + 7999 t9 + 10801 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 4 2 none
Polytope 118
Image of polytope 118 PALP id: 118
grdb id: 519671
Integer points: [ 1 0 0 -1 0 -2 -1 -1 0]
[ 0 1 0 0 -1 -2 -1 -1 0]
[ 0 0 1 -1 -1 -1 -1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 2 1 none
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 119
Image of polytope 119 PALP id: 119
grdb id: 519672
Integer points: [ 1 0 0 0 -1 -1 -1 0 0]
[ 0 1 0 -2 1 -1 0 -1 0]
[ 0 0 1 -1 1 -1 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
2 rank 1, B4 x + y + z + x-1*y*z + 2*y-1 + 2*x-1 + y-2*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 120
Image of polytope 120 PALP id: 120
grdb id: 519668
Integer points: [ 1 0 0 -1 -2 -2 -1 -1 0]
[ 0 1 0 -1 0 1 0 1 0]
[ 0 0 1 -1 -1 0 0 0 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 6 1 none
Polytope 121
Image of polytope 121 PALP id: 121
grdb id: 519664
Integer points: [ 1 0 0 -2 -3 -1 -2 -1 0]
[ 0 1 0 0 -1 -1 -1 0 0]
[ 0 0 1 -1 -1 1 0 0 0]
Degree: 48
Hilbert function: 1 + 27 t + 125 t2 + 343 t3 + 729 t4 + 1331 t5 + 2197 t6 + 3375 t7 + 4913 t8 + 6859 t9 + 9261 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
6 rank 2, number 32 x + y + z + 2*x-1 + x-1*y-1*z + x-2*z-1 + 2*x-2*y-1 + x-3*y-1*z-1
21 rank 3, number 27 x + y + z + 3*x-1 + x-1*y-1*z + x-2*z-1 + 2*x-2*y-1 + x-3*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 122
Image of polytope 122 PALP id: 122
grdb id: 519649
Integer points: [ 1 0 0 -1 1 0 0 0 0]
[ 0 1 0 -1 -1 2 -1 0 1]
[ 0 0 1 -1 -1 1 -1 0 1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? y2*z + 2*y*z + x + y + z + x*y-1*z-1 + 2*y-1*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 123
Image of polytope 123 PALP id: 123
grdb id: 519655
Integer points: [ 1 -1 0 0 1 1 1 0 0]
[ 0 0 1 0 -1 -2 -1 0 -1]
[ 0 0 0 1 0 -2 -1 0 -1]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
79 ? x + y + z + x*y-1 + 2*x*y-1*z-1 + x-1 + 2*y-1*z-1 + x*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 124
Image of polytope 124 PALP id: 124
grdb id: 519618
Integer points: [ 1 0 -2 0 -2 -1 -1 -1 0]
[ 0 1 -1 0 -2 0 -1 0 0]
[ 0 0 0 1 -1 1 0 0 0]
Degree: 48
Hilbert function: 1 + 27 t + 125 t2 + 343 t3 + 729 t4 + 1331 t5 + 2197 t6 + 3375 t7 + 4913 t8 + 6859 t9 + 9261 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
117 ? x + y + z + x-1*z + 2*x-1 + 2*x-1*y-1 + x-2*y-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 125
Image of polytope 125 PALP id: 125
grdb id: 519568
Integer points: [ 1 0 -1 0 -2 0 -1 -1 0]
[ 0 1 -1 0 1 1 1 0 0]
[ 0 0 0 1 -1 1 0 0 0]
Degree: 54
Hilbert function: 1 + 30 t + 140 t2 + 385 t3 + 819 t4 + 1496 t5 + 2470 t6 + 3795 t7 + 5525 t8 + 7714 t9 + 10416 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 8 1 none
Polytope 126
Image of polytope 126 PALP id: 126
grdb id: 519550
Integer points: [ 1 0 -1 0 -2 0 -1 -1 0]
[ 0 1 1 0 -1 -1 0 -1 0]
[ 0 0 0 1 -1 1 0 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 8 1 none
Polytope 127
Image of polytope 127 PALP id: 127
grdb id: 519609
Integer points: [ 1 0 -1 0 -1 -1 -1 0 0]
[ 0 1 0 0 1 -2 -1 0 -1]
[ 0 0 0 1 -1 0 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
76 ? x + y + z + x-1*y*z-1 + 2*y-1 + x-1 + 2*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 128
Image of polytope 128 PALP id: 128
grdb id: 519656
Integer points: [ 1 0 -1 0 -1 1 0 1 0]
[ 0 1 0 0 1 -2 -1 -1 0]
[ 0 0 0 1 -1 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + 2*x*y-1 + x-1*y*z-1 + x*y-2 + 2*y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 129
Image of polytope 129 PALP id: 129
grdb id: 519654
Integer points: [ 1 0 -1 0 0 -1 -1 0 0]
[ 0 1 0 -1 0 -2 -1 -1 0]
[ 0 0 0 0 1 -2 -1 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
37 rank 3, number 17 x + y + z + y-1 + x-1 + 2*y-1*z-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 130
Image of polytope 130 PALP id: 130
grdb id: 519646
Integer points: [ 1 0 0 -2 -2 0 -1 -1 0]
[ 0 1 0 0 -1 -1 0 -1 0]
[ 0 0 1 -1 -1 1 0 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
42 rank 2, number 29 x + y + z + y-1*z + 2*x-1 + 2*x-1*y-1 + x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 131
Image of polytope 131 PALP id: 131
grdb id: 519549
Integer points: [ 1 0 0 -2 -1 -2 -2 -1 0]
[ 0 1 0 -1 0 -1 -1 0 0]
[ 0 0 1 -1 1 1 0 0 0]
Degree: 50
Hilbert function: 1 + 28 t + 130 t2 + 357 t3 + 759 t4 + 1386 t5 + 2288 t6 + 3515 t7 + 5117 t8 + 7144 t9 + 9646 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 8 1 none
Polytope 132
Image of polytope 132 PALP id: 132
grdb id: 519645
Integer points: [ 1 0 0 -2 0 -2 -1 -1 0]
[ 0 1 -1 -1 0 -2 -1 0 0]
[ 0 0 0 0 1 -1 0 0 0]
Degree: 48
Hilbert function: 1 + 27 t + 125 t2 + 343 t3 + 729 t4 + 1331 t5 + 2197 t6 + 3375 t7 + 4913 t8 + 6859 t9 + 9261 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 5 1 none
Polytope 133
Image of polytope 133 PALP id: 133
grdb id: 519639
Integer points: [ 1 0 0 -2 0 -1 -1 0 -1]
[ 0 1 -1 -1 0 -2 -1 0 0]
[ 0 0 0 0 1 -1 0 0 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 6 1 none
Polytope 134
Image of polytope 134 PALP id: 134
grdb id: 519650
Integer points: [ 1 0 0 -1 -2 -1 -1 -1 0]
[ 0 1 0 -1 -1 -1 0 -1 0]
[ 0 0 1 -1 0 1 0 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
155 ? x + y + z + 2*x-1 + x-1*y-1*z + 2*x-1*y-1 + x-1*y-1*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 135
Image of polytope 135 PALP id: 135
grdb id: 519651
Integer points: [ 1 0 0 0 -2 -2 -1 -1 0]
[ 0 1 -1 0 0 1 0 1 0]
[ 0 0 0 1 -1 0 0 0 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 5 1 none
Polytope 136
Image of polytope 136 PALP id: 136
grdb id: 519634
Integer points: [ 1 0 0 0 -1 -2 -1 -1 0]
[ 0 1 -1 0 -1 1 0 1 0]
[ 0 0 0 1 -1 0 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 6 1 none
Polytope 137
Image of polytope 137 PALP id: 137
grdb id: 519633
Integer points: [ 1 0 0 0 -1 -2 -1 -1 0]
[ 0 1 0 -1 0 -1 0 -1 0]
[ 0 0 1 -1 1 -1 0 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 2 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 138
Image of polytope 138 PALP id: 138
grdb id: 519610
Integer points: [ 1 -1 0 -1 0 -3 -2 0 -1]
[ 0 0 1 -1 0 -2 -1 0 -1]
[ 0 0 0 0 1 -2 -1 0 -1]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
152 rank 3, number 22 x + y + z + x-1 + x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*y-1*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 139
Image of polytope 139 PALP id: 139
grdb id: 519584
Integer points: [ 1 0 -1 0 -3 -1 -2 -1 0]
[ 0 1 -1 0 -2 0 -1 0 0]
[ 0 0 0 1 -1 1 0 0 0]
Degree: 54
Hilbert function: 1 + 30 t + 140 t2 + 385 t3 + 819 t4 + 1496 t5 + 2470 t6 + 3795 t7 + 5525 t8 + 7714 t9 + 10416 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 4 1 none
Polytope 140
Image of polytope 140 PALP id: 140
grdb id: 519620
Integer points: [ 1 0 0 -2 0 -3 -1 -1 0]
[ 0 1 -1 -1 0 -2 -1 0 0]
[ 0 0 0 0 1 -1 0 0 0]
Degree: 52
Hilbert function: 1 + 29 t + 135 t2 + 371 t3 + 789 t4 + 1441 t5 + 2379 t6 + 3655 t7 + 5321 t8 + 7429 t9 + 10031 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 6 1 none
Polytope 141
Image of polytope 141 PALP id: 141
grdb id: 519623
Integer points: [ 1 0 0 -2 0 -3 -1 -1 0]
[ 0 1 -1 1 0 1 0 1 0]
[ 0 0 0 0 1 -1 0 0 0]
Degree: 50
Hilbert function: 1 + 28 t + 130 t2 + 357 t3 + 759 t4 + 1386 t5 + 2288 t6 + 3515 t7 + 5117 t8 + 7144 t9 + 9646 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 6 1 none
Polytope 142
Image of polytope 142 PALP id: 142
grdb id: 519273
Integer points: [ 1 -1 0 0 -1 2 0 0 1]
[ 0 0 1 0 -1 -1 -1 0 -1]
[ 0 0 0 1 -1 -1 -1 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
148 ? x + y + z + x2*y-1*z-1 + 3*x*y-1*z-1 + x-1 + 3*y-1*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Polytope 143
Image of polytope 143 PALP id: 143
grdb id: 519318
Integer points: [ 1 0 0 -2 0 -2 -1 -1 0]
[ 0 1 -1 1 0 1 0 1 0]
[ 0 0 0 0 1 -1 0 0 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
125 ? x + y + z + 2*x-1*y + y-1 + 2*x-1 + x-2*y + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Polytope 144
Image of polytope 144 PALP id: 144
grdb id: 519198
Integer points: [ 1 0 0 -1 0 -2 -1 -1 0]
[ 0 1 -1 1 0 -2 -1 0 0]
[ 0 0 0 0 1 -1 0 0 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 4 1 none
Polytope 145
Image of polytope 145 PALP id: 145
grdb id: 519319
Integer points: [ 1 0 0 0 -1 -2 -1 -1 0]
[ 0 1 -1 0 0 1 1 0 0]
[ 0 0 0 1 -1 0 0 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
140 ? x + y + z + 2*x-1*y + y-1 + 2*x-1 + x-2*y + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Polytope 146
Image of polytope 146 PALP id: 146
grdb id: 519320
Integer points: [ 1 0 0 0 -1 -2 -1 -1 0]
[ 0 1 -1 0 1 1 1 0 0]
[ 0 0 0 1 -1 0 0 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
139 ? x + y + z + 2*x-1*y + x-1*y*z-1 + y-1 + 2*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Polytope 147
Image of polytope 147 PALP id: 147
grdb id: 519309
Integer points: [ 1 0 0 0 0 -2 -1 -1 0]
[ 0 1 -1 0 -1 1 0 1 0]
[ 0 0 0 1 -1 0 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
126 ? x + y + z + 2*x-1*y + y-1 + 2*x-1 + x-2*y + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Polytope 148
Image of polytope 148 PALP id: 148
grdb id: 519310
Integer points: [ 1 0 0 0 0 -2 -1 0 -1]
[ 0 1 -1 0 1 1 1 0 0]
[ 0 0 0 1 -1 0 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
104 ? x + y + z + y*z-1 + 2*x-1*y + y-1 + 2*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Polytope 149
Image of polytope 149 PALP id: 149
grdb id: 519311
Integer points: [ 1 0 0 0 0 -2 -1 0 -1]
[ 0 1 0 0 -1 1 1 0 0]
[ 0 0 1 -1 0 0 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
43 ? x + y + z + 2*x-1*y + z-1 + y-1 + 2*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Polytope 150
Image of polytope 150 PALP id: 150
grdb id: 519308
Integer points: [ 1 0 0 0 1 -2 -1 0 -1]
[ 0 1 -1 0 0 1 1 0 0]
[ 0 0 0 1 -1 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
103 ? x + y + z + x*z-1 + 2*x-1*y + y-1 + 2*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Polytope 151
Image of polytope 151 PALP id: 151
grdb id: 519314
Integer points: [ 1 0 1 -1 0 -2 -1 0 0]
[ 0 1 -1 -1 0 0 0 -1 0]
[ 0 0 0 0 1 -1 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
131 ? x + y + z + x*y-1 + 2*y-1 + 2*x-1 + x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Polytope 152
Image of polytope 152 PALP id: 152
grdb id: 519315
Integer points: [ 1 -1 0 -2 0 2 1 0 -1]
[ 0 0 1 1 0 -2 -1 0 1]
[ 0 0 0 0 1 -1 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
32 ? x + y + z + 2*x*y-1 + 2*x-1*y + x2*y-2*z-1 + x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Polytope 153
Image of polytope 153 PALP id: 153
grdb id: 430103
Integer points: [ 1 0 0 0 0 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 1 0 0]
[ 0 0 1 -1 0 -1 1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
2 rank 1, B4 x + y + z + x-1*y*z + z-1 + y-1 + 2*x-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 154
Image of polytope 154 PALP id: 154
grdb id: 430100
Integer points: [ 1 0 0 0 -1 -1 -1 -1 0]
[ 0 1 0 -1 1 0 -1 0 0]
[ 0 0 1 -1 0 1 -1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 2 1 none
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Polytope 155
Image of polytope 155 PALP id: 155
grdb id: 430096
Integer points: [ 1 0 0 -2 -2 -3 1 -1 0]
[ 0 1 0 0 -1 -1 1 0 0]
[ 0 0 1 -1 0 -1 1 0 0]
Degree: 48
Hilbert function: 1 + 27 t + 125 t2 + 343 t3 + 729 t4 + 1331 t5 + 2197 t6 + 3375 t7 + 4913 t8 + 6859 t9 + 9261 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
6 rank 2, number 32 x*y*z + x + y + z + 2*x-1 + x-2*z-1 + x-2*y-1 + x-3*y-1*z-1
21 rank 3, number 27 x*y*z + x + y + z + 3*x-1 + x-2*z-1 + x-2*y-1 + x-3*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Polytope 156
Image of polytope 156 PALP id: 156
grdb id: 430089
Integer points: [ 1 -1 0 0 -1 -1 -1 -1 0]
[ 0 0 1 0 0 -1 -1 -1 0]
[ 0 0 0 1 -1 -1 1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
61 rank 2, number 27 x + y + z + x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 157
Image of polytope 157 PALP id: 157
grdb id: 430027
Integer points: [ 1 0 -1 -1 0 -1 -1 -1 0]
[ 0 1 -1 1 0 1 0 0 0]
[ 0 0 0 0 1 -1 1 0 0]
Degree: 50
Hilbert function: 1 + 28 t + 130 t2 + 357 t3 + 759 t4 + 1386 t5 + 2288 t6 + 3515 t7 + 5117 t8 + 7144 t9 + 9646 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 6 1 none
Polytope 158
Image of polytope 158 PALP id: 158
grdb id: 430054
Integer points: [ 1 0 -1 0 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 1 0 0 0]
[ 0 0 0 1 -1 0 1 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 6 1 none
Polytope 159
Image of polytope 159 PALP id: 159
grdb id: 430072
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 0 0 0]
[ 0 0 1 -1 0 0 1 0 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 5 1 none
Polytope 160
Image of polytope 160 PALP id: 160
grdb id: 430082
Integer points: [ 1 0 0 -1 0 -1 -1 -1 0]
[ 0 1 -1 0 0 -1 1 0 0]
[ 0 0 0 0 1 -1 -1 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
37 rank 3, number 17 x + y + z + x-1*y*z-1 + y-1 + x-1 + 2*x-1*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 161
Image of polytope 161 PALP id: 161
grdb id: 430078
Integer points: [ 1 0 0 0 -1 -1 -1 -1 0]
[ 0 1 0 -1 -1 1 -1 0 0]
[ 0 0 1 -1 0 0 -1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
111 ? x + y + z + x-1*y + 2*x-1 + y-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 162
Image of polytope 162 PALP id: 162
grdb id: 430088
Integer points: [ 1 0 0 0 0 -1 -1 -1 0]
[ 0 1 -1 0 1 0 0 0 0]
[ 0 0 0 1 -1 -1 1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
47 ? x + y + z + y*z-1 + x-1*z + y-1 + 2*x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 163
Image of polytope 163 PALP id: 163
grdb id: 430073
Integer points: [ 1 -1 0 0 0 1 2 1 0]
[ 0 0 1 0 -1 -1 -1 -1 0]
[ 0 0 0 1 -1 0 -1 -1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
57 ? x + y + z + x2*y-1*z-1 + x*y-1 + 2*x*y-1*z-1 + x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 164
Image of polytope 164 PALP id: 164
grdb id: 430087
Integer points: [ 1 -1 0 0 0 1 2 1 0]
[ 0 0 1 0 -1 0 -1 -1 0]
[ 0 0 0 1 -1 1 1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
61 rank 2, number 27 x2*y-1*z + x*z + x + y + z + 2*x*y-1 + x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 165
Image of polytope 165 PALP id: 165
grdb id: 430057
Integer points: [ 1 0 -1 -1 0 -1 -1 -1 0]
[ 0 1 -1 1 0 1 2 0 0]
[ 0 0 0 0 1 -1 -1 0 0]
Degree: 48
Hilbert function: 1 + 27 t + 125 t2 + 343 t3 + 729 t4 + 1331 t5 + 2197 t6 + 3375 t7 + 4913 t8 + 6859 t9 + 9261 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
90 rank 3, number 28 x + y + z + x-1*y2*z-1 + x-1*y + x-1*y*z-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 166
Image of polytope 166 PALP id: 166
grdb id: 430038
Integer points: [ 1 0 -1 -1 0 -2 0 -1 0]
[ 0 1 -1 1 0 0 -1 0 0]
[ 0 0 0 0 1 -1 1 0 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
113 rank 3, number 26 x + y + z + x-1*y + y-1*z + x-1 + x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Polytope 167
Image of polytope 167 PALP id: 167
grdb id: 430039
Integer points: [ 1 0 -1 0 -1 -2 0 -1 0]
[ 0 1 -1 0 1 0 1 0 0]
[ 0 0 0 1 0 -1 1 0 0]
Degree: 50
Hilbert function: 1 + 28 t + 130 t2 + 357 t3 + 759 t4 + 1386 t5 + 2288 t6 + 3515 t7 + 5117 t8 + 7144 t9 + 9646 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
84 ? y*z + x + y + z + x-1*y + x-1 + x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Polytope 168
Image of polytope 168 PALP id: 168
grdb id: 430091
Integer points: [ 1 0 -1 0 0 -2 -1 -1 0]
[ 0 1 -1 0 1 -1 0 0 0]
[ 0 0 0 1 -1 1 1 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
86 ? x + y + z + y*z-1 + x-1*z + 2*x-1 + x-1*y-1 + x-2*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 169
Image of polytope 169 PALP id: 169
grdb id: 430034
Integer points: [ 1 0 0 -1 -2 -1 -2 -1 0]
[ 0 1 0 -1 -1 0 -1 0 0]
[ 0 0 1 -1 0 1 -1 0 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 6 1 none
Polytope 170
Image of polytope 170 PALP id: 170
grdb id: 430083
Integer points: [ 1 0 0 -1 -1 -2 0 -1 0]
[ 0 1 0 0 -1 -1 1 0 0]
[ 0 0 1 -1 0 -1 1 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
42 rank 2, number 29 y*z + x + y + z + 2*x-1 + x-1*z-1 + x-1*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 171
Image of polytope 171 PALP id: 171
grdb id: 430081
Integer points: [ 1 0 0 -1 0 -1 -2 -1 0]
[ 0 1 -1 0 0 -1 -2 -1 0]
[ 0 0 0 0 1 -1 -1 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
155 ? x + y + z + y-1 + x-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 172
Image of polytope 172 PALP id: 172
grdb id: 430092
Integer points: [ 1 0 0 -1 0 -1 -2 -1 0]
[ 0 1 -1 1 0 -1 0 0 0]
[ 0 0 0 0 1 -1 -1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
98 rank 3, number 21 x + y + z + x-1*y + y-1 + 2*x-1 + x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 173
Image of polytope 173 PALP id: 173
grdb id: 430080
Integer points: [ 1 0 0 0 -1 -1 -2 -1 0]
[ 0 1 0 -1 -1 0 -1 0 0]
[ 0 0 1 -1 0 1 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
63 ? x + y + z + x-1*z + 2*x-1 + y-1*z-1 + x-1*y-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 174
Image of polytope 174 PALP id: 174
grdb id: 430090
Integer points: [ 1 0 0 1 0 -1 -2 -1 0]
[ 0 1 -1 1 0 1 0 0 0]
[ 0 0 0 0 1 -1 -1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
47 ? x*y + x + y + z + x-1*y*z-1 + y-1 + 2*x-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 175
Image of polytope 175 PALP id: 175
grdb id: 430077
Integer points: [ 1 0 1 0 -1 0 -2 0 -1]
[ 0 1 -1 0 1 -1 1 0 0]
[ 0 0 0 1 1 -1 1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
28 rank 2, number 25 x + y + z + x-1*y*z + x*y-1 + x-2*y*z + 2*x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 176
Image of polytope 176 PALP id: 176
grdb id: 430040
Integer points: [ 1 0 0 -2 -2 2 1 -1 0]
[ 0 1 0 0 -1 1 1 0 0]
[ 0 0 1 -1 0 1 1 0 0]
Degree: 50
Hilbert function: 1 + 28 t + 130 t2 + 357 t3 + 759 t4 + 1386 t5 + 2288 t6 + 3515 t7 + 5117 t8 + 7144 t9 + 9646 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
163 ? x2*y*z + x*y*z + x + y + z + x-1 + x-2*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Polytope 177
Image of polytope 177 PALP id: 177
grdb id: 429952
Integer points: [ 1 -1 0 0 -1 -1 -1 -1 0]
[ 0 0 1 0 -1 0 -1 -1 0]
[ 0 0 0 1 -1 1 1 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
158 ? x + y + z + x-1*z + x-1 + x-1*y-1*z + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 178
Image of polytope 178 PALP id: 178
grdb id: 429956
Integer points: [ 1 0 -1 0 0 -1 -1 -1 0]
[ 0 1 -1 0 1 1 0 0 0]
[ 0 0 0 1 -1 0 1 0 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
130 rank 3, number 24 x + y + z + y*z-1 + x-1*y + x-1*z + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 179
Image of polytope 179 PALP id: 179
grdb id: 429954
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 1 0 0]
[ 0 0 1 -1 0 -1 0 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
102 ? x + y + z + x-1*y + 2*x-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 180
Image of polytope 180 PALP id: 180
grdb id: 429937
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 1 0 0]
[ 0 0 1 -1 0 0 -1 0 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
93 ? x + y + z + x-1*y + x-1*y*z-1 + 2*x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 181
Image of polytope 181 PALP id: 181
grdb id: 429933
Integer points: [ 1 0 0 -1 0 1 -1 0 -1]
[ 0 1 -1 1 0 -1 -1 0 0]
[ 0 0 0 0 1 -1 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + x-1*y + x*y-1*z-1 + y-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 182
Image of polytope 182 PALP id: 182
grdb id: 429927
Integer points: [ 1 0 0 0 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 1 0 0 0]
[ 0 0 0 1 -1 0 1 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
123 ? x + y + z + x-1*y + x-1*z + y-1 + 2*x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 183
Image of polytope 183 PALP id: 183
grdb id: 429943
Integer points: [ 1 0 0 0 -1 0 -1 -1 0]
[ 0 1 -1 0 0 -1 0 0 0]
[ 0 0 0 1 -1 1 1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
98 rank 3, number 21 x + y + z + y-1*z + x-1*z + y-1 + 2*x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 184
Image of polytope 184 PALP id: 184
grdb id: 429942
Integer points: [ 1 0 0 1 0 -1 -1 -1 0]
[ 0 1 -1 -1 0 0 0 0 0]
[ 0 0 0 0 1 -1 1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
65 ? x + y + z + x*y-1 + x-1*z + y-1 + 2*x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 185
Image of polytope 185 PALP id: 185
grdb id: 429953
Integer points: [ 1 -1 0 0 -1 0 2 1 0]
[ 0 0 1 0 0 -1 -1 -1 0]
[ 0 0 0 1 1 -1 -1 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
148 ? x + y + z + x2*y-1*z-1 + x-1*z + 2*x*y-1*z-1 + x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 186
Image of polytope 186 PALP id: 186
grdb id: 429925
Integer points: [ 1 0 0 -1 -1 0 -2 -1 0]
[ 0 1 -1 -1 1 0 0 0 0]
[ 0 0 0 0 0 1 -1 0 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 5 1 none
Polytope 187
Image of polytope 187 PALP id: 187
grdb id: 429859
Integer points: [ 1 0 0 -1 -1 0 -2 -1 0]
[ 0 1 -1 -1 1 0 1 0 0]
[ 0 0 0 0 0 1 -1 0 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 6 1 none
Polytope 188
Image of polytope 188 PALP id: 188
grdb id: 429899
Integer points: [ 1 0 0 -1 -1 0 -1 -1 0]
[ 0 1 -1 1 -1 0 -2 0 0]
[ 0 0 0 0 0 1 -1 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
123 ? x + y + z + x-1*y + y-1 + 2*x-1 + x-1*y-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 189
Image of polytope 189 PALP id: 189
grdb id: 429939
Integer points: [ 1 0 0 -1 0 -2 0 -1 0]
[ 0 1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 1 -1 1 0 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
93 ? x + y + z + y-1*z + y-1 + x-1 + 2*x-1*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 190
Image of polytope 190 PALP id: 190
grdb id: 429935
Integer points: [ 1 0 0 -1 0 -2 0 -1 0]
[ 0 1 -1 1 0 0 1 0 0]
[ 0 0 0 0 1 -1 1 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
142 ? y*z + x + y + z + x-1*y + y-1 + 2*x-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 191
Image of polytope 191 PALP id: 191
grdb id: 430367
Integer points: [ 1 0 0 -1 -1 0 -1 -1 0]
[ 0 1 -1 -1 1 0 1 0 0]
[ 0 0 0 0 0 1 -1 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
92 ? x + y + z + x-1*y + x-1*y*z-1 + y-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Polytope 192
Image of polytope 192 PALP id: 192
grdb id: 430369
Integer points: [ 1 0 0 0 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 -1 1 0 0]
[ 0 0 0 1 -1 0 0 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
140 ? x + y + z + x-1*y + y-1 + 2*x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Polytope 193
Image of polytope 193 PALP id: 193
grdb id: 430358
Integer points: [ 1 0 0 0 0 -1 -1 -1 0]
[ 0 1 -1 0 1 1 -1 0 0]
[ 0 0 0 1 -1 0 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
87 ? x + y + z + y*z-1 + x-1*y + y-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Polytope 194
Image of polytope 194 PALP id: 194
grdb id: 430360
Integer points: [ 1 0 0 0 0 -1 -1 -1 0]
[ 0 1 0 0 -1 1 -1 0 0]
[ 0 0 1 -1 0 0 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
43 ? x + y + z + x-1*y + z-1 + y-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Polytope 195
Image of polytope 195 PALP id: 195
grdb id: 430357
Integer points: [ 1 0 0 0 1 -1 -1 0 -1]
[ 0 1 -1 0 0 1 -1 0 0]
[ 0 0 0 1 -1 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
103 ? x + y + z + x*z-1 + x-1*y + y-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Polytope 196
Image of polytope 196 PALP id: 196
grdb id: 430351
Integer points: [ 1 0 1 -1 0 0 -2 -1 0]
[ 0 1 -1 1 -1 0 0 0 0]
[ 0 0 0 0 0 1 -1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
131 ? x + y + z + x*y-1 + x-1*y + y-1 + 2*x-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Polytope 197
Image of polytope 197 PALP id: 197
grdb id: 255744
Integer points: [ 1 0 0 -1 1 0 0 -1 0]
[ 0 1 0 1 -1 0 -1 0 0]
[ 0 0 1 1 -1 -1 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
2 rank 1, B4 x + y + z + x-1*y*z + x*y-1*z-1 + z-1 + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 6 Lattice Minkowski decompositions of facet 3
Polytope 198
Image of polytope 198 PALP id: 198
grdb id: 255743
Integer points: [ 1 0 0 -1 0 -1 1 0 0]
[ 0 1 -1 0 0 1 0 -1 0]
[ 0 0 0 0 1 1 -1 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
28 rank 2, number 25 x + y + z + x-1*y*z + x*z-1 + y-1 + x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Polytope 199
Image of polytope 199 PALP id: 199
grdb id: 255736
Integer points: [ 1 -1 0 0 -1 -1 0 -1 0]
[ 0 0 1 0 -1 0 1 -1 0]
[ 0 0 0 1 -1 -1 1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
61 rank 2, number 27 y*z + x + y + z + x-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Polytope 200
Image of polytope 200 PALP id: 200
grdb id: 255739
Integer points: [ 1 -1 0 0 1 1 0 1 0]
[ 0 0 1 0 0 -1 -1 -1 0]
[ 0 0 0 1 -1 0 -1 -1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
61 rank 2, number 27 x + y + z + x*z-1 + x*y-1 + x*y-1*z-1 + x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Polytope 201
Image of polytope 201 PALP id: 201
grdb id: 255741
Integer points: [ 1 0 0 0 0 -1 1 -1 0]
[ 0 1 0 0 -1 0 1 -1 0]
[ 0 0 1 -1 0 0 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
47 ? x*y + x + y + z + z-1 + y-1 + x-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Polytope 202
Image of polytope 202 PALP id: 202
grdb id: 255738
Integer points: [ 1 -1 0 -1 0 2 -1 1 0]
[ 0 0 1 1 0 -1 0 -1 0]
[ 0 0 0 0 1 -1 1 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
148 ? x + y + z + x2*y-1*z-1 + x-1*y + x-1*z + x*y-1*z-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Polytope 203
Image of polytope 203 PALP id: 203
grdb id: 255737
Integer points: [ 1 0 0 -1 0 -1 -1 -2 0]
[ 0 1 -1 0 0 1 0 1 0]
[ 0 0 0 0 1 0 -1 -1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
42 rank 2, number 29 x + y + z + x-1*y + y-1 + x-1 + x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Polytope 204
Image of polytope 204 PALP id: 204
grdb id: 255870
Integer points: [ 1 -1 0 0 -1 -1 1 0 0]
[ 0 0 1 0 0 -1 1 1 0]
[ 0 0 0 1 -1 0 1 1 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
158 ? x*y*z + y*z + x + y + z + x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 205
Image of polytope 205 PALP id: 205
grdb id: 255862
Integer points: [ 1 -1 0 0 0 1 1 1 0]
[ 0 0 1 0 -1 -1 -1 0 0]
[ 0 0 0 1 -1 0 -1 1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
57 ? x*z + x + y + z + x*y-1 + x*y-1*z-1 + x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 206
Image of polytope 206 PALP id: 206
grdb id: 255875
Integer points: [ 1 0 0 -1 -1 0 -1 0 0]
[ 0 1 -1 0 -1 0 -1 -1 0]
[ 0 0 0 0 0 1 -1 1 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
86 ? x + y + z + y-1*z + y-1 + x-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 207
Image of polytope 207 PALP id: 207
grdb id: 255869
Integer points: [ 1 0 0 -1 -1 0 -1 0 0]
[ 0 1 -1 0 1 0 0 -1 0]
[ 0 0 0 0 0 1 -1 1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
63 ? x + y + z + x-1*y + y-1*z + y-1 + x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 208
Image of polytope 208 PALP id: 208
grdb id: 255877
Integer points: [ 1 0 0 -1 0 -1 -1 0 0]
[ 0 1 -1 0 0 0 -1 1 0]
[ 0 0 0 0 1 -1 -1 1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
37 rank 3, number 17 y*z + x + y + z + y-1 + x-1 + x-1*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 209
Image of polytope 209 PALP id: 209
grdb id: 255871
Integer points: [ 1 0 0 -1 0 0 -1 -1 0]
[ 0 1 -1 0 0 1 -1 1 0]
[ 0 0 0 0 1 -1 0 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
37 rank 3, number 17 x + y + z + y*z-1 + x-1*y*z-1 + y-1 + x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 210
Image of polytope 210 PALP id: 210
grdb id: 255876
Integer points: [ 1 0 0 -1 0 0 1 1 0]
[ 0 1 -1 0 0 1 0 1 0]
[ 0 0 0 0 1 -1 -1 -1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
63 ? x*y*z-1 + x + y + z + x*z-1 + y*z-1 + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 211
Image of polytope 211 PALP id: 211
grdb id: 255878
Integer points: [ 1 0 0 -1 0 1 0 1 0]
[ 0 1 -1 0 0 1 -1 0 0]
[ 0 0 0 0 1 0 -1 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
160 ? x*y + x + y + z + x*z-1 + y-1 + x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 212
Image of polytope 212 PALP id: 212
grdb id: 255879
Integer points: [ 1 0 0 -1 1 0 0 -1 0]
[ 0 1 -1 0 -1 0 1 1 0]
[ 0 0 0 0 0 1 -1 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? x + y + z + y*z-1 + x*y-1 + x-1*y*z-1 + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 213
Image of polytope 213 PALP id: 213
grdb id: 255880
Integer points: [ 1 0 0 0 0 -1 0 -1 0]
[ 0 1 0 0 -1 0 1 1 0]
[ 0 0 1 -1 0 0 1 1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
98 rank 3, number 21 y*z + x + y + z + x-1*y*z + z-1 + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 214
Image of polytope 214 PALP id: 214
grdb id: 255838
Integer points: [ 1 0 0 -1 0 -1 -1 -1 0]
[ 0 1 -1 0 0 1 0 1 0]
[ 0 0 0 0 1 0 -1 -1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
102 ? x + y + z + x-1*y + x-1*y*z-1 + y-1 + x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 10 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 215
Image of polytope 215 PALP id: 215
grdb id: 255837
Integer points: [ 1 0 0 0 -1 0 -1 0 0]
[ 0 1 0 0 0 -1 0 -1 0]
[ 0 0 1 -1 0 0 -1 1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
69 ? x + y + z + y-1*z + z-1 + y-1 + x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 10 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 216
Image of polytope 216 PALP id: 216
grdb id: 255836
Integer points: [ 1 0 0 0 -1 0 0 -1 0]
[ 0 1 0 0 0 -1 -1 0 0]
[ 0 0 1 -1 0 0 1 1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
105 ? x + y + z + y-1*z + x-1*z + z-1 + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 10 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 217
Image of polytope 217 PALP id: 217
grdb id: 255835
Integer points: [ 1 0 1 -1 -1 0 0 -1 0]
[ 0 1 -1 1 0 -1 0 -1 0]
[ 0 0 0 0 0 0 1 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
69 ? x + y + z + x*y-1 + x-1*y + y-1 + x-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 10 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 218
Image of polytope 218 PALP id: 218
grdb id: 255779
Integer points: [ 1 0 0 0 0 0 0 -1 0]
[ 0 1 0 1 -1 0 -1 0 0]
[ 0 0 1 -1 1 -1 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
43 ? x + y + z + y*z-1 + y-1*z + z-1 + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 12 irreducible and admissible
Polytope 219
Image of polytope 219 PALP id: 219
grdb id: 255778
Integer points: [ 1 0 1 -1 0 -1 0 1 0]
[ 0 1 -1 1 -1 0 0 0 0]
[ 0 0 0 0 0 0 1 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
87 ? x + y + z + x*z-1 + x*y-1 + x-1*y + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 12 irreducible and admissible
Polytope 220
Image of polytope 220 PALP id: 220
grdb id: 543857
Integer points: [ 1 0 0 -1 -4 -2 -3 -1 -2 0]
[ 0 1 0 -1 -1 -1 -1 0 0 0]
[ 0 0 1 1 -2 0 -1 0 -1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
14 rank 1, B5 x + y + z + 3*x-1 + x-1*y-1*z + 2*x-2*z-1 + 3*x-2*y-1 + 3*x-3*y-1*z-1 + x-4*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 221
Image of polytope 221 PALP id: 221
grdb id: 543846
Integer points: [ 1 0 0 -5 -1 -3 -2 -1 -1 0]
[ 0 1 0 -3 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 1 0 0 0 0 0]
Degree: 64
Hilbert function: 1 + 35 t + 165 t2 + 455 t3 + 969 t4 + 1771 t5 + 2925 t6 + 4495 t7 + 6545 t8 + 9139 t9 + 12341 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 26 1 none
Image of facet 4 1 none
Polytope 222
Image of polytope 222 PALP id: 222
grdb id: 543868
Integer points: [ 1 0 0 -4 -5 -2 -3 -1 -2 0]
[ 0 1 0 -2 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 -2 0 -1 0 -1 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 27 1 none
Polytope 223
Image of polytope 223 PALP id: 223
grdb id: 543853
Integer points: [ 1 0 0 2 -5 -3 -1 1 -2 0]
[ 0 1 0 2 -2 -1 0 1 -1 0]
[ 0 0 1 1 -2 -1 0 1 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 26 1 none
Polytope 224
Image of polytope 224 PALP id: 224
grdb id: 543776
Integer points: [ 1 0 0 -2 -2 -2 -1 -1 -1 0]
[ 0 1 0 -2 0 -1 -1 0 0 0]
[ 0 0 1 -1 1 0 0 1 0 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 4 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 225
Image of polytope 225 PALP id: 225
grdb id: 543733
Integer points: [ 1 0 -1 0 -2 -1 -1 -1 0 0]
[ 0 1 -2 0 2 1 0 -1 0 -1]
[ 0 0 0 1 -1 0 0 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 12 1 none
Polytope 226
Image of polytope 226 PALP id: 226
grdb id: 543680
Integer points: [ 1 0 0 -2 -2 -1 -2 -1 -2 0]
[ 0 1 0 -1 -1 0 -1 0 -1 0]
[ 0 0 1 -1 2 1 1 0 0 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 14 1 none
Image of facet 9 1 irreducible and admissible
Polytope 227
Image of polytope 227 PALP id: 227
grdb id: 543783
Integer points: [ 1 0 0 1 -3 -2 -1 0 -1 0]
[ 0 1 0 -1 -1 -1 -1 -1 0 0]
[ 0 0 1 -1 -1 -1 -1 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 2 1 none
Image of facet 13 2 irreducible and admissible
Polytope 228
Image of polytope 228 PALP id: 228
grdb id: 543787
Integer points: [ 1 0 0 2 -3 1 -1 0 -2 -1]
[ 0 1 0 -2 1 -1 0 0 1 1]
[ 0 0 1 -1 0 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 4 1 none
Image of facet 9 2 irreducible and admissible
Polytope 229
Image of polytope 229 PALP id: 229
grdb id: 543794
Integer points: [ 1 0 0 2 -3 -1 -2 1 0 -1]
[ 0 1 0 2 -2 0 -1 1 0 -1]
[ 0 0 1 -1 0 0 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
81 ? x2*y2*z-1 + 2*x*y + x + y + z + 3*x-1 + 2*x-1*y-1 + 3*x-2*y-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Polytope 230
Image of polytope 230 PALP id: 230
grdb id: 543740
Integer points: [ 1 0 1 0 -4 -2 -1 0 -1 0]
[ 0 1 -1 0 -2 -1 -1 -1 0 0]
[ 0 0 0 1 -1 0 0 0 0 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 4 1 none
Image of facet 12 1 none
Polytope 231
Image of polytope 231 PALP id: 231
grdb id: 518837
Integer points: [ 1 0 0 -1 1 -1 0 0 -1 0]
[ 0 1 0 -1 -1 1 -1 0 0 0]
[ 0 0 1 1 -1 -1 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
0 rank 1, B3 x + y + z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 232
Image of polytope 232 PALP id: 232
grdb id: 518814
Integer points: [ 1 0 0 -2 0 -1 -1 0 -1 0]
[ 0 1 0 1 -2 -1 0 -1 1 0]
[ 0 0 1 0 -1 -1 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Polytope 233
Image of polytope 233 PALP id: 233
grdb id: 518809
Integer points: [ 1 0 0 -1 -1 -2 -1 -1 0 0]
[ 0 1 0 1 -2 0 0 -1 0 -1]
[ 0 0 1 -1 0 -1 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 4 1 none
Polytope 234
Image of polytope 234 PALP id: 234
grdb id: 518827
Integer points: [ 1 -1 0 0 2 1 1 1 0 0]
[ 0 0 1 0 -2 -2 -1 -1 0 -1]
[ 0 0 0 1 -1 -2 0 -1 0 -1]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 6 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 235
Image of polytope 235 PALP id: 235
grdb id: 518832
Integer points: [ 1 -1 0 1 0 1 0 1 0 0]
[ 0 0 1 0 -1 -1 0 0 0 0]
[ 0 0 0 2 -2 -1 -1 1 0 1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
25 ? x*z2 + 2*x*z + x + y + 2*z + x*y-1*z-1 + 2*z-1 + x-1 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 236
Image of polytope 236 PALP id: 236
grdb id: 518808
Integer points: [ 1 0 -1 0 -2 -1 -1 -1 0 0]
[ 0 1 -1 0 0 2 0 1 0 1]
[ 0 0 0 1 -1 -2 0 -1 0 -1]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 8 1 none
Polytope 237
Image of polytope 237 PALP id: 237
grdb id: 518830
Integer points: [ 1 0 0 0 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 -1 2 1 0 1 0]
[ 0 0 0 1 1 -2 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + 2*y*z-1 + x-1*y2*z-2 + 3*x-1*y*z-1 + y-1 + 3*x-1 + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Polytope 238
Image of polytope 238 PALP id: 238
grdb id: 518811
Integer points: [ 1 0 -3 0 -3 -1 -2 -1 -1 0]
[ 0 1 -2 0 -2 -1 -1 0 -1 0]
[ 0 0 0 1 -1 1 0 0 0 0]
Degree: 52
Hilbert function: 1 + 29 t + 135 t2 + 371 t3 + 789 t4 + 1441 t5 + 2379 t6 + 3655 t7 + 5321 t8 + 7429 t9 + 10031 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 6 1 none
Polytope 239
Image of polytope 239 PALP id: 239
grdb id: 518822
Integer points: [ 1 0 0 -3 -3 -1 -2 -1 -1 0]
[ 0 1 0 -1 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 0 1 0 0 0 0]
Degree: 52
Hilbert function: 1 + 29 t + 135 t2 + 371 t3 + 789 t4 + 1441 t5 + 2379 t6 + 3655 t7 + 5321 t8 + 7429 t9 + 10031 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 28 1 none
Polytope 240
Image of polytope 240 PALP id: 240
grdb id: 518813
Integer points: [ 1 0 0 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 0 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 1 0 0 0 0 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 28 1 none
Polytope 241
Image of polytope 241 PALP id: 241
grdb id: 518780
Integer points: [ 1 0 0 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 0 1 -2 -1 0 -1 0]
[ 0 0 1 -1 -1 0 0 0 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 29 1 none
Polytope 242
Image of polytope 242 PALP id: 242
grdb id: 518778
Integer points: [ 1 0 0 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 0 1 -2 -1 0 -1 0]
[ 0 0 1 -1 0 -2 -1 0 -1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 17 1 none
Polytope 243
Image of polytope 243 PALP id: 243
grdb id: 518821
Integer points: [ 1 0 0 -1 -2 -3 -1 -2 -1 0]
[ 0 1 0 -1 0 -1 0 -1 0 0]
[ 0 0 1 -1 1 1 0 0 1 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 8 1 none
Polytope 244
Image of polytope 244 PALP id: 244
grdb id: 518826
Integer points: [ 1 0 0 -1 -1 -3 -2 -1 -1 0]
[ 0 1 0 -1 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 1 0 0 0 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 5 1 none
Polytope 245
Image of polytope 245 PALP id: 245
grdb id: 518819
Integer points: [ 1 0 0 -1 -1 -3 -2 -1 -2 0]
[ 0 1 0 1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 1 -1 0 0 -1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
14 rank 1, B5 x + y + z + x-1*y*z-1 + 3*x-1 + x-1*y-1*z + 2*x-2*z-1 + 2*x-2*y-1 + x-3*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 246
Image of polytope 246 PALP id: 246
grdb id: 518831
Integer points: [ 1 0 1 0 -1 -3 -1 0 -2 -1]
[ 0 1 -1 0 1 0 0 0 0 0]
[ 0 0 0 1 -1 -2 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 6 1 none
Polytope 247
Image of polytope 247 PALP id: 247
grdb id: 518788
Integer points: [ 1 0 -3 0 -4 -1 -2 -1 -1 0]
[ 0 1 -2 0 -2 -1 -1 0 -1 0]
[ 0 0 0 1 -1 1 0 0 0 0]
Degree: 58
Hilbert function: 1 + 32 t + 150 t2 + 413 t3 + 879 t4 + 1606 t5 + 2652 t6 + 4075 t7 + 5933 t8 + 8284 t9 + 11186 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 29 1 none
Polytope 248
Image of polytope 248 PALP id: 248
grdb id: 518810
Integer points: [ 1 0 0 0 -3 -4 -2 -1 -1 0]
[ 0 1 -1 0 1 2 1 0 1 0]
[ 0 0 0 1 -1 -1 0 0 0 0]
Degree: 48
Hilbert function: 1 + 27 t + 125 t2 + 343 t3 + 729 t4 + 1331 t5 + 2197 t6 + 3375 t7 + 4913 t8 + 6859 t9 + 9261 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 4 1 none
Polytope 249
Image of polytope 249 PALP id: 249
grdb id: 518799
Integer points: [ 1 0 0 -2 -2 -5 -3 -1 -2 0]
[ 0 1 0 0 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 0 -2 -1 0 -1 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 31 1 none
Polytope 250
Image of polytope 250 PALP id: 250
grdb id: 518658
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 -1 -1 1 0 -1 0 0]
[ 0 0 1 -1 1 -1 0 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
28 rank 2, number 25 x + y + z + x-1*y*z-1 + 2*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 251
Image of polytope 251 PALP id: 251
grdb id: 518702
Integer points: [ 1 0 -1 -1 0 -2 -1 -1 0 0]
[ 0 1 1 -2 0 -2 -1 0 -1 0]
[ 0 0 0 0 1 -1 0 0 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 19 1 none
Polytope 252
Image of polytope 252 PALP id: 252
grdb id: 518749
Integer points: [ 1 0 -1 -1 0 -2 -1 -1 0 0]
[ 0 1 1 -2 0 -1 0 -1 0 -1]
[ 0 0 0 0 1 -1 0 0 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 18 1 none
Polytope 253
Image of polytope 253 PALP id: 253
grdb id: 518411
Integer points: [ 1 0 -1 -1 0 -2 -1 -1 0 0]
[ 0 1 1 -2 0 1 0 -1 0 -1]
[ 0 0 0 0 1 -1 0 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 21 1 none
Polytope 254
Image of polytope 254 PALP id: 254
grdb id: 518681
Integer points: [ 1 0 -1 0 -2 -2 -1 -2 -1 0]
[ 0 1 1 0 0 -2 0 -1 -1 0]
[ 0 0 0 1 -1 -1 0 -1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
63 ? x + y + z + x-1*y + 2*x-1 + 2*x-1*y-1 + x-2*z-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 255
Image of polytope 255 PALP id: 255
grdb id: 518706
Integer points: [ 1 0 -1 0 -2 -1 -1 -1 0 0]
[ 0 1 1 0 0 -2 0 -1 0 -1]
[ 0 0 0 1 -1 0 0 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 19 1 none
Polytope 256
Image of polytope 256 PALP id: 256
grdb id: 518650
Integer points: [ 1 0 0 -2 -1 0 -1 -1 0 0]
[ 0 1 0 0 -2 -1 0 -1 0 -1]
[ 0 0 1 -1 0 1 0 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 8 1 none
Polytope 257
Image of polytope 257 PALP id: 257
grdb id: 518653
Integer points: [ 1 0 0 -2 0 -2 -1 -2 -1 0]
[ 0 1 0 0 -1 -2 -1 -1 0 0]
[ 0 0 1 -1 1 1 1 0 0 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
108 ? x + y + z + y-1*z + 2*x-1 + 2*x-1*y-1*z + x-2*z-1 + 2*x-2*y-1 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 258
Image of polytope 258 PALP id: 258
grdb id: 518659
Integer points: [ 1 0 0 -1 -2 -2 -1 -2 -1 0]
[ 0 1 0 -1 0 -2 0 -1 -1 0]
[ 0 0 1 -1 -1 -1 0 -1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
63 ? x + y + z + 2*x-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-2*z-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 259
Image of polytope 259 PALP id: 259
grdb id: 518726
Integer points: [ 1 0 0 -1 1 -2 0 -1 0 -1]
[ 0 1 0 0 -1 -1 -1 -1 0 0]
[ 0 0 1 1 -1 -1 -1 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 2 1 none
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Polytope 260
Image of polytope 260 PALP id: 260
grdb id: 518755
Integer points: [ 1 0 0 0 -2 -2 -1 -1 -1 0]
[ 0 1 -1 0 0 -1 0 -1 0 0]
[ 0 0 0 1 -1 -2 0 -1 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
76 ? x + y + z + y-1 + 2*x-1 + 2*x-1*z-1 + 2*x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 261
Image of polytope 261 PALP id: 261
grdb id: 518743
Integer points: [ 1 0 0 1 -2 -1 -1 0 -1 0]
[ 0 1 0 -1 0 -1 0 -1 0 0]
[ 0 0 1 -1 1 -1 0 -1 1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 2 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 262
Image of polytope 262 PALP id: 262
grdb id: 518727
Integer points: [ 1 0 0 1 -1 -1 0 -1 0 -1]
[ 0 1 0 1 1 -2 -1 -1 0 0]
[ 0 0 1 -1 0 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x*y*z-1 + x + y + z + x-1*y + 2*y-1 + 3*x-1 + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 2 irreducible and admissible
Polytope 263
Image of polytope 263 PALP id: 263
grdb id: 518745
Integer points: [ 1 0 1 0 -2 -2 -1 0 -1 0]
[ 0 1 -1 0 0 -1 -1 -1 0 0]
[ 0 0 0 1 -1 0 0 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Image of facet 5 1 none
Polytope 264
Image of polytope 264 PALP id: 264
grdb id: 518725
Integer points: [ 1 0 1 0 -1 -2 -1 -1 0 0]
[ 0 1 -1 0 1 -1 0 -1 0 -1]
[ 0 0 0 1 -1 0 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Image of facet 6 1 none
Polytope 265
Image of polytope 265 PALP id: 265
grdb id: 518647
Integer points: [ 1 0 1 0 0 -2 0 -1 -1 0]
[ 0 1 -1 0 -2 0 -1 -1 0 0]
[ 0 0 0 1 -1 -1 0 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
29 rank 2, number 23 x + y + z + x*y-1 + 2*y-1 + 2*x-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 266
Image of polytope 266 PALP id: 266
grdb id: 518758
Integer points: [ 1 -1 0 0 0 -1 -1 0 0 0]
[ 0 0 1 0 2 -2 -1 1 0 -1]
[ 0 0 0 1 1 -2 -1 1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? y2*z + 2*y*z + x + y + z + x-1 + 2*y-1*z-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 5 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 267
Image of polytope 267 PALP id: 267
grdb id: 518587
Integer points: [ 1 0 -1 -1 0 -1 -1 -1 0 0]
[ 0 1 1 -2 0 2 0 -1 0 -1]
[ 0 0 0 0 1 -1 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
121 ? x + y + z + x-1*y2*z-1 + x-1*y + 2*y-1 + 3*x-1 + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 2 irreducible and admissible
Polytope 268
Image of polytope 268 PALP id: 268
grdb id: 518644
Integer points: [ 1 0 -1 0 -2 -2 -1 -2 -1 0]
[ 0 1 -1 0 0 2 1 1 0 0]
[ 0 0 0 1 -1 -1 0 -1 0 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
150 ? x + y + z + 2*x-1*y + x-2*y2*z-1 + 2*x-1 + 2*x-2*y*z-1 + x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 269
Image of polytope 269 PALP id: 269
grdb id: 518747
Integer points: [ 1 -1 0 0 -2 -3 -2 -1 0 -1]
[ 0 0 1 0 -2 -2 -1 -1 0 -1]
[ 0 0 0 1 -1 -2 -1 0 0 -1]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
57 ? x + y + z + x-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 270
Image of polytope 270 PALP id: 270
grdb id: 518488
Integer points: [ 1 0 -1 -1 0 -2 -1 -1 0 0]
[ 0 1 1 -2 0 -3 -1 0 -1 0]
[ 0 0 0 0 1 -1 0 0 0 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 21 1 none
Polytope 271
Image of polytope 271 PALP id: 271
grdb id: 518715
Integer points: [ 1 0 0 -2 -3 -1 -2 -1 -1 0]
[ 0 1 0 -1 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 0 1 0 0 0 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
125 ? x + y + z + 3*x-1 + x-1*y-1*z + 2*x-1*y-1 + 3*x-2*y-1 + x-2*y-1*z-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Polytope 272
Image of polytope 272 PALP id: 272
grdb id: 518626
Integer points: [ 1 0 0 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 -2 0 -2 -1 -1 0 0]
[ 0 0 1 -1 1 -1 0 0 0 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 4 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 273
Image of polytope 273 PALP id: 273
grdb id: 518708
Integer points: [ 1 0 0 -1 -1 -3 -2 -1 -1 0]
[ 0 1 0 -1 1 0 0 0 0 0]
[ 0 0 1 0 -1 -2 -1 0 -1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
140 ? x + y + z + x-1*y*z-1 + 3*x-1 + 2*x-1*z-1 + x-1*y-1 + 3*x-2*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Polytope 274
Image of polytope 274 PALP id: 274
grdb id: 518730
Integer points: [ 1 0 0 -1 0 -3 -2 -1 -1 0]
[ 0 1 0 -1 -1 0 0 0 0 0]
[ 0 0 1 0 1 -2 -1 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
126 ? x + y + z + y-1*z + 3*x-1 + 2*x-1*z-1 + x-1*y-1 + 3*x-2*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Polytope 275
Image of polytope 275 PALP id: 275
grdb id: 518641
Integer points: [ 1 0 0 0 -3 -1 -2 -1 -1 0]
[ 0 1 -1 0 -2 0 -1 -1 0 0]
[ 0 0 0 1 -1 1 0 0 0 0]
Degree: 50
Hilbert function: 1 + 28 t + 130 t2 + 357 t3 + 759 t4 + 1386 t5 + 2288 t6 + 3515 t7 + 5117 t8 + 7144 t9 + 9646 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 8 1 none
Image of facet 4 1 none
Polytope 276
Image of polytope 276 PALP id: 276
grdb id: 518711
Integer points: [ 1 0 0 0 -1 -3 -2 -1 -1 0]
[ 0 1 -1 0 1 0 0 0 0 0]
[ 0 0 0 1 -1 -2 -1 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
164 ? x + y + z + x-1*y*z-1 + y-1 + 3*x-1 + 2*x-1*z-1 + 3*x-2*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Polytope 277
Image of polytope 277 PALP id: 277
grdb id: 518605
Integer points: [ 1 0 1 -2 0 -3 -1 0 -1 0]
[ 0 1 -1 -1 0 -1 -1 -1 0 0]
[ 0 0 0 0 1 -1 0 0 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Image of facet 6 1 none
Polytope 278
Image of polytope 278 PALP id: 278
grdb id: 518139
Integer points: [ 1 0 -1 -1 0 -1 -1 -1 0 0]
[ 0 1 1 -2 0 -2 -1 0 -1 0]
[ 0 0 0 0 1 -1 0 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
110 ? x + y + z + x-1*y + 2*y-1 + 3*x-1 + 3*x-1*y-1 + x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Polytope 279
Image of polytope 279 PALP id: 279
grdb id: 518133
Integer points: [ 1 0 -1 0 -1 -1 -1 -1 0 0]
[ 0 1 1 0 -1 -2 -1 0 -1 0]
[ 0 0 0 1 -1 0 0 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
153 ? x + y + z + x-1*y + 2*y-1 + 3*x-1 + 3*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Polytope 280
Image of polytope 280 PALP id: 280
grdb id: 518145
Integer points: [ 1 0 -1 0 -1 -1 -1 -1 0 0]
[ 0 1 1 0 0 -2 0 -1 0 -1]
[ 0 0 0 1 -1 0 0 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
149 ? x + y + z + x-1*y + 2*y-1 + 3*x-1 + x-1*z-1 + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Polytope 281
Image of polytope 281 PALP id: 281
grdb id: 518136
Integer points: [ 1 0 -1 0 0 -1 -1 -1 0 0]
[ 0 1 1 0 -1 -2 -1 0 -1 0]
[ 0 0 0 1 -1 0 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
132 ? x + y + z + x-1*y + 2*y-1 + 3*x-1 + y-1*z-1 + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Polytope 282
Image of polytope 282 PALP id: 282
grdb id: 518120
Integer points: [ 1 0 -1 1 0 -2 -1 -1 0 0]
[ 0 1 1 -1 0 -2 -1 0 -1 0]
[ 0 0 0 0 1 -1 0 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 4 2 none
Polytope 283
Image of polytope 283 PALP id: 283
grdb id: 518147
Integer points: [ 1 0 0 0 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 -2 0 -1 0 -1]
[ 0 0 1 -1 0 0 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
64 ? x + y + z + x-1*y + z-1 + 2*y-1 + 3*x-1 + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Polytope 284
Image of polytope 284 PALP id: 284
grdb id: 518146
Integer points: [ 1 0 0 0 -1 -1 -1 -1 0 0]
[ 0 1 0 1 1 -2 -1 0 -1 0]
[ 0 0 1 -1 0 0 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
114 ? x + y + z + y*z-1 + x-1*y + 2*y-1 + 3*x-1 + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Polytope 285
Image of polytope 285 PALP id: 285
grdb id: 518148
Integer points: [ 1 0 0 1 -1 -1 0 -1 0 -1]
[ 0 1 0 0 1 -2 0 0 -1 -1]
[ 0 0 1 -1 0 0 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
143 ? x + y + z + x*z-1 + x-1*y + 2*y-1 + 3*x-1 + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Polytope 286
Image of polytope 286 PALP id: 286
grdb id: 518129
Integer points: [ 1 0 1 -2 0 0 0 -1 0 -1]
[ 0 1 -1 1 0 -2 -1 0 0 1]
[ 0 0 0 0 1 -1 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 4 1 none
Polytope 287
Image of polytope 287 PALP id: 287
grdb id: 518150
Integer points: [ 1 0 1 0 1 -2 0 -1 0 -1]
[ 0 1 -1 0 -1 -1 -1 -1 0 0]
[ 0 0 0 1 -1 0 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
83 ? x + y + z + x*y-1 + x*y-1*z-1 + 3*y-1 + 2*x-1 + 3*x-1*y-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Polytope 288
Image of polytope 288 PALP id: 288
grdb id: 518000
Integer points: [ 1 -1 0 0 -2 2 -1 0 1 0]
[ 0 0 1 0 -1 -1 -1 -1 -1 0]
[ 0 0 0 1 -1 -1 -1 -1 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
68 ? x + y + z + x2*y-1*z-1 + 4*x*y-1*z-1 + x-1 + 6*y-1*z-1 + 4*x-1*y-1*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 13 2 irreducible and admissible
Polytope 289
Image of polytope 289 PALP id: 289
grdb id: 518175
Integer points: [ 1 0 0 -2 0 2 1 -1 0 -1]
[ 0 1 -1 1 0 -2 -1 0 0 1]
[ 0 0 0 0 1 -1 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
81 ? x + y + z + 2*x*y-1 + 2*x-1*y + x2*y-2*z-1 + y-1 + 2*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 6 irreducible and admissible
Polytope 290
Image of polytope 290 PALP id: 290
grdb id: 518098
Integer points: [ 1 0 0 0 -2 -2 -1 -1 -2 0]
[ 0 1 -1 0 0 2 0 1 1 0]
[ 0 0 0 1 -1 -1 0 0 -1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
105 ? x + y + z + 2*x-1*y + x-2*y2*z-1 + y-1 + 2*x-1 + 2*x-2*y*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 291
Image of polytope 291 PALP id: 291
grdb id: 429084
Integer points: [ 1 0 0 -1 -2 -1 -2 -1 -1 0]
[ 0 1 0 -1 0 1 1 0 1 0]
[ 0 0 1 -1 -1 1 0 0 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
74 ? x + y + z + x-1*y*z + 2*x-1*y + x-1 + x-2*y + x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 292
Image of polytope 292 PALP id: 292
grdb id: 429072
Integer points: [ 1 0 0 1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 0 1 -1 0 -1 0]
[ 0 0 1 -1 1 0 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 2 1 none
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 293
Image of polytope 293 PALP id: 293
grdb id: 429074
Integer points: [ 1 -1 0 0 1 1 1 1 0 0]
[ 0 0 1 0 0 -1 -2 -1 0 -1]
[ 0 0 0 1 -1 0 -2 -1 0 -1]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 6 1 none
Polytope 294
Image of polytope 294 PALP id: 294
grdb id: 429082
Integer points: [ 1 0 0 -1 0 -1 1 1 0 0]
[ 0 1 0 0 -1 -1 0 0 0 0]
[ 0 0 1 0 0 1 -2 -1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + 2*x*z-1 + x*z-2 + 2*z-1 + y-1 + x-1 + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 295
Image of polytope 295 PALP id: 295
grdb id: 429083
Integer points: [ 1 0 0 0 -1 -2 -2 -1 -1 0]
[ 0 1 -1 0 -1 -1 -2 -1 0 0]
[ 0 0 0 1 -1 0 -1 0 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 5 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 296
Image of polytope 296 PALP id: 296
grdb id: 429080
Integer points: [ 1 0 0 0 -1 -2 -2 -1 -1 0]
[ 0 1 -1 0 -1 1 0 0 1 0]
[ 0 0 0 1 -1 0 -1 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
37 rank 3, number 17 x + y + z + 2*x-1*y + y-1 + x-1 + x-2*y + x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 297
Image of polytope 297 PALP id: 297
grdb id: 429077
Integer points: [ 1 0 0 0 -1 -1 -2 -1 -1 0]
[ 0 1 0 -1 -1 1 -1 0 -1 0]
[ 0 0 1 -1 0 0 -1 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 6 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 298
Image of polytope 298 PALP id: 298
grdb id: 429073
Integer points: [ 1 0 0 0 0 -2 -1 -1 0 -1]
[ 0 1 -1 0 -1 -1 -2 -1 0 0]
[ 0 0 0 1 -1 0 -1 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 6 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 299
Image of polytope 299 PALP id: 299
grdb id: 429081
Integer points: [ 1 0 1 0 0 -1 -1 0 -1 0]
[ 0 1 -1 0 -2 -1 1 -1 0 0]
[ 0 0 0 1 -1 -1 1 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
29 rank 2, number 23 x + y + z + x-1*y*z + x*y-1 + 2*y-1 + 2*x-1 + y-2*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 300
Image of polytope 300 PALP id: 300
grdb id: 429076
Integer points: [ 1 0 0 -2 0 -2 -3 -1 -1 0]
[ 0 1 -1 -1 0 -1 -2 -1 0 0]
[ 0 0 0 0 1 -1 -1 0 0 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 6 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 301
Image of polytope 301 PALP id: 301
grdb id: 429079
Integer points: [ 1 0 0 0 -2 -2 -3 -1 -1 0]
[ 0 1 -1 0 0 1 1 0 1 0]
[ 0 0 0 1 -1 0 -1 0 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
155 ? x + y + z + 2*x-1*y + y-1 + x-1 + x-2*y + x-2*z-1 + x-3*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 302
Image of polytope 302 PALP id: 302
grdb id: 428928
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 1 -1 0 -1 -1 0 0]
[ 0 0 1 0 -1 1 1 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Polytope 303
Image of polytope 303 PALP id: 303
grdb id: 429058
Integer points: [ 1 0 0 0 -1 0 -1 0 0 -1]
[ 0 1 0 -1 0 -1 0 -1 0 0]
[ 0 0 1 -1 -1 1 1 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
29 rank 2, number 23 x + y + z + y-1*z + x-1*z + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 304
Image of polytope 304 PALP id: 304
grdb id: 428956
Integer points: [ 1 -1 0 0 -1 -1 -1 -1 -1 0]
[ 0 0 1 0 -1 0 -1 -1 -1 0]
[ 0 0 0 1 -1 1 2 0 1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
61 rank 2, number 27 x + y + z + x-1*z + x-1*y-1*z2 + x-1 + 3*x-1*y-1*z + 3*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Polytope 305
Image of polytope 305 PALP id: 305
grdb id: 428833
Integer points: [ 1 0 -1 0 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 1 0 2 1 0 0]
[ 0 0 0 1 -1 1 -1 0 0 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 306
Image of polytope 306 PALP id: 306
grdb id: 429015
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 0 -1 0 -1 0]
[ 0 0 1 -1 0 1 2 0 1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
42 rank 2, number 29 x + y + z + x-1*z + x-1*y-1*z2 + 2*x-1 + 2*x-1*y-1*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 307
Image of polytope 307 PALP id: 307
grdb id: 428993
Integer points: [ 1 -1 0 0 1 1 1 1 0 0]
[ 0 0 1 0 -1 0 -2 -1 0 -1]
[ 0 0 0 1 0 1 -2 -1 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
148 ? x*z + x + y + z + x*y-1 + 2*x*y-1*z-1 + x-1 + 2*y-1*z-1 + x*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 308
Image of polytope 308 PALP id: 308
grdb id: 429028
Integer points: [ 1 0 -2 0 -2 0 -1 -1 -1 0]
[ 0 1 -1 0 -1 -1 -1 0 -1 0]
[ 0 0 0 1 -1 1 1 0 0 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
93 ? x + y + z + y-1*z + 2*x-1 + x-1*y-1*z + 2*x-1*y-1 + x-2*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 309
Image of polytope 309 PALP id: 309
grdb id: 428988
Integer points: [ 1 0 -1 -1 0 -2 0 -1 0 0]
[ 0 1 0 -2 0 -2 -1 -1 0 -1]
[ 0 0 0 0 1 -1 1 0 0 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
133 ? x + y + z + y-1*z + 2*y-1 + x-1 + x-1*y-1 + x-1*y-2 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Polytope 310
Image of polytope 310 PALP id: 310
grdb id: 428887
Integer points: [ 1 0 -1 0 -2 -2 0 -1 -1 0]
[ 0 1 -1 0 0 1 1 1 0 0]
[ 0 0 0 1 -1 -1 1 0 0 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
133 ? y*z + x + y + z + 2*x-1*y + 3*x-1 + x-2*y*z-1 + x-1*y-1 + x-2*z-1
150 ? y*z + x + y + z + 2*x-1*y + 2*x-1 + x-2*y*z-1 + x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 311
Image of polytope 311 PALP id: 311
grdb id: 428935
Integer points: [ 1 0 -1 0 -2 -1 -2 -2 -1 0]
[ 0 1 -1 0 -1 0 -1 -1 0 0]
[ 0 0 0 1 -1 1 1 0 0 0]
Degree: 48
Hilbert function: 1 + 27 t + 125 t2 + 343 t3 + 729 t4 + 1331 t5 + 2197 t6 + 3375 t7 + 4913 t8 + 6859 t9 + 9261 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Polytope 312
Image of polytope 312 PALP id: 312
grdb id: 428884
Integer points: [ 1 0 -1 0 -2 0 -2 -1 -1 0]
[ 0 1 1 0 0 -1 -1 0 -1 0]
[ 0 0 0 1 -1 1 -1 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
63 ? x + y + z + x-1*y + y-1*z + 2*x-1 + 2*x-1*y-1 + x-2*z-1 + x-2*y-1*z-1
105 ? x + y + z + x-1*y + y-1*z + 3*x-1 + 2*x-1*y-1 + x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 313
Image of polytope 313 PALP id: 313
grdb id: 428920
Integer points: [ 1 0 -1 0 -2 1 0 -1 -1 0]
[ 0 1 -1 0 1 1 1 1 0 0]
[ 0 0 0 1 -1 1 1 0 0 0]
Degree: 50
Hilbert function: 1 + 28 t + 130 t2 + 357 t3 + 759 t4 + 1386 t5 + 2288 t6 + 3515 t7 + 5117 t8 + 7144 t9 + 9646 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 314
Image of polytope 314 PALP id: 314
grdb id: 428886
Integer points: [ 1 0 -1 0 -1 -2 -2 -1 -2 0]
[ 0 1 -1 0 1 -1 1 0 0 0]
[ 0 0 0 1 0 -1 -1 0 -1 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
86 ? x + y + z + x-1*y + 2*x-1 + x-2*y*z-1 + x-1*y-1 + 2*x-2*z-1 + x-2*y-1*z-1
142 ? x + y + z + x-1*y + 3*x-1 + x-2*y*z-1 + x-1*y-1 + 2*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 315
Image of polytope 315 PALP id: 315
grdb id: 429012
Integer points: [ 1 0 -1 0 -1 -1 -1 -1 0 0]
[ 0 1 0 0 0 1 -2 -1 0 -1]
[ 0 0 0 1 -1 -1 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + x-1*y*z-1 + 2*y-1 + x-1 + x-1*z-1 + 2*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 316
Image of polytope 316 PALP id: 316
grdb id: 429019
Integer points: [ 1 0 -1 0 0 -1 -2 -1 -1 0]
[ 0 1 -1 0 1 1 0 0 0 0]
[ 0 0 0 1 -1 0 1 0 1 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 6 1 none
Polytope 317
Image of polytope 317 PALP id: 317
grdb id: 429035
Integer points: [ 1 0 0 -2 0 -2 -1 -1 -1 0]
[ 0 1 -1 1 0 1 0 1 0 0]
[ 0 0 0 0 1 -1 1 0 0 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 6 1 none
Polytope 318
Image of polytope 318 PALP id: 318
grdb id: 429005
Integer points: [ 1 0 0 -2 0 -1 -1 -1 0 -1]
[ 0 1 -1 -1 0 -2 0 -1 0 0]
[ 0 0 0 0 1 -1 1 0 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
142 ? x + y + z + x-1*z + y-1 + 2*x-1 + x-1*y-1 + x-2*y-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Polytope 319
Image of polytope 319 PALP id: 319
grdb id: 429026
Integer points: [ 1 0 0 -1 -2 -1 -2 -1 -1 0]
[ 0 1 0 -1 -1 0 -2 -1 0 0]
[ 0 0 1 -1 0 1 -1 0 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
102 ? x + y + z + x-1*z + 2*x-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-2*y-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 320
Image of polytope 320 PALP id: 320
grdb id: 428832
Integer points: [ 1 0 0 -1 0 -1 -2 -1 -1 0]
[ 0 1 -1 1 0 -2 -2 -1 0 0]
[ 0 0 0 0 1 -1 -1 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 4 1 none
Polytope 321
Image of polytope 321 PALP id: 321
grdb id: 429049
Integer points: [ 1 0 0 -1 0 0 -2 -1 -1 0]
[ 0 1 -1 0 0 -1 1 1 0 0]
[ 0 0 0 0 1 1 -2 -1 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
66 rank 2, number 24 x + y + z + y-1*z + 2*x-1*y*z-1 + y-1 + x-1 + 2*x-1*z-1 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 322
Image of polytope 322 PALP id: 322
grdb id: 429043
Integer points: [ 1 0 0 -1 0 0 -2 -1 -1 0]
[ 0 1 -1 0 0 1 1 1 0 0]
[ 0 0 0 0 1 -1 -2 -1 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? x + y + z + y*z-1 + 2*x-1*y*z-1 + y-1 + x-1 + 2*x-1*z-1 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 323
Image of polytope 323 PALP id: 323
grdb id: 429039
Integer points: [ 1 0 0 0 -1 -2 -2 -1 -1 0]
[ 0 1 -1 0 0 1 1 0 1 0]
[ 0 0 0 1 -1 0 -1 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
104 ? x + y + z + 2*x-1*y + y-1 + 2*x-1 + x-2*y + x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 324
Image of polytope 324 PALP id: 324
grdb id: 429054
Integer points: [ 1 0 0 0 -1 -2 -2 -1 -1 0]
[ 0 1 0 -1 -1 -1 -1 0 -1 0]
[ 0 0 1 -1 0 0 -1 0 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
111 ? x + y + z + 2*x-1 + y-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 325
Image of polytope 325 PALP id: 325
grdb id: 429059
Integer points: [ 1 0 0 0 -1 -2 -2 -1 -1 0]
[ 0 1 0 -1 0 -1 -1 -1 0 0]
[ 0 0 1 -1 1 0 1 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
160 ? x + y + z + x-1*z + 2*x-1 + y-1*z-1 + 2*x-1*y-1 + x-2*y-1*z + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 326
Image of polytope 326 PALP id: 326
grdb id: 429061
Integer points: [ 1 0 0 0 -1 -1 -2 -1 -1 0]
[ 0 1 -1 0 -1 1 0 0 0 0]
[ 0 0 0 1 -1 -1 -1 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
76 ? x + y + z + x-1*y*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 327
Image of polytope 327 PALP id: 327
grdb id: 429062
Integer points: [ 1 0 0 0 -1 -1 -2 -1 -1 0]
[ 0 1 -1 0 0 0 1 1 0 0]
[ 0 0 0 1 -1 1 0 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 5 1 none
Polytope 328
Image of polytope 328 PALP id: 328
grdb id: 429040
Integer points: [ 1 0 0 0 0 -1 -2 -1 -1 0]
[ 0 1 -1 0 -1 0 1 0 1 0]
[ 0 0 0 1 -1 -1 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
103 ? x + y + z + 2*x-1*y + y-1 + 2*x-1 + x-2*y + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 329
Image of polytope 329 PALP id: 329
grdb id: 428969
Integer points: [ 1 0 0 0 0 -1 -2 -1 0 -1]
[ 0 1 -1 0 1 0 -1 0 0 -1]
[ 0 0 0 1 -1 1 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 6 1 none
Polytope 330
Image of polytope 330 PALP id: 330
grdb id: 429041
Integer points: [ 1 0 0 0 0 -1 -2 -1 -1 0]
[ 0 1 0 0 -1 -1 0 0 0 0]
[ 0 0 1 -1 0 1 1 0 1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
164 ? x + y + z + 2*x-1*z + z-1 + y-1 + 2*x-1 + x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 331
Image of polytope 331 PALP id: 331
grdb id: 429042
Integer points: [ 1 0 0 0 0 -1 -1 -1 0 0]
[ 0 1 0 0 -1 0 -2 -1 -1 0]
[ 0 0 1 -1 0 0 -2 -1 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
76 ? x + y + z + z-1 + y-1 + x-1 + 2*y-1*z-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 332
Image of polytope 332 PALP id: 332
grdb id: 429052
Integer points: [ 1 0 0 0 1 0 -2 -1 0 -1]
[ 0 1 -1 0 -1 -1 1 0 0 1]
[ 0 0 0 1 -1 -1 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
80 ? x + y + z + 2*x-1*y + x*y-1*z-1 + y-1 + 2*x-1 + x-2*y + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 333
Image of polytope 333 PALP id: 333
grdb id: 429045
Integer points: [ 1 0 0 0 1 0 -2 -1 0 -1]
[ 0 1 -1 0 0 1 1 1 0 0]
[ 0 0 0 1 -1 -1 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
77 ? x + y + z + x*z-1 + y*z-1 + 2*x-1*y + y-1 + 2*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 334
Image of polytope 334 PALP id: 334
grdb id: 429010
Integer points: [ 1 0 1 -1 0 -2 -2 -1 0 0]
[ 0 1 -1 -1 0 0 -1 0 -1 0]
[ 0 0 0 0 1 -1 -1 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
95 ? x + y + z + x*y-1 + 2*y-1 + 2*x-1 + x-1*y-1 + x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 335
Image of polytope 335 PALP id: 335
grdb id: 429060
Integer points: [ 1 -1 0 0 -2 1 2 -1 0 1]
[ 0 0 1 0 0 -1 -1 0 0 0]
[ 0 0 0 1 1 -1 -2 1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + 2*x*z-1 + 2*x-1*z + x2*y-1*z-2 + x*y-1*z-1 + x-1 + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 336
Image of polytope 336 PALP id: 336
grdb id: 429055
Integer points: [ 1 -1 0 0 0 2 2 1 1 0]
[ 0 0 1 0 -1 -1 -2 -1 -1 0]
[ 0 0 0 1 -1 -1 -1 0 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
79 ? x + y + z + x2*y-1*z-1 + 2*x*y-1 + x2*y-2*z-1 + 2*x*y-1*z-1 + x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 337
Image of polytope 337 PALP id: 337
grdb id: 429050
Integer points: [ 1 0 -1 0 0 2 -2 1 0 -1]
[ 0 1 1 0 -1 -1 2 -1 0 1]
[ 0 0 0 1 -1 -1 1 -1 0 1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
55 rank 2, number 19 x + y + z + 2*x-1*y*z + x-2*y2*z + x2*y-1*z-1 + x-1*y + 2*x*y-1*z-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 338
Image of polytope 338 PALP id: 338
grdb id: 428968
Integer points: [ 1 -1 0 0 -1 -1 -3 -2 0 -1]
[ 0 0 1 0 -1 0 -2 -1 0 -1]
[ 0 0 0 1 0 -1 -2 -1 0 -1]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
57 ? x + y + z + x-1 + x-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*y-1*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 339
Image of polytope 339 PALP id: 339
grdb id: 428567
Integer points: [ 1 0 -1 0 0 -1 0 0 -1 0]
[ 0 1 1 0 -1 -1 -1 -1 0 0]
[ 0 0 0 1 -1 0 1 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
145 ? x + y + z + x-1*y + y-1*z + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 340
Image of polytope 340 PALP id: 340
grdb id: 428572
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 0 -1 -1 0 -1 0]
[ 0 0 1 -1 1 -1 1 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
160 ? x + y + z + x-1*z + 2*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 341
Image of polytope 341 PALP id: 341
grdb id: 428575
Integer points: [ 1 0 1 -1 0 1 -1 0 -1 0]
[ 0 1 -1 1 0 1 -1 0 0 -1]
[ 0 0 0 0 1 -1 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x*y*z-1 + x + y + z + x*y-1 + x-1*y + 2*y-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 342
Image of polytope 342 PALP id: 342
grdb id: 428500
Integer points: [ 1 0 1 -1 -1 0 -1 -1 0 0]
[ 0 1 -1 1 -1 0 2 0 0 -1]
[ 0 0 0 0 0 1 -1 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
159 ? x + y + z + x-1*y2*z-1 + x*y-1 + x-1*y + 2*y-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 343
Image of polytope 343 PALP id: 343
grdb id: 428413
Integer points: [ 1 -1 0 0 1 -2 1 0 -1 0]
[ 0 0 1 0 0 -1 -1 -1 -1 0]
[ 0 0 0 1 1 -1 -1 -1 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
68 ? x*z + x + y + z + x*y-1*z-1 + x-1 + 3*y-1*z-1 + 3*x-1*y-1*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Polytope 344
Image of polytope 344 PALP id: 344
grdb id: 428318
Integer points: [ 1 0 0 -1 0 -2 0 -1 -1 0]
[ 0 1 -1 1 0 -1 -1 -1 0 0]
[ 0 0 0 0 1 -1 1 0 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 8 1 none
Polytope 345
Image of polytope 345 PALP id: 345
grdb id: 428555
Integer points: [ 1 0 0 0 -2 -2 0 -1 -1 0]
[ 0 1 -1 0 0 1 1 1 0 0]
[ 0 0 0 1 -1 -1 1 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
105 ? y*z + x + y + z + 2*x-1*y + y-1 + 2*x-1 + x-2*y*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 346
Image of polytope 346 PALP id: 346
grdb id: 428554
Integer points: [ 1 0 0 0 -1 -2 -1 -1 -1 0]
[ 0 1 -1 0 -1 -1 0 -1 0 0]
[ 0 0 0 1 -1 0 1 0 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
92 ? x + y + z + x-1*z + y-1 + 2*x-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 347
Image of polytope 347 PALP id: 347
grdb id: 428552
Integer points: [ 1 0 0 0 0 -1 -2 -1 0 -1]
[ 0 1 -1 0 -1 0 -1 -1 0 0]
[ 0 0 0 1 -1 1 0 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
87 ? x + y + z + x-1*z + y-1 + 2*x-1 + y-1*z-1 + 2*x-1*y-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 348
Image of polytope 348 PALP id: 348
grdb id: 428553
Integer points: [ 1 0 0 0 0 -1 -2 -1 -1 0]
[ 0 1 0 0 -1 0 -1 0 -1 0]
[ 0 0 1 -1 0 1 0 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
95 ? x + y + z + x-1*z + z-1 + y-1 + 2*x-1 + 2*x-1*y-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 349
Image of polytope 349 PALP id: 349
grdb id: 428561
Integer points: [ 1 0 0 0 0 1 -2 -1 0 -1]
[ 0 1 0 0 -1 -1 0 0 0 0]
[ 0 0 1 -1 0 0 -1 0 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? x + y + z + x*y-1 + z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 350
Image of polytope 350 PALP id: 350
grdb id: 428509
Integer points: [ 1 0 1 -1 -1 0 -2 -1 0 0]
[ 0 1 -1 1 -1 0 -1 0 -1 0]
[ 0 0 0 0 0 1 -1 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 6 1 none
Polytope 351
Image of polytope 351 PALP id: 351
grdb id: 428562
Integer points: [ 1 0 1 -1 -1 0 -2 -1 0 0]
[ 0 1 -1 1 -1 0 0 0 0 -1]
[ 0 0 0 0 0 1 -1 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 5 1 none
Polytope 352
Image of polytope 352 PALP id: 352
grdb id: 428415
Integer points: [ 1 0 1 -1 -1 0 -2 -1 0 0]
[ 0 1 -1 1 -1 0 1 0 0 -1]
[ 0 0 0 0 0 1 -1 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 6 1 none
Polytope 353
Image of polytope 353 PALP id: 353
grdb id: 428577
Integer points: [ 1 -1 0 0 0 -2 2 -1 1 0]
[ 0 0 1 0 -1 -1 0 -1 0 0]
[ 0 0 0 1 -1 -1 1 -1 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
68 ? x2*z + 2*x*z + x + y + z + x-1 + y-1*z-1 + 2*x-1*y-1*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 354
Image of polytope 354 PALP id: 354
grdb id: 429566
Integer points: [ 1 0 1 -1 -1 0 -1 -1 0 0]
[ 0 1 -1 1 -1 0 -1 0 -1 0]
[ 0 0 0 0 0 1 -1 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
106 ? x + y + z + x*y-1 + x-1*y + 2*y-1 + 2*x-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Polytope 355
Image of polytope 355 PALP id: 355
grdb id: 429564
Integer points: [ 1 0 1 -1 0 0 -1 0 0 -1]
[ 0 1 -1 1 0 -1 -1 -1 0 0]
[ 0 0 0 0 1 -1 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
132 ? x + y + z + x*y-1 + x-1*y + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Polytope 356
Image of polytope 356 PALP id: 356
grdb id: 429574
Integer points: [ 1 0 1 -1 0 0 -1 0 -1 0]
[ 0 1 -1 1 0 0 -1 0 0 -1]
[ 0 0 0 0 1 -1 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
64 ? x + y + z + x*y-1 + x-1*y + z-1 + 2*y-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Polytope 357
Image of polytope 357 PALP id: 357
grdb id: 429572
Integer points: [ 1 0 1 -1 0 1 -1 0 0 -1]
[ 0 1 -1 1 0 -1 -1 -1 0 0]
[ 0 0 0 0 1 -1 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
129 ? x + y + z + x*y-1 + x-1*y + x*y-1*z-1 + 2*y-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Polytope 358
Image of polytope 358 PALP id: 358
grdb id: 429573
Integer points: [ 1 0 1 -1 0 1 -1 0 -1 0]
[ 0 1 -1 1 0 0 -1 0 0 -1]
[ 0 0 0 0 1 -1 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
114 ? x + y + z + x*z-1 + x*y-1 + x-1*y + 2*y-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Polytope 359
Image of polytope 359 PALP id: 359
grdb id: 254904
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 0]
[ 0 1 0 -1 0 1 -1 0 0 0]
[ 0 0 1 -1 -1 0 -1 1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 6 1 none
Polytope 360
Image of polytope 360 PALP id: 360
grdb id: 254911
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 0 -1 -1 -1 0]
[ 0 0 1 -1 0 0 1 -1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
76 ? x + y + z + z-1 + y-1 + x-1 + x-1*y-1*z + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Polytope 361
Image of polytope 361 PALP id: 361
grdb id: 254912
Integer points: [ 1 -1 0 0 1 1 0 2 1 0]
[ 0 0 1 0 -1 0 -1 -1 -1 0]
[ 0 0 0 1 0 -1 -1 -1 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
79 ? x + y + z + x2*y-1*z-1 + x*z-1 + x*y-1 + 2*x*y-1*z-1 + x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Polytope 362
Image of polytope 362 PALP id: 362
grdb id: 254875
Integer points: [ 1 0 -1 0 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 1 1 0 0 0]
[ 0 0 0 1 -1 0 1 1 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
152 rank 3, number 22 x + y + z + x-1*y*z + x-1*y + x-1*z + x-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 363
Image of polytope 363 PALP id: 363
grdb id: 254859
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 1 0 0 0]
[ 0 0 1 -1 0 -1 0 1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
57 ? x + y + z + x-1*y + x-1*z + x-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 364
Image of polytope 364 PALP id: 364
grdb id: 254860
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 0 1 0 0]
[ 0 0 1 -1 0 0 1 -1 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
158 ? x + y + z + x-1*y + x-1*z + x-1*y*z-1 + x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 365
Image of polytope 365 PALP id: 365
grdb id: 254877
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 0 1 0 0]
[ 0 0 1 -1 0 0 1 1 0 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
41 ? x + y + z + x-1*y*z + x-1*y + x-1*z + x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 366
Image of polytope 366 PALP id: 366
grdb id: 254841
Integer points: [ 1 0 0 -1 -1 -1 -1 0 -1 0]
[ 0 1 0 0 -1 1 1 1 0 0]
[ 0 0 1 -1 0 0 -1 1 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
42 rank 2, number 29 y*z + x + y + z + x-1*y + x-1*y*z-1 + 2*x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 367
Image of polytope 367 PALP id: 367
grdb id: 254887
Integer points: [ 1 0 0 -1 0 1 -1 -1 -1 0]
[ 0 1 -1 0 0 1 -1 1 0 0]
[ 0 0 0 0 1 0 -1 -1 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
66 rank 2, number 24 x*y + x + y + z + x-1*y*z-1 + y-1 + x-1 + 2*x-1*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 368
Image of polytope 368 PALP id: 368
grdb id: 254896
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 0]
[ 0 1 0 -1 0 -1 1 -1 0 0]
[ 0 0 1 -1 -1 0 0 -1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? x + y + z + x-1*y + 2*x-1 + y-1*z-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 369
Image of polytope 369 PALP id: 369
grdb id: 254882
Integer points: [ 1 0 0 0 -1 1 0 -1 -1 0]
[ 0 1 -1 0 1 -1 -1 -1 0 0]
[ 0 0 0 1 0 -1 -1 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + x-1*y + x*y-1*z-1 + y-1 + 2*x-1 + y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Polytope 370
Image of polytope 370 PALP id: 370
grdb id: 254883
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 0]
[ 0 1 -1 0 1 -1 0 0 0 0]
[ 0 0 0 1 -1 0 -1 1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + y*z-1 + x-1*z + y-1 + 2*x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 371
Image of polytope 371 PALP id: 371
grdb id: 254878
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 0]
[ 0 1 0 0 -1 1 -1 1 0 0]
[ 0 0 1 -1 0 1 -1 1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
29 rank 2, number 23 y*z + x + y + z + x-1*y*z + z-1 + y-1 + 2*x-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 372
Image of polytope 372 PALP id: 372
grdb id: 254885
Integer points: [ 1 0 0 1 0 0 -1 -1 -1 0]
[ 0 1 -1 -1 0 -1 0 0 0 0]
[ 0 0 0 0 1 -1 -1 1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + x*y-1 + x-1*z + y-1 + 2*x-1 + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 373
Image of polytope 373 PALP id: 373
grdb id: 254900
Integer points: [ 1 -1 0 0 -1 -1 2 0 1 0]
[ 0 0 1 0 1 0 -1 -1 -1 0]
[ 0 0 0 1 0 1 -1 -1 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
68 ? x + y + z + x2*y-1*z-1 + x-1*y + x-1*z + 2*x*y-1*z-1 + x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 374
Image of polytope 374 PALP id: 374
grdb id: 254899
Integer points: [ 1 -1 0 0 -1 0 -1 -1 -1 0]
[ 0 0 1 0 0 -1 -1 -2 -1 0]
[ 0 0 0 1 -1 1 1 1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
61 rank 2, number 27 x + y + z + y-1*z + x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 375
Image of polytope 375 PALP id: 375
grdb id: 254864
Integer points: [ 1 0 -1 0 -2 -1 1 0 -1 0]
[ 0 1 -1 0 0 1 1 1 0 0]
[ 0 0 0 1 -1 0 1 1 0 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
113 rank 3, number 26 x*y*z + y*z + x + y + z + x-1*y + x-1 + x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 376
Image of polytope 376 PALP id: 376
grdb id: 254876
Integer points: [ 1 0 -1 0 -2 0 -2 -1 -1 0]
[ 0 1 -1 0 0 -1 1 1 0 0]
[ 0 0 0 1 -1 1 -1 0 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
86 ? x + y + z + x-1*y + y-1*z + 2*x-1 + x-2*y*z-1 + x-1*y-1 + x-2*z-1
142 ? x + y + z + x-1*y + y-1*z + 3*x-1 + x-2*y*z-1 + x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Polytope 377
Image of polytope 377 PALP id: 377
grdb id: 254857
Integer points: [ 1 0 -1 0 -1 -2 -1 -2 -1 0]
[ 0 1 -1 0 -1 -1 0 -1 0 0]
[ 0 0 0 1 -1 0 1 -1 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 6 1 none
Polytope 378
Image of polytope 378 PALP id: 378
grdb id: 254829
Integer points: [ 1 0 -1 0 -1 -2 -1 -2 -1 0]
[ 0 1 -1 0 -1 -1 0 -1 0 0]
[ 0 0 0 1 -1 0 1 1 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
86 ? x + y + z + x-1*z + 2*x-1 + x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 379
Image of polytope 379 PALP id: 379
grdb id: 254851
Integer points: [ 1 0 0 -1 -1 0 -1 -2 -1 0]
[ 0 1 -1 -1 1 0 1 1 0 0]
[ 0 0 0 0 0 1 -1 -1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 6 1 none
Polytope 380
Image of polytope 380 PALP id: 380
grdb id: 254828
Integer points: [ 1 0 0 -1 0 -1 -2 -2 -1 0]
[ 0 1 -1 0 0 -2 -1 -2 -1 0]
[ 0 0 0 0 1 -1 -1 -1 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
42 rank 2, number 29 x + y + z + y-1 + x-1 + 2*x-1*y-1 + x-1*y-2*z-1 + x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 381
Image of polytope 381 PALP id: 381
grdb id: 254895
Integer points: [ 1 0 0 -1 0 -1 -2 -2 -1 0]
[ 0 1 -1 1 0 1 0 1 0 0]
[ 0 0 0 0 1 -1 -1 -1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
98 rank 3, number 21 x + y + z + x-1*y + x-1*y*z-1 + y-1 + 2*x-1 + x-2*y*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 382
Image of polytope 382 PALP id: 382
grdb id: 254890
Integer points: [ 1 0 0 -1 0 -1 0 -2 -1 0]
[ 0 1 -1 0 0 0 -1 -1 -1 0]
[ 0 0 0 0 1 -1 1 -1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
160 ? x + y + z + y-1*z + y-1 + x-1 + x-1*z-1 + 2*x-1*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 383
Image of polytope 383 PALP id: 383
grdb id: 254881
Integer points: [ 1 0 0 -1 0 -1 0 -2 -1 0]
[ 0 1 -1 0 0 1 -1 1 0 0]
[ 0 0 0 0 1 0 -1 -1 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
28 rank 2, number 25 x + y + z + x-1*y + y-1 + x-1 + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 384
Image of polytope 384 PALP id: 384
grdb id: 254901
Integer points: [ 1 0 0 0 -1 -1 -1 -2 -1 0]
[ 0 1 -1 0 0 1 -1 0 0 0]
[ 0 0 0 1 -1 0 0 -1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 5 1 none
Polytope 385
Image of polytope 385 PALP id: 385
grdb id: 254897
Integer points: [ 1 0 0 0 -1 -1 -1 -2 -1 0]
[ 0 1 0 -1 -1 -1 0 -1 0 0]
[ 0 0 1 -1 0 -1 1 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
111 ? x + y + z + x-1*z + 2*x-1 + y-1*z-1 + x-1*y-1 + x-1*y-1*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Polytope 386
Image of polytope 386 PALP id: 386
grdb id: 254880
Integer points: [ 1 0 0 0 -1 -1 0 -2 -1 0]
[ 0 1 -1 0 1 0 -1 1 0 0]
[ 0 0 0 1 0 -1 1 -1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
47 ? x + y + z + x-1*y + y-1*z + y-1 + 2*x-1 + x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 387
Image of polytope 387 PALP id: 387
grdb id: 254886
Integer points: [ 1 0 0 0 0 -1 -1 -2 -1 0]
[ 0 1 -1 0 1 -1 0 -1 0 0]
[ 0 0 0 1 -1 1 1 1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
47 ? x + y + z + y*z-1 + x-1*z + y-1 + 2*x-1 + x-1*y-1*z + x-2*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 388
Image of polytope 388 PALP id: 388
grdb id: 254888
Integer points: [ 1 0 0 1 0 -1 -1 -2 0 -1]
[ 0 1 -1 1 0 0 -1 0 0 0]
[ 0 0 0 0 1 -1 -1 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x*y + x + y + z + y-1 + 2*x-1 + x-1*z-1 + x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 389
Image of polytope 389 PALP id: 389
grdb id: 255697
Integer points: [ 1 0 0 -1 -1 0 -1 -1 -1 0]
[ 0 1 0 0 -1 1 1 1 0 0]
[ 0 0 1 -1 0 -1 0 -1 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
102 ? x + y + z + y*z-1 + x-1*y + x-1*y*z-1 + 2*x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 390
Image of polytope 390 PALP id: 390
grdb id: 255547
Integer points: [ 1 0 0 -1 -1 0 -1 0 -1 0]
[ 0 1 -1 1 -1 0 -1 -1 0 0]
[ 0 0 0 0 0 1 -1 1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
69 ? x + y + z + x-1*y + y-1*z + y-1 + 2*x-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 391
Image of polytope 391 PALP id: 391
grdb id: 255698
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 1 1 -1 0 0]
[ 0 0 0 0 1 0 -1 -1 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? x + y + z + x-1*y + x-1*y*z-1 + y-1 + x-1 + 2*x-1*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 392
Image of polytope 392 PALP id: 392
grdb id: 255687
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 0]
[ 0 1 0 1 -1 0 -1 1 0 0]
[ 0 0 1 -1 1 -1 0 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
160 ? x + y + z + x-1*y + y-1*z + x-1*y*z-1 + 2*x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 393
Image of polytope 393 PALP id: 393
grdb id: 255691
Integer points: [ 1 0 0 -1 0 -1 0 -1 -1 0]
[ 0 1 -1 0 0 -1 -1 -1 -1 0]
[ 0 0 0 0 1 -1 1 1 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
102 ? x + y + z + y-1*z + y-1 + x-1 + x-1*y-1*z + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 394
Image of polytope 394 PALP id: 394
grdb id: 255699
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 1 0 1 0 0]
[ 0 0 0 1 -1 0 1 1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
105 ? x + y + z + x-1*y*z + x-1*y + x-1*z + y-1 + 2*x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 395
Image of polytope 395 PALP id: 395
grdb id: 255714
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 1 1 0 0 0]
[ 0 0 0 1 -1 0 -1 1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
69 ? x + y + z + x-1*y + x-1*z + x-1*y*z-1 + y-1 + 2*x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 396
Image of polytope 396 PALP id: 396
grdb id: 255695
Integer points: [ 1 0 0 0 -1 -1 0 -1 -1 0]
[ 0 1 -1 0 1 0 -1 0 0 0]
[ 0 0 0 1 0 -1 1 1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
69 ? x + y + z + x-1*y + y-1*z + x-1*z + y-1 + 2*x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 397
Image of polytope 397 PALP id: 397
grdb id: 255717
Integer points: [ 1 0 0 0 -1 -1 0 0 0 0]
[ 0 1 0 0 0 1 -1 -1 -1 0]
[ 0 0 1 -1 0 0 1 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? x + y + z + x-1*y + y-1*z + z-1 + 2*y-1 + x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 398
Image of polytope 398 PALP id: 398
grdb id: 255711
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 0]
[ 0 1 -1 0 1 1 -1 1 0 0]
[ 0 0 0 1 -1 0 0 -1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
126 ? x + y + z + y*z-1 + x-1*y + x-1*y*z-1 + y-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 399
Image of polytope 399 PALP id: 399
grdb id: 255706
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 0 0 -1 0 0]
[ 0 0 1 -1 0 -1 1 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
95 ? x + y + z + x-1*z + z-1 + y-1 + 2*x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 400
Image of polytope 400 PALP id: 400
grdb id: 255713
Integer points: [ 1 0 0 0 1 -1 1 -1 0 -1]
[ 0 1 -1 0 0 1 -1 -1 0 0]
[ 0 0 0 1 -1 0 -1 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + x*z-1 + x-1*y + x*y-1*z-1 + y-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 401
Image of polytope 401 PALP id: 401
grdb id: 255726
Integer points: [ 1 0 0 1 0 -1 0 -1 -1 0]
[ 0 1 -1 -1 0 0 -1 0 0 0]
[ 0 0 0 0 1 -1 1 1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + x*y-1 + y-1*z + x-1*z + y-1 + 2*x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 402
Image of polytope 402 PALP id: 402
grdb id: 255667
Integer points: [ 1 0 0 -1 -1 0 -2 0 -1 0]
[ 0 1 -1 -1 1 0 0 1 0 0]
[ 0 0 0 0 0 1 -1 1 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
102 ? y*z + x + y + z + x-1*y + y-1 + x-1 + x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 9 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Polytope 403
Image of polytope 403 PALP id: 403
grdb id: 255692
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 -1 0 -2 -1 0]
[ 0 0 0 0 1 -1 1 -1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
63 ? x + y + z + x-1*z + y-1 + x-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 404
Image of polytope 404 PALP id: 404
grdb id: 255703
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 0 -1 -2 -1 0]
[ 0 0 0 0 1 -1 0 -1 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
37 rank 3, number 17 x + y + z + y-1 + x-1 + x-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 405
Image of polytope 405 PALP id: 405
grdb id: 255693
Integer points: [ 1 0 1 0 -1 0 -2 -2 -1 0]
[ 0 1 -1 -1 1 0 1 0 0 0]
[ 0 0 0 0 0 1 -1 -1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
147 ? x + y + z + x*y-1 + x-1*y + y-1 + 2*x-1 + x-2*y*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 406
Image of polytope 406 PALP id: 406
grdb id: 255715
Integer points: [ 1 0 1 0 -1 0 -1 -2 -1 0]
[ 0 1 -1 -1 1 0 0 0 0 0]
[ 0 0 0 0 0 1 -1 -1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
145 ? x + y + z + x*y-1 + x-1*y + y-1 + 2*x-1 + x-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 407
Image of polytope 407 PALP id: 407
grdb id: 255334
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 1 -1 1 0 0]
[ 0 0 0 1 -1 0 0 -1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
87 ? x + y + z + x-1*y + x-1*y*z-1 + y-1 + 2*x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 9 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 408
Image of polytope 408 PALP id: 408
grdb id: 255339
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 0 0 0 0]
[ 0 0 1 -1 0 1 -1 1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
147 ? x + y + z + y-1*z + x-1*z + z-1 + y-1 + 2*x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 9 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 409
Image of polytope 409 PALP id: 409
grdb id: 61986
Integer points: [ 1 0 0 -1 0 0 -1 -1 -1 0]
[ 0 1 -1 0 0 -1 1 0 1 0]
[ 0 0 0 0 1 -1 1 -1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
28 rank 2, number 25 x + y + z + x-1*y*z + x-1*y + y-1 + x-1 + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 5 Lattice Minkowski decompositions of facet 3
Polytope 410
Image of polytope 410 PALP id: 410
grdb id: 61987
Integer points: [ 1 0 0 -1 1 0 0 -1 0 0]
[ 0 1 0 1 -1 0 -1 0 1 0]
[ 0 0 1 1 -1 -1 0 0 1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
29 rank 2, number 23 y*z + x + y + z + x-1*y*z + x*y-1*z-1 + z-1 + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 5 Lattice Minkowski decompositions of facet 3
Polytope 411
Image of polytope 411 PALP id: 411
grdb id: 62089
Integer points: [ 1 0 0 -1 0 -1 1 0 1 0]
[ 0 1 -1 0 0 1 1 -1 0 0]
[ 0 0 0 0 1 0 -1 1 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
66 rank 2, number 24 x*y*z-1 + x + y + z + x*z-1 + x-1*y + y-1*z + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Polytope 412
Image of polytope 412 PALP id: 412
grdb id: 62088
Integer points: [ 1 0 0 0 -1 0 -1 -1 -1 0]
[ 0 1 0 -1 0 0 1 0 -1 0]
[ 0 0 1 0 0 -1 0 -1 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
47 ? x + y + z + x-1*y + z-1 + y-1 + x-1 + x-1*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Polytope 413
Image of polytope 413 PALP id: 413
grdb id: 62091
Integer points: [ 1 0 0 0 0 -1 1 1 -1 0]
[ 0 1 0 0 -1 0 1 0 -1 0]
[ 0 0 1 -1 0 0 0 -1 1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x*y + x + y + z + x*z-1 + z-1 + y-1 + x-1 + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Polytope 414
Image of polytope 414 PALP id: 414
grdb id: 62075
Integer points: [ 1 0 0 -1 0 -1 -1 0 -1 0]
[ 0 1 -1 0 0 0 -1 -1 -1 0]
[ 0 0 0 0 1 -1 0 1 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
37 rank 3, number 17 x + y + z + y-1*z + y-1 + x-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Polytope 415
Image of polytope 415 PALP id: 415
grdb id: 62076
Integer points: [ 1 0 0 -1 0 -1 -1 0 -1 0]
[ 0 1 -1 0 0 0 1 1 1 0]
[ 0 0 0 0 1 -1 0 1 1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
63 ? y*z + x + y + z + x-1*y*z + x-1*y + y-1 + x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Polytope 416
Image of polytope 416 PALP id: 416
grdb id: 62073
Integer points: [ 1 0 0 -1 0 -1 -1 0 -1 0]
[ 0 1 -1 0 0 1 0 -1 1 0]
[ 0 0 0 0 1 -1 -1 1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? x + y + z + x-1*y + y-1*z + x-1*y*z-1 + y-1 + x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Polytope 417
Image of polytope 417 PALP id: 417
grdb id: 62079
Integer points: [ 1 0 0 -1 0 -1 0 -1 -1 0]
[ 0 1 -1 0 0 -1 1 0 1 0]
[ 0 0 0 0 1 0 -1 -1 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? x + y + z + y*z-1 + x-1*y*z-1 + y-1 + x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Polytope 418
Image of polytope 418 PALP id: 418
grdb id: 62077
Integer points: [ 1 0 0 -1 0 1 0 1 1 0]
[ 0 1 -1 0 0 1 1 0 1 0]
[ 0 0 0 0 1 0 -1 -1 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
160 ? x*y + x*y*z-1 + x + y + z + x*z-1 + y*z-1 + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Polytope 419
Image of polytope 419 PALP id: 419
grdb id: 62084
Integer points: [ 1 0 0 0 -1 0 1 0 -1 0]
[ 0 1 0 0 0 -1 0 -1 -1 0]
[ 0 0 1 -1 0 0 -1 1 1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + x*z-1 + y-1*z + z-1 + y-1 + x-1 + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Polytope 420
Image of polytope 420 PALP id: 420
grdb id: 62083
Integer points: [ 1 0 0 0 0 -1 -1 0 1 0]
[ 0 1 0 0 -1 0 0 -1 1 0]
[ 0 0 1 -1 0 0 1 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x*y + x + y + z + x-1*z + z-1 + y-1 + x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Polytope 421
Image of polytope 421 PALP id: 421
grdb id: 62070
Integer points: [ 1 0 0 0 0 -1 0 -1 -1 0]
[ 0 1 0 0 -1 0 -1 0 1 0]
[ 0 0 1 -1 0 0 1 -1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + x-1*y + y-1*z + z-1 + y-1 + x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Polytope 422
Image of polytope 422 PALP id: 422
grdb id: 62074
Integer points: [ 1 0 1 -1 0 -1 0 0 -1 0]
[ 0 1 -1 1 -1 0 0 -1 -1 0]
[ 0 0 0 0 0 0 1 -1 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + x*y-1 + x-1*y + y-1 + x-1 + y-1*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Polytope 423
Image of polytope 423 PALP id: 423
grdb id: 62055
Integer points: [ 1 0 0 0 -1 0 0 -1 -1 0]
[ 0 1 0 0 0 -1 -1 0 -1 0]
[ 0 0 1 -1 0 0 1 -1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
65 ? x + y + z + y-1*z + z-1 + y-1 + x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 10 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 424
Image of polytope 424 PALP id: 424
grdb id: 62056
Integer points: [ 1 0 0 0 0 -1 0 -1 -1 0]
[ 0 1 0 0 -1 0 -1 0 -1 0]
[ 0 0 1 -1 0 0 1 1 1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
69 ? x + y + z + y-1*z + x-1*z + z-1 + y-1 + x-1 + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 10 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 425
Image of polytope 425 PALP id: 425
grdb id: 62054
Integer points: [ 1 0 0 0 0 0 0 -1 -1 0]
[ 0 1 0 1 -1 0 -1 0 1 0]
[ 0 0 1 -1 1 -1 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
147 ? x + y + z + y*z-1 + x-1*y + y-1*z + z-1 + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 10 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 426
Image of polytope 426 PALP id: 426
grdb id: 62053
Integer points: [ 1 0 1 -1 0 -1 0 0 1 0]
[ 0 1 -1 1 -1 0 0 1 0 0]
[ 0 0 0 0 0 0 1 -1 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
103 ? x + y + z + x*z-1 + y*z-1 + x*y-1 + x-1*y + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 10 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 427
Image of polytope 427 PALP id: 427
grdb id: 547520
Integer points: [ 1 1 1 -3 -1 1 -1 0 1 -1 1]
[ 0 2 0 -2 -1 1 0 0 0 -1 1]
[ 0 0 2 -2 0 1 -1 0 1 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
1 rank 1, B2 x*y2 + 2*x*y*z + x*z2 + 2*x*y + 2*x*z + x + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 4 Lattice Minkowski decompositions of facet 16
Polytope 428
Image of polytope 428 PALP id: 428
grdb id: 547516
Integer points: [ 1 0 0 -4 -1 -2 -3 0 -1 -2 0]
[ 0 1 1 -3 0 -1 -2 1 0 -1 0]
[ 0 0 2 -2 1 0 -1 1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
2 rank 1, B4 y*z2 + 2*y*z + x + y + 4*x-1*z + 4*x-1 + 6*x-2*y-1 + 2*x-2*y-1*z-1 + 4*x-3*y-2*z-1 + x-4*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 2 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Polytope 429
Image of polytope 429 PALP id: 429
grdb id: 547519
Integer points: [ 1 0 0 -1 0 0 0 0 0 0 0]
[ 0 1 1 -2 0 -1 1 0 1 0 1]
[ 0 0 4 -4 1 -2 3 0 2 -1 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 4 2 none
Image of facet 13 2 irreducible and admissible
Polytope 430
Image of polytope 430 PALP id: 430
grdb id: 547517
Integer points: [ 1 0 1 -5 -2 0 -3 -1 1 -2 0]
[ 0 1 0 -2 -1 0 -1 0 0 -1 0]
[ 0 0 2 -2 0 1 -1 0 1 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 33 1 none
Polytope 431
Image of polytope 431 PALP id: 431
grdb id: 547515
Integer points: [ 1 1 0 -6 -3 -2 -1 0 -1 0 1]
[ 0 2 0 -4 -2 -1 0 1 -1 0 1]
[ 0 0 1 -1 0 0 0 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 34 1 none
Image of facet 4 1 none
Polytope 432
Image of polytope 432 PALP id: 432
grdb id: 547285
Integer points: [ 1 0 0 -2 -2 -1 -1 -1 -2 -2 0]
[ 0 1 0 -2 1 -1 0 1 -1 0 0]
[ 0 0 1 1 -2 1 0 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
2 rank 1, B4 x + y + z + 2*x-1*y*z-1 + 4*x-1 + 2*x-1*y-1*z + x-2*y*z-2 + 3*x-2*z-1 + 3*x-2*y-1 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 9 1 irreducible and admissible
Polytope 433
Image of polytope 433 PALP id: 433
grdb id: 547298
Integer points: [ 1 0 -2 0 -2 -2 -1 -1 -1 0 0]
[ 0 1 -1 1 -1 -1 0 0 0 1 0]
[ 0 0 0 2 -2 -1 -1 0 1 1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
2 rank 1, B4 y*z2 + 2*y*z + x + y + 2*x-1*z + 4*x-1 + 2*x-1*z-1 + x-2*y-1 + 2*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Polytope 434
Image of polytope 434 PALP id: 434
grdb id: 547270
Integer points: [ 1 0 -2 0 -1 0 -1 -1 -1 0 0]
[ 0 1 -1 1 0 1 0 0 0 0 0]
[ 0 0 0 2 -2 1 -1 0 1 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 37 1 none
Polytope 435
Image of polytope 435 PALP id: 435
grdb id: 547294
Integer points: [ 1 0 0 -1 -2 -1 -1 -1 0 0 0]
[ 0 1 1 -2 -1 0 -1 0 1 0 -1]
[ 0 0 2 -2 0 0 -1 1 1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 4 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 436
Image of polytope 436 PALP id: 436
grdb id: 547297
Integer points: [ 1 0 -2 1 -3 0 -1 -2 1 0 -1]
[ 0 1 -1 0 0 0 0 0 0 0 0]
[ 0 0 0 2 -2 1 0 -1 1 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 38 1 none
Polytope 437
Image of polytope 437 PALP id: 437
grdb id: 547296
Integer points: [ 1 0 0 1 -3 0 -1 -2 1 0 -1]
[ 0 1 0 -2 2 -1 0 1 -1 0 1]
[ 0 0 1 -2 2 -1 0 1 -1 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 13 2 irreducible and admissible
Image of facet 6 1 none
Polytope 438
Image of polytope 438 PALP id: 438
grdb id: 547289
Integer points: [ 1 1 -3 0 -1 0 -1 -2 1 0 -1]
[ 0 2 -2 0 1 1 0 -1 1 0 -1]
[ 0 0 0 1 -1 0 0 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 39 1 none
Polytope 439
Image of polytope 439 PALP id: 439
grdb id: 547284
Integer points: [ 1 1 -3 0 0 0 -1 -2 1 0 -1]
[ 0 2 -2 0 2 1 0 -1 1 0 -1]
[ 0 0 0 1 -1 0 0 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 40 1 none
Image of facet 1 4 irreducible and admissible
Polytope 440
Image of polytope 440 PALP id: 440
grdb id: 547295
Integer points: [ 1 1 0 -2 -3 -2 -1 0 -1 0 1]
[ 0 2 0 -2 -2 -1 0 1 -1 0 1]
[ 0 0 1 -1 0 0 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 5 1 none
Image of facet 13 2 irreducible and admissible
Polytope 441
Image of polytope 441 PALP id: 441
grdb id: 547275
Integer points: [ 1 0 0 -4 -2 -3 -1 -2 -1 -1 0]
[ 0 1 0 -2 -2 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 1 0 1 0 0 0 0]
Degree: 56
Hilbert function: 1 + 31 t + 145 t2 + 399 t3 + 849 t4 + 1551 t5 + 2561 t6 + 3935 t7 + 5729 t8 + 7999 t9 + 10801 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 4 1 none
Image of facet 37 1 none
Polytope 442
Image of polytope 442 PALP id: 442
grdb id: 547266
Integer points: [ 1 1 -3 0 1 0 -1 -2 1 0 -1]
[ 0 2 -2 0 3 1 0 -1 1 0 -1]
[ 0 0 0 1 -1 0 0 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 41 1 none
Polytope 443
Image of polytope 443 PALP id: 443
grdb id: 547281
Integer points: [ 1 0 0 -1 -4 -2 -3 -1 -2 -1 0]
[ 0 1 0 -1 -1 0 -1 0 -1 0 0]
[ 0 0 1 -1 2 1 1 0 0 1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 4 1 none
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 14 1 none
Polytope 444
Image of polytope 444 PALP id: 444
grdb id: 547292
Integer points: [ 1 1 -3 0 -4 -2 -1 0 -1 0 1]
[ 0 2 -2 0 -3 -1 0 1 -1 0 1]
[ 0 0 0 1 -1 0 0 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 13 2 irreducible and admissible
Image of facet 6 1 none
Polytope 445
Image of polytope 445 PALP id: 445
grdb id: 547283
Integer points: [ 1 0 0 -5 -6 -4 -3 -2 -1 -2 0]
[ 0 1 0 -2 -3 -2 -1 -1 0 -1 0]
[ 0 0 1 -2 -2 -1 -1 0 0 -1 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 42 1 none
Image of facet 9 1 irreducible and admissible
Polytope 446
Image of polytope 446 PALP id: 446
grdb id: 547191
Integer points: [ 1 -1 0 1 1 1 1 1 0 0 0]
[ 0 0 1 0 -2 -1 0 -1 0 -1 0]
[ 0 0 0 2 -2 -1 1 0 0 -1 1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
68 ? x*z2 + 2*x*z + x + y + 2*z + 2*x*y-1 + 2*x*y-1*z-1 + x-1 + 2*y-1*z-1 + x*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 4 irreducible and admissible
Polytope 447
Image of polytope 447 PALP id: 447
grdb id: 547199
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 2 -2 -1 0 1 -1 0 1]
[ 0 0 1 2 -2 -1 0 1 -1 0 1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
135 ? x-1*y2*z2 + 2*y*z + x + y + z + 4*x-1*y*z + 6*x-1 + 2*y-1*z-1 + 4*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 13 2 irreducible and admissible
Polytope 448
Image of polytope 448 PALP id: 448
grdb id: 547194
Integer points: [ 1 0 0 0 -2 -1 -1 0 -1 0 0]
[ 0 1 -1 1 -1 0 -1 0 0 1 0]
[ 0 0 0 2 -2 0 -1 1 -1 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
60 rank 2, number 18 y*z2 + 2*y*z + x + y + 2*z + y-1 + 2*x-1 + 2*x-1*z-1 + 2*x-1*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 4 irreducible and admissible
Polytope 449
Image of polytope 449 PALP id: 449
grdb id: 547192
Integer points: [ 1 1 -2 0 0 0 -1 0 1 -1 0]
[ 0 2 -1 0 -2 -1 -1 0 1 0 1]
[ 0 0 0 1 -1 0 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 4 1 none
Image of facet 9 2 irreducible and admissible
Polytope 450
Image of polytope 450 PALP id: 450
grdb id: 547203
Integer points: [ 1 1 -1 0 -2 -1 0 -1 0 1 0]
[ 0 2 -2 0 0 0 1 -1 0 1 -1]
[ 0 0 0 1 -1 0 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 4 2 none
Polytope 451
Image of polytope 451 PALP id: 451
grdb id: 547197
Integer points: [ 1 0 -1 1 -3 0 -1 -2 1 0 -1]
[ 0 1 -1 0 0 0 0 0 0 0 0]
[ 0 0 0 2 -2 1 0 -1 1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
157 ? x*z2 + 2*x*z + x + y + 4*z + 6*x-1 + 2*x-1*z-1 + x-1*y-1 + 4*x-2*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 13 2 irreducible and admissible
Polytope 452
Image of polytope 452 PALP id: 452
grdb id: 547200
Integer points: [ 1 0 0 -3 1 0 -1 -2 1 0 -1]
[ 0 1 0 -2 2 1 0 -1 1 0 -1]
[ 0 0 1 -2 2 1 0 -1 1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
156 ? x*y2*z2 + 2*x*y*z + 4*y*z + x + y + z + 6*x-1 + 2*x-1*y-1*z-1 + 4*x-2*y-1*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 13 2 irreducible and admissible
Polytope 453
Image of polytope 453 PALP id: 453
grdb id: 547195
Integer points: [ 1 0 0 1 -3 0 -1 -2 1 0 -1]
[ 0 1 -1 0 0 0 0 0 0 0 0]
[ 0 0 0 2 -2 1 0 -1 1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
71 ? x*z2 + 2*x*z + x + y + 4*z + y-1 + 6*x-1 + 2*x-1*z-1 + 4*x-2*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 13 2 irreducible and admissible
Polytope 454
Image of polytope 454 PALP id: 454
grdb id: 547184
Integer points: [ 1 0 0 2 -3 -2 -1 0 1 -1 0]
[ 0 1 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 0 1 -1 -1 -1 -1 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 2 1 none
Image of facet 43 2 irreducible and admissible
Polytope 455
Image of polytope 455 PALP id: 455
grdb id: 547196
Integer points: [ 1 0 1 1 -3 0 -1 -2 1 0 -1]
[ 0 1 -1 0 0 0 0 0 0 0 0]
[ 0 0 0 2 -2 1 0 -1 1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
101 ? x*z2 + 2*x*z + x + y + 4*z + x*y-1 + 6*x-1 + 2*x-1*z-1 + 4*x-2*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 13 2 irreducible and admissible
Polytope 456
Image of polytope 456 PALP id: 456
grdb id: 547202
Integer points: [ 1 1 -3 0 1 0 -1 -2 1 0 -1]
[ 0 2 -2 0 2 1 0 -1 1 0 -1]
[ 0 0 0 1 -1 0 0 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
99 ? x*y2 + x*y2*z-1 + 2*x*y + x + 4*y + z + 6*x-1 + 2*x-1*y-1 + 4*x-2*y-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 13 2 irreducible and admissible
Polytope 457
Image of polytope 457 PALP id: 457
grdb id: 547176
Integer points: [ 1 0 1 0 -4 -2 -1 0 -1 0 1]
[ 0 1 -2 0 2 1 0 -1 1 0 -1]
[ 0 0 0 1 -1 0 0 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 4 1 none
Image of facet 12 1 none
Polytope 458
Image of polytope 458 PALP id: 458
grdb id: 517603
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 1 0 0 -2 0 -1 1 0 -1]
[ 0 0 2 1 -1 -2 0 -1 1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 4 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 459
Image of polytope 459 PALP id: 459
grdb id: 517604
Integer points: [ 1 0 0 -1 -1 -3 -2 -2 -1 -1 0]
[ 0 1 0 -1 1 -1 0 -1 0 0 0]
[ 0 0 1 -1 1 1 1 0 0 1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 4 1 none
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 460
Image of polytope 460 PALP id: 460
grdb id: 543561
Integer points: [ 1 0 0 -2 -2 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 -2 -2 -1 -1 0 -1 0]
[ 0 0 1 0 -1 -2 0 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 8 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 461
Image of polytope 461 PALP id: 461
grdb id: 543560
Integer points: [ 1 0 0 -2 -1 -2 -2 -1 -1 -1 0]
[ 0 1 0 -2 1 0 -1 0 0 -1 0]
[ 0 0 1 -1 1 1 0 0 1 0 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 462
Image of polytope 462 PALP id: 462
grdb id: 543573
Integer points: [ 1 0 0 -1 0 -1 -1 -1 0 0 0]
[ 0 1 0 1 -2 -2 -1 0 -1 -1 0]
[ 0 0 1 1 -1 -2 -1 0 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
25 ? x + y + z + x-1*y*z + 2*y-1 + 3*x-1 + 2*y-1*z-1 + y-2*z-1 + 3*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 9 1 irreducible and admissible
Polytope 463
Image of polytope 463 PALP id: 463
grdb id: 543553
Integer points: [ 1 0 0 1 -2 0 0 -1 -1 1 0]
[ 0 1 0 -2 0 -2 -1 -1 0 -1 0]
[ 0 0 1 0 -1 -1 0 -1 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + 2*x*y-1 + x*y-2 + 2*y-1 + 2*x-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 464
Image of polytope 464 PALP id: 464
grdb id: 543516
Integer points: [ 1 0 -2 0 -2 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 -2 2 1 0 -1 1 0]
[ 0 0 0 1 1 -2 -1 0 1 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 45 1 none
Polytope 465
Image of polytope 465 PALP id: 465
grdb id: 543543
Integer points: [ 1 0 0 -2 -2 -1 -2 -1 -1 0 0]
[ 0 1 0 0 -2 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 1 2 0 1 0 1 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 46 1 none
Polytope 466
Image of polytope 466 PALP id: 466
grdb id: 543539
Integer points: [ 1 0 0 -3 -3 -2 -2 -1 -1 -1 0]
[ 0 1 0 -1 -2 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 0 1 0 1 0 0 0]
Degree: 50
Hilbert function: 1 + 28 t + 130 t2 + 357 t3 + 759 t4 + 1386 t5 + 2288 t6 + 3515 t7 + 5117 t8 + 7144 t9 + 9646 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
73 ? x + y + z + 2*x-1 + 2*x-1*y-1*z + 2*x-1*y-1 + x-2*y-1 + x-2*y-2*z + x-3*y-1*z-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 47 1 Lattice Minkowski decompositions of facet 47
Polytope 467
Image of polytope 467 PALP id: 467
grdb id: 543567
Integer points: [ 1 0 0 -2 -3 -2 -2 -1 -1 -1 0]
[ 0 1 0 -1 -2 -2 -1 0 -1 -1 0]
[ 0 0 1 -1 0 1 0 0 1 0 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 6 1 none
Image of facet 9 1 irreducible and admissible
Polytope 468
Image of polytope 468 PALP id: 468
grdb id: 543552
Integer points: [ 1 0 0 -2 -3 -2 -1 -2 -1 -1 0]
[ 0 1 0 0 -2 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 0 1 1 0 0 0 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
41 ? x + y + z + x-1 + 2*x-1*y-1*z + 2*x-1*y-1 + x-2*z-1 + x-2*y-1 + x-2*y-2*z + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 48 1 Lattice Minkowski decompositions of facet 48
Polytope 469
Image of polytope 469 PALP id: 469
grdb id: 543566
Integer points: [ 1 0 0 -2 -2 -3 -1 -1 -2 0 -1]
[ 0 1 0 0 -2 -2 0 -1 -1 0 -1]
[ 0 0 1 -1 -1 -2 0 0 -1 0 -1]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
37 rank 3, number 17 x + y + z + 2*x-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 470
Image of polytope 470 PALP id: 470
grdb id: 543529
Integer points: [ 1 0 0 -1 -3 -3 -2 -2 -1 -1 0]
[ 0 1 0 1 -1 -2 0 -1 0 -1 0]
[ 0 0 1 -1 -1 0 -1 0 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
57 ? x + y + z + x-1*y*z-1 + x-1 + 2*x-1*y-1 + 2*x-2*z-1 + 2*x-2*y-1 + x-3*y-1*z-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 47 1 Lattice Minkowski decompositions of facet 47
Polytope 471
Image of polytope 471 PALP id: 471
grdb id: 543572
Integer points: [ 1 0 0 0 -2 -3 -2 -1 -1 -1 0]
[ 0 1 -1 0 1 0 0 0 1 0 0]
[ 0 0 0 1 -2 -2 -1 0 -1 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 5 1 none
Image of facet 9 1 irreducible and admissible
Polytope 472
Image of polytope 472 PALP id: 472
grdb id: 543525
Integer points: [ 1 0 -1 0 -2 -3 -1 -2 -1 -1 0]
[ 0 1 -1 0 2 2 1 1 0 1 0]
[ 0 0 0 1 -1 -2 0 -1 0 -1 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 27 1 none
Polytope 473
Image of polytope 473 PALP id: 473
grdb id: 543519
Integer points: [ 1 0 0 -4 -1 -2 -3 -2 -1 -1 0]
[ 0 1 0 -3 0 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 1 1 0 0 0 0 0]
Degree: 58
Hilbert function: 1 + 32 t + 150 t2 + 413 t3 + 879 t4 + 1606 t5 + 2652 t6 + 4075 t7 + 5933 t8 + 8284 t9 + 11186 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 8 1 none
Image of facet 26 1 none
Polytope 474
Image of polytope 474 PALP id: 474
grdb id: 543569
Integer points: [ 1 0 0 -1 -1 1 0 -1 1 0 1]
[ 0 1 0 0 2 -3 -1 1 -2 0 -1]
[ 0 0 1 -1 -1 3 1 -1 2 0 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 8 1 none
Image of facet 9 1 irreducible and admissible
Polytope 475
Image of polytope 475 PALP id: 475
grdb id: 543557
Integer points: [ 1 0 0 0 -2 -4 -2 -1 -3 -1 0]
[ 0 1 -1 0 0 2 1 0 1 1 0]
[ 0 0 0 1 -1 -1 0 0 -1 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 4 1 none
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 476
Image of polytope 476 PALP id: 476
grdb id: 543492
Integer points: [ 1 0 0 -4 -5 -1 -3 -2 -1 -1 0]
[ 0 1 0 -2 -3 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 -1 1 0 0 0 0 0]
Degree: 56
Hilbert function: 1 + 31 t + 145 t2 + 399 t3 + 849 t4 + 1551 t5 + 2561 t6 + 3935 t7 + 5729 t8 + 7999 t9 + 10801 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 4 1 none
Image of facet 45 1 none
Polytope 477
Image of polytope 477 PALP id: 477
grdb id: 542868
Integer points: [ 1 0 -1 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 1 0 -1 -1 0 -1 0 -1 0]
[ 0 0 0 1 -1 2 1 1 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Polytope 478
Image of polytope 478 PALP id: 478
grdb id: 543399
Integer points: [ 1 0 -2 1 0 -1 -1 0 -1 0 1]
[ 0 1 1 -2 0 -1 0 -1 1 0 -1]
[ 0 0 0 0 1 -1 0 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 18 1 none
Polytope 479
Image of polytope 479 PALP id: 479
grdb id: 543390
Integer points: [ 1 0 -2 1 0 0 0 -1 1 0 -1]
[ 0 1 1 -2 0 -2 -1 0 -1 0 1]
[ 0 0 0 0 1 -1 0 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 19 1 none
Polytope 480
Image of polytope 480 PALP id: 480
grdb id: 543000
Integer points: [ 1 0 -1 0 -2 -2 -2 -1 -2 -1 0]
[ 0 1 1 0 1 -2 0 0 -1 -1 0]
[ 0 0 0 1 -1 -1 -1 0 -1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
47 ? x + y + z + x-1*y + 3*x-1 + x-2*y*z-1 + 2*x-1*y-1 + 3*x-2*z-1 + 3*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 481
Image of polytope 481 PALP id: 481
grdb id: 542986
Integer points: [ 1 0 -1 0 -2 0 -1 -1 -1 0 0]
[ 0 1 -2 0 1 1 1 0 -1 0 -1]
[ 0 0 0 1 -1 1 0 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 26 1 none
Polytope 482
Image of polytope 482 PALP id: 482
grdb id: 543365
Integer points: [ 1 0 -1 0 0 -2 -1 -1 0 -1 0]
[ 0 1 1 0 -2 -2 -1 0 -1 -2 0]
[ 0 0 0 1 -1 -1 0 0 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 4 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 483
Image of polytope 483 PALP id: 483
grdb id: 543309
Integer points: [ 1 0 0 -2 -1 0 -1 0 -1 0 0]
[ 0 1 0 0 -2 -2 0 -1 -1 0 -1]
[ 0 0 1 -1 0 1 0 1 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
43 ? x + y + z + 2*y-1*z + 2*y-1 + 2*x-1 + y-2*z + 2*x-1*y-1 + x-2*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 484
Image of polytope 484 PALP id: 484
grdb id: 543360
Integer points: [ 1 0 0 -1 -2 -2 -2 -1 -1 -1 0]
[ 0 1 0 -1 -2 0 -1 -1 0 0 0]
[ 0 0 1 -1 -1 1 0 0 1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 8 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 485
Image of polytope 485 PALP id: 485
grdb id: 543364
Integer points: [ 1 0 0 0 -2 -2 -1 -1 -2 0 -1]
[ 0 1 -1 0 -2 0 0 -1 -1 0 0]
[ 0 0 0 1 -1 1 1 0 0 0 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 4 1 none
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 486
Image of polytope 486 PALP id: 486
grdb id: 543405
Integer points: [ 1 0 1 -2 0 1 -1 0 1 -1 0]
[ 0 1 -2 1 0 1 1 0 -1 0 -1]
[ 0 0 0 0 1 -1 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
24 ? x*y*z-1 + x + y + z + 2*x*y-1 + 2*x-1*y + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 2 irreducible and admissible
Polytope 487
Image of polytope 487 PALP id: 487
grdb id: 542864
Integer points: [ 1 0 -1 0 -2 -2 -1 -2 -1 -2 0]
[ 0 1 -1 0 -1 2 1 1 0 0 0]
[ 0 0 0 1 -1 -1 0 -1 0 -1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
98 rank 3, number 21 x + y + z + 2*x-1*y + x-2*y2*z-1 + 3*x-1 + 3*x-2*y*z-1 + x-1*y-1 + 3*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 488
Image of polytope 488 PALP id: 488
grdb id: 543412
Integer points: [ 1 0 -1 0 0 -1 -1 0 0 0 0]
[ 0 1 0 -1 1 -2 -1 0 -1 0 1]
[ 0 0 0 0 2 -2 -1 1 -1 0 1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
3 ? y*z2 + 2*y*z + x + y + 2*z + y-1 + x-1 + 2*y-1*z-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 6 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 489
Image of polytope 489 PALP id: 489
grdb id: 543400
Integer points: [ 1 0 0 -1 0 -1 -1 -1 0 0 0]
[ 0 1 0 1 2 -2 -1 0 -1 0 1]
[ 0 0 1 1 1 -2 -1 0 -1 0 1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
134 ? y2*z + 2*y*z + x + y + z + x-1*y*z + 3*x-1 + 2*y-1*z-1 + 3*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Polytope 490
Image of polytope 490 PALP id: 490
grdb id: 543326
Integer points: [ 1 0 0 -1 2 -2 1 0 -1 0 -1]
[ 0 1 0 0 -1 -1 -1 -1 -1 0 0]
[ 0 0 1 1 -1 -1 -1 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 2 1 none
Image of facet 13 1 irreducible and admissible
Polytope 491
Image of polytope 491 PALP id: 491
grdb id: 543392
Integer points: [ 1 0 0 1 -1 -2 -1 0 1 -1 0]
[ 0 1 0 -2 2 1 1 0 -1 0 -1]
[ 0 0 1 0 -1 0 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 6 1 none
Image of facet 9 2 irreducible and admissible
Polytope 492
Image of polytope 492 PALP id: 492
grdb id: 543393
Integer points: [ 1 0 0 2 -2 -1 0 -1 1 -1 0]
[ 0 1 0 -1 0 -1 -1 0 -1 0 0]
[ 0 0 1 -1 1 -1 -1 1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 2 1 none
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 9 1 irreducible and admissible
Polytope 493
Image of polytope 493 PALP id: 493
grdb id: 543404
Integer points: [ 1 0 1 -2 0 -2 -1 0 -1 0 1]
[ 0 1 -2 1 0 2 0 -1 1 0 -1]
[ 0 0 0 0 1 -1 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 5 1 none
Image of facet 9 2 irreducible and admissible
Polytope 494
Image of polytope 494 PALP id: 494
grdb id: 543411
Integer points: [ 1 1 -1 -1 0 -2 -1 0 0 0 1]
[ 0 2 0 -2 0 -2 -1 1 0 -1 1]
[ 0 0 0 0 1 -1 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 6 irreducible and admissible
Image of facet 5 1 none
Polytope 495
Image of polytope 495 PALP id: 495
grdb id: 543396
Integer points: [ 1 -1 0 0 -3 -3 -2 -1 -2 0 -1]
[ 0 0 1 0 -2 -3 -1 -1 -2 0 -1]
[ 0 0 0 1 -2 -2 -1 0 -1 0 -1]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
79 ? x + y + z + x-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*y-1*z-1 + 3*x-2*y-2*z-1 + x-3*y-2*z-2 + x-3*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 9 1 irreducible and admissible
Polytope 496
Image of polytope 496 PALP id: 496
grdb id: 543104
Integer points: [ 1 0 -2 1 0 1 0 -1 1 0 -1]
[ 0 1 1 -2 0 -3 -1 0 -1 0 1]
[ 0 0 0 0 1 -1 0 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 21 1 none
Polytope 497
Image of polytope 497 PALP id: 497
grdb id: 543050
Integer points: [ 1 0 -1 0 -2 0 -1 -1 -1 0 0]
[ 0 1 1 0 -3 -1 -2 -1 0 -1 0]
[ 0 0 0 1 -1 1 0 0 0 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 26 1 none
Image of facet 4 1 none
Polytope 498
Image of polytope 498 PALP id: 498
grdb id: 543408
Integer points: [ 1 0 0 -1 -3 -3 -2 -1 -2 -1 0]
[ 0 1 0 -1 0 -1 0 0 -1 0 0]
[ 0 0 1 0 -2 -2 -1 0 -1 -1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
104 ? x + y + z + 3*x-1 + 2*x-1*z-1 + x-1*y-1 + 3*x-2*z-1 + 2*x-2*y-1*z-1 + x-3*z-2 + x-3*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 9 1 irreducible and admissible
Polytope 499
Image of polytope 499 PALP id: 499
grdb id: 543409
Integer points: [ 1 0 0 0 -2 -3 -2 -1 -1 -1 0]
[ 0 1 0 -1 -1 0 0 0 -1 0 0]
[ 0 0 1 1 -1 -2 -1 0 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
103 ? x + y + z + y-1*z + 3*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + 3*x-2*z-1 + x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 9 1 irreducible and admissible
Polytope 500
Image of polytope 500 PALP id: 500
grdb id: 543323
Integer points: [ 1 0 1 -2 0 -3 -1 0 -1 0 1]
[ 0 1 -2 1 0 2 0 -1 1 0 -1]
[ 0 0 0 0 1 -1 0 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 6 1 none
Image of facet 9 2 irreducible and admissible
Polytope 501
Image of polytope 501 PALP id: 501
grdb id: 543398
Integer points: [ 1 1 -1 -1 0 -2 -1 0 0 0 1]
[ 0 2 0 -2 0 -3 -1 -1 0 1 1]
[ 0 0 0 0 1 -1 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 6 irreducible and admissible
Image of facet 6 1 none
Polytope 502
Image of polytope 502 PALP id: 502
grdb id: 543291
Integer points: [ 1 0 -2 0 -2 -4 -3 -1 -1 -2 0]
[ 0 1 -1 0 -2 -3 -2 -1 0 -1 0]
[ 0 0 0 1 -1 -2 -1 0 0 -1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
42 rank 2, number 29 x + y + z + 2*x-1 + 2*x-1*y-1 + x-2*y-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1 + 2*x-3*y-2*z-1 + x-4*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 503
Image of polytope 503 PALP id: 503
grdb id: 542890
Integer points: [ 1 0 -1 0 -1 -3 -1 -2 -1 -2 0]
[ 0 1 -1 0 2 3 1 2 0 1 0]
[ 0 0 0 1 -1 -2 0 -1 0 -1 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 14 1 none
Polytope 504
Image of polytope 504 PALP id: 504
grdb id: 542501
Integer points: [ 1 0 -2 1 0 1 0 -1 1 0 -1]
[ 0 1 1 -2 0 -2 -1 0 -1 0 1]
[ 0 0 0 0 1 -1 0 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
162 ? x + y + z + 2*x*y-1 + 2*x-1*y + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + x*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Polytope 505
Image of polytope 505 PALP id: 505
grdb id: 542498
Integer points: [ 1 0 0 0 -2 1 -1 0 1 -1 0]
[ 0 1 0 0 1 -2 1 0 -1 0 -1]
[ 0 0 1 -1 0 0 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
71 ? x + y + z + 2*x*y-1 + 2*x-1*y + z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Polytope 506
Image of polytope 506 PALP id: 506
grdb id: 542503
Integer points: [ 1 0 0 0 1 -2 0 -1 1 0 -1]
[ 0 1 0 -1 -2 1 -1 0 -1 0 1]
[ 0 0 1 -1 0 0 0 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
124 ? x + y + z + 2*x*y-1 + 2*x-1*y + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Polytope 507
Image of polytope 507 PALP id: 507
grdb id: 542502
Integer points: [ 1 0 0 1 -2 1 -1 0 -1 0 1]
[ 0 1 0 -1 1 -2 0 -1 1 0 -1]
[ 0 0 1 -1 0 0 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
135 ? x + y + z + 2*x*y-1 + 2*x-1*y + x*y-1*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Polytope 508
Image of polytope 508 PALP id: 508
grdb id: 542497
Integer points: [ 1 0 0 1 -2 1 -1 0 1 -1 0]
[ 0 1 0 0 1 -2 1 0 -1 0 -1]
[ 0 0 1 -1 0 0 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
127 ? x + y + z + x*z-1 + 2*x*y-1 + 2*x-1*y + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Polytope 509
Image of polytope 509 PALP id: 509
grdb id: 542505
Integer points: [ 1 0 0 0 0 -1 0 0 0 0 0]
[ 0 1 1 -1 -1 0 -1 0 0 0 1]
[ 0 0 2 -2 0 0 -1 -1 0 1 1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
71 ? y*z2 + 2*y*z + x + y + 2*z + 2*z-1 + y-1 + x-1 + 2*y-1*z-1 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 8 irreducible and admissible
Polytope 510
Image of polytope 510 PALP id: 510
grdb id: 542507
Integer points: [ 1 1 -1 -1 0 1 1 0 0 0 -1]
[ 0 2 -2 0 0 0 1 -1 0 1 -1]
[ 0 0 0 0 1 -1 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
136 ? x*y2 + 2*x*y + x + 2*y + z + x*z-1 + 2*y-1 + x-1 + 2*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 8 irreducible and admissible
Polytope 511
Image of polytope 511 PALP id: 511
grdb id: 542506
Integer points: [ 1 1 -1 -1 0 1 1 0 0 0 -1]
[ 0 2 -2 0 0 1 1 1 0 -1 -1]
[ 0 0 0 0 1 -1 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
135 ? x*y2 + 2*x*y + x*y*z-1 + x + 2*y + z + 2*y-1 + x-1 + 2*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 8 irreducible and admissible
Polytope 512
Image of polytope 512 PALP id: 512
grdb id: 516974
Integer points: [ 1 0 -2 0 0 -1 -1 -1 0 -1 0]
[ 0 1 1 0 -2 1 -1 0 -1 1 0]
[ 0 0 0 1 -1 1 -1 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
32 ? x + y + z + x-1*y*z + 2*x-1*y + 2*y-1 + 3*x-1 + x-2*y + y-2*z-1 + x-1*y-1*z-1
8 ? x + y + z + x-1*y*z + 2*x-1*y + 2*y-1 + 2*x-1 + x-2*y + y-2*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 513
Image of polytope 513 PALP id: 513
grdb id: 516973
Integer points: [ 1 0 0 0 -2 -3 -1 -2 -1 -1 0]
[ 0 1 -1 0 0 1 1 1 0 1 0]
[ 0 0 0 1 -1 -1 1 0 0 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 4 1 none
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 514
Image of polytope 514 PALP id: 514
grdb id: 516961
Integer points: [ 1 0 0 -1 2 -1 -1 0 1 -1 0]
[ 0 1 0 0 -1 1 -1 -1 -1 0 0]
[ 0 0 1 1 -1 0 -1 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 2 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Polytope 515
Image of polytope 515 PALP id: 515
grdb id: 516967
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 -1 2 1 0 1 0]
[ 0 0 1 -1 0 -1 2 1 0 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
25 ? x-1*y2*z2 + 2*y*z + x + y + z + 3*x-1*y*z + z-1 + y-1 + 3*x-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Polytope 516
Image of polytope 516 PALP id: 516
grdb id: 516920
Integer points: [ 1 0 -1 0 0 -1 -1 -1 0 -1 0]
[ 0 1 1 0 -2 0 -2 -1 -1 0 0]
[ 0 0 0 1 -1 1 -1 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 4 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 517
Image of polytope 517 PALP id: 517
grdb id: 516923
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 1 -2 0 -1 0 -1]
[ 0 0 1 -1 0 0 -2 0 -1 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 8 1 none
Polytope 518
Image of polytope 518 PALP id: 518
grdb id: 516960
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 0 1 -2 0 -1 0 -1]
[ 0 0 1 1 -1 0 -2 0 -1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
80 ? x + y + z + x-1*y*z + x-1*y + 3*x-1 + 2*y-1*z-1 + x-1*z-1 + 3*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 519
Image of polytope 519 PALP id: 519
grdb id: 516943
Integer points: [ 1 0 0 -1 0 -2 -1 -1 0 0 -1]
[ 0 1 -1 0 0 -1 -2 -1 -1 0 0]
[ 0 0 0 0 1 -2 -2 -1 -1 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
28 rank 2, number 25 x + y + z + y-1 + x-1 + 2*y-1*z-1 + 2*x-1*z-1 + x-1*y-1*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 520
Image of polytope 520 PALP id: 520
grdb id: 516939
Integer points: [ 1 0 0 -1 0 -1 -2 -1 -1 0 0]
[ 0 1 0 0 1 -2 -1 0 -1 0 -1]
[ 0 0 1 -1 1 0 -1 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 8 1 none
Polytope 521
Image of polytope 521 PALP id: 521
grdb id: 516902
Integer points: [ 1 0 0 0 -1 -2 -2 -1 -1 -1 0]
[ 0 1 0 -1 1 0 -1 0 -1 0 0]
[ 0 0 1 -1 0 1 1 0 0 1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 8 1 none
Polytope 522
Image of polytope 522 PALP id: 522
grdb id: 516968
Integer points: [ 1 0 0 0 -1 0 -1 0 0 -1 0]
[ 0 1 0 -1 -1 1 1 1 0 0 0]
[ 0 0 1 0 1 -2 -1 -1 0 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
25 ? x + y + z + 2*y*z-1 + y*z-2 + 2*z-1 + x-1*y*z-1 + y-1 + 2*x-1 + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 523
Image of polytope 523 PALP id: 523
grdb id: 516969
Integer points: [ 1 0 0 0 0 -2 -2 -1 -1 -1 0]
[ 0 1 0 -1 0 0 -1 0 -1 0 0]
[ 0 0 1 0 -1 -1 -2 0 -1 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 5 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 524
Image of polytope 524 PALP id: 524
grdb id: 516952
Integer points: [ 1 0 0 0 1 -2 -1 -1 0 0 -1]
[ 0 1 -1 0 -1 1 -1 0 -1 0 1]
[ 0 0 0 1 -1 0 -1 0 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 6 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 525
Image of polytope 525 PALP id: 525
grdb id: 516955
Integer points: [ 1 0 0 0 1 -2 -1 -1 0 0 -1]
[ 0 1 -1 0 0 -1 -2 -1 -1 0 0]
[ 0 0 0 1 -1 0 -1 0 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 6 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 526
Image of polytope 526 PALP id: 526
grdb id: 516949
Integer points: [ 1 -1 0 0 -1 0 -1 -1 0 0 0]
[ 0 0 1 0 -1 2 -2 -1 1 0 -1]
[ 0 0 0 1 0 1 -2 -1 1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? y2*z + 2*y*z + x + y + z + x-1 + 2*y-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 527
Image of polytope 527 PALP id: 527
grdb id: 516922
Integer points: [ 1 0 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 1 2 2 0 1 0 1]
[ 0 0 0 1 0 -1 -2 0 -1 0 -1]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 528
Image of polytope 528 PALP id: 528
grdb id: 516954
Integer points: [ 1 0 0 2 -1 0 -2 -1 1 -1 0]
[ 0 1 0 -1 1 -1 0 0 -1 0 0]
[ 0 0 1 -1 0 -1 1 0 -1 1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 2 1 none
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 529
Image of polytope 529 PALP id: 529
grdb id: 516853
Integer points: [ 1 0 -3 0 -3 -1 -2 -2 -1 -1 0]
[ 0 1 -2 0 -2 0 -1 -1 0 -1 0]
[ 0 0 0 1 -1 1 1 0 0 0 0]
Degree: 52
Hilbert function: 1 + 29 t + 135 t2 + 371 t3 + 789 t4 + 1441 t5 + 2379 t6 + 3655 t7 + 5321 t8 + 7429 t9 + 10031 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 29 1 none
Polytope 530
Image of polytope 530 PALP id: 530
grdb id: 516888
Integer points: [ 1 0 -1 0 -1 -2 -3 -2 -1 -1 0]
[ 0 1 -1 0 1 0 -2 -1 0 -1 0]
[ 0 0 0 1 0 -1 -2 -1 0 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 31 1 none
Polytope 531
Image of polytope 531 PALP id: 531
grdb id: 516938
Integer points: [ 1 0 0 -2 -3 -3 -1 -2 -1 -1 0]
[ 0 1 0 -1 -2 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 0 -1 1 0 0 0 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 6 1 none
Polytope 532
Image of polytope 532 PALP id: 532
grdb id: 516898
Integer points: [ 1 0 0 -2 -3 -1 -3 -2 -1 -1 0]
[ 0 1 0 0 -1 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 -1 1 0 0 0 0 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
41 ? x + y + z + x-1 + x-1*y-1*z + 2*x-1*y-1 + x-2*z-1 + x-2*y-1 + x-3*y-1*z-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 50 1 Lattice Minkowski decompositions of facet 50
Polytope 533
Image of polytope 533 PALP id: 533
grdb id: 516916
Integer points: [ 1 0 0 -2 -3 -1 -2 -2 -1 -1 0]
[ 0 1 0 -2 -2 0 -1 -1 0 -1 0]
[ 0 0 1 -1 0 1 1 0 0 0 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
133 ? x + y + z + x-1*z + 3*x-1 + x-1*y-1 + x-2*y-1*z + 3*x-2*y-1 + x-2*y-2*z-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Polytope 534
Image of polytope 534 PALP id: 534
grdb id: 516901
Integer points: [ 1 0 0 -2 -1 -3 -2 -2 -1 -1 0]
[ 0 1 0 -1 0 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 1 0 1 0 0 0 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 28 1 none
Polytope 535
Image of polytope 535 PALP id: 535
grdb id: 516881
Integer points: [ 1 0 0 -1 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 1 0 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 -1 1 0 0 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
57 ? x + y + z + x-1*y*z-1 + x-1 + x-1*y-1*z + 2*x-1*y-1 + x-2*z-1 + 2*x-2*y-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 51 1 Lattice Minkowski decompositions of facet 51
Polytope 536
Image of polytope 536 PALP id: 536
grdb id: 516925
Integer points: [ 1 0 0 -1 -1 -2 -3 -1 -2 0 -1]
[ 0 1 0 -1 1 1 0 0 0 0 0]
[ 0 0 1 0 0 -1 -2 0 -1 0 -1]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 28 1 none
Polytope 537
Image of polytope 537 PALP id: 537
grdb id: 516940
Integer points: [ 1 0 0 0 -2 -1 -3 -2 -1 -1 0]
[ 0 1 -1 0 -1 0 -2 -1 -1 0 0]
[ 0 0 0 1 -1 1 -1 0 0 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 8 2 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 538
Image of polytope 538 PALP id: 538
grdb id: 516830
Integer points: [ 1 0 0 0 -2 -1 -3 -1 -2 0 -1]
[ 0 1 0 1 -1 0 -2 0 -1 0 -1]
[ 0 0 1 -1 1 1 0 0 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 29 1 none
Polytope 539
Image of polytope 539 PALP id: 539
grdb id: 516907
Integer points: [ 1 0 0 0 -1 -2 -3 -1 -2 -1 0]
[ 0 1 -1 0 -1 1 1 0 0 1 0]
[ 0 0 0 1 -1 0 -1 0 -1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
76 ? x + y + z + 2*x-1*y + y-1 + 2*x-1 + x-2*y + x-1*y-1*z-1 + 2*x-2*z-1 + x-3*y*z-1
164 ? x + y + z + 2*x-1*y + y-1 + 3*x-1 + x-2*y + x-1*y-1*z-1 + 2*x-2*z-1 + x-3*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 540
Image of polytope 540 PALP id: 540
grdb id: 516945
Integer points: [ 1 0 0 0 -1 -2 -3 -1 -1 -2 0]
[ 0 1 -1 0 0 -1 -2 -1 0 -1 0]
[ 0 0 0 1 -1 0 -1 0 0 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 6 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 541
Image of polytope 541 PALP id: 541
grdb id: 516953
Integer points: [ 1 0 0 0 -1 -2 -3 -2 -1 -1 0]
[ 0 1 0 -1 0 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 1 1 0 0 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
47 ? x + y + z + x-1*z + 3*x-1 + y-1*z-1 + x-1*y-1 + x-2*y-1*z + 3*x-2*y-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Polytope 542
Image of polytope 542 PALP id: 542
grdb id: 516958
Integer points: [ 1 0 0 0 -1 -2 -3 -2 -1 -1 0]
[ 0 1 0 -1 1 1 1 1 1 0 0]
[ 0 0 1 -1 1 1 0 0 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 6 1 none
Polytope 543
Image of polytope 543 PALP id: 543
grdb id: 516964
Integer points: [ 1 0 0 0 -1 -1 -3 -2 -1 -1 0]
[ 0 1 -1 0 -1 1 0 0 0 0 0]
[ 0 0 0 1 -1 -1 -2 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 5 1 none
Polytope 544
Image of polytope 544 PALP id: 544
grdb id: 516865
Integer points: [ 1 0 0 -3 -3 -4 -1 -2 -1 -1 0]
[ 0 1 0 -1 -2 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 0 -1 1 0 0 0 0]
Degree: 50
Hilbert function: 1 + 28 t + 130 t2 + 357 t3 + 759 t4 + 1386 t5 + 2288 t6 + 3515 t7 + 5117 t8 + 7144 t9 + 9646 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
73 ? x + y + z + 2*x-1 + x-1*y-1*z + 2*x-1*y-1 + x-2*y-1 + x-3*y-1*z-1 + x-3*y-2 + x-4*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 51 1 Lattice Minkowski decompositions of facet 51
Polytope 545
Image of polytope 545 PALP id: 545
grdb id: 516963
Integer points: [ 1 -1 0 0 0 2 3 1 2 0 1]
[ 0 0 1 0 -1 -1 -3 -1 -2 0 -1]
[ 0 0 0 1 -1 -1 -2 0 -1 0 -1]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 6 1 none
Polytope 546
Image of polytope 546 PALP id: 546
grdb id: 516490
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 1 -1 1 0 1 0 0]
[ 0 0 0 1 -1 -1 1 0 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + x-1*y*z + 2*x-1*y + x-1*y*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 547
Image of polytope 547 PALP id: 547
grdb id: 516473
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 -1 0 -1 0 0]
[ 0 0 1 -1 0 0 2 1 1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
63 ? x + y + z + x-1*y + 2*x-1*z + x-1*y-1*z2 + 2*x-1 + 2*x-1*y-1*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 548
Image of polytope 548 PALP id: 548
grdb id: 516715
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 0 -1 -1 0 -1 -1 0]
[ 0 0 1 -1 1 -1 2 0 1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
28 rank 2, number 25 x + y + z + x-1*z + x-1*y-1*z2 + 2*x-1 + 3*x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 9 1 irreducible and admissible
Polytope 549
Image of polytope 549 PALP id: 549
grdb id: 515974
Integer points: [ 1 0 -1 -1 0 -2 0 -1 -1 0 0]
[ 0 1 1 -2 0 -2 -1 -1 0 -1 0]
[ 0 0 0 0 1 -1 1 0 0 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 29 1 none
Polytope 550
Image of polytope 550 PALP id: 550
grdb id: 516414
Integer points: [ 1 0 -1 -1 0 -2 0 -1 -1 0 0]
[ 0 1 1 -2 0 -1 -1 0 -1 0 -1]
[ 0 0 0 0 1 -1 1 0 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 28 1 none
Polytope 551
Image of polytope 551 PALP id: 551
grdb id: 516600
Integer points: [ 1 0 -1 0 -2 -1 0 -1 -1 0 0]
[ 0 1 1 0 0 -2 -1 0 -1 0 -1]
[ 0 0 0 1 -1 0 1 0 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 28 1 none
Polytope 552
Image of polytope 552 PALP id: 552
grdb id: 516002
Integer points: [ 1 0 -1 0 -2 -1 0 -1 -1 0 0]
[ 0 1 1 0 0 -2 1 0 -1 0 -1]
[ 0 0 0 1 -1 0 1 0 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 29 1 none
Polytope 553
Image of polytope 553 PALP id: 553
grdb id: 516413
Integer points: [ 1 0 -1 0 -2 0 -2 -1 -2 -1 0]
[ 0 1 1 0 1 -1 -1 0 0 -1 0]
[ 0 0 0 1 -1 1 -1 0 -1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
47 ? x + y + z + x-1*y + y-1*z + 3*x-1 + x-2*y*z-1 + 2*x-1*y-1 + 2*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 554
Image of polytope 554 PALP id: 554
grdb id: 516542
Integer points: [ 1 0 -1 0 -1 -2 -2 -2 -1 -1 0]
[ 0 1 1 0 -1 0 -2 -1 0 -1 0]
[ 0 0 0 1 -1 -1 -1 -1 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
111 ? x + y + z + x-1*y + 2*x-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-2*z-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 555
Image of polytope 555 PALP id: 555
grdb id: 516755
Integer points: [ 1 0 -1 0 -1 -1 -1 0 -1 -1 0]
[ 0 1 0 0 1 -1 -2 -1 -1 0 0]
[ 0 0 0 1 -1 -1 0 0 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + x-1*y*z-1 + 2*y-1 + x-1 + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 556
Image of polytope 556 PALP id: 556
grdb id: 516514
Integer points: [ 1 0 -1 0 -1 -1 0 -1 -1 0 0]
[ 0 1 1 0 1 -2 1 0 -1 0 -1]
[ 0 0 0 1 -1 0 1 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
159 ? y*z + x + y + z + x-1*y + x-1*y*z-1 + 2*y-1 + 3*x-1 + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Polytope 557
Image of polytope 557 PALP id: 557
grdb id: 516557
Integer points: [ 1 0 -1 0 0 -2 -2 -1 -2 -1 0]
[ 0 1 -1 0 1 -1 1 1 0 0 0]
[ 0 0 0 1 1 -1 -1 0 -1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
98 rank 3, number 21 y*z + x + y + z + 2*x-1*y + 3*x-1 + x-2*y*z-1 + x-1*y-1 + 2*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 558
Image of polytope 558 PALP id: 558
grdb id: 516371
Integer points: [ 1 0 0 -2 -1 -2 0 -1 -1 0 0]
[ 0 1 0 0 -2 -1 -1 0 -1 0 -1]
[ 0 0 1 -1 0 -1 1 0 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
43 ? x + y + z + y-1*z + 2*y-1 + 2*x-1 + 2*x-1*y-1 + x-2*z-1 + x-1*y-2 + x-2*y-1*z-1
131 ? x + y + z + y-1*z + 2*y-1 + 2*x-1 + 3*x-1*y-1 + x-2*z-1 + x-1*y-2 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 559
Image of polytope 559 PALP id: 559
grdb id: 516571
Integer points: [ 1 0 0 -1 0 0 -2 -1 -1 0 0]
[ 0 1 0 1 -1 -1 1 0 0 -1 0]
[ 0 0 1 1 -1 1 1 1 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
29 rank 2, number 23 x + y + z + x-1*y*z + y-1*z + 2*x-1*z + x-2*y*z + 2*y-1 + 2*x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 560
Image of polytope 560 PALP id: 560
grdb id: 516725
Integer points: [ 1 0 0 0 -1 -2 -2 -1 -1 -1 0]
[ 0 1 -1 0 1 0 -1 0 -1 0 0]
[ 0 0 0 1 0 -1 -2 0 -1 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + x-1*y + y-1 + 2*x-1 + 2*x-1*z-1 + 2*x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 561
Image of polytope 561 PALP id: 561
grdb id: 516684
Integer points: [ 1 0 0 0 -1 -2 -2 -1 -1 -1 0]
[ 0 1 -1 0 1 1 0 1 0 0 0]
[ 0 0 0 1 -1 0 1 0 0 1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 6 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 562
Image of polytope 562 PALP id: 562
grdb id: 516794
Integer points: [ 1 0 0 0 0 -2 -2 -1 -1 -1 0]
[ 0 1 -1 0 -1 1 1 0 0 1 0]
[ 0 0 0 1 -1 0 -1 0 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
77 ? x + y + z + 2*x-1*y + y-1 + 2*x-1 + x-2*y + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 563
Image of polytope 563 PALP id: 563
grdb id: 516792
Integer points: [ 1 0 0 0 0 -2 -2 -1 -1 -1 0]
[ 0 1 -1 0 1 0 1 1 0 0 0]
[ 0 0 0 1 -1 -1 -2 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + y*z-1 + 2*x-1*y*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + x-2*y*z-2 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 564
Image of polytope 564 PALP id: 564
grdb id: 516785
Integer points: [ 1 0 0 0 0 -2 -2 -1 -1 0 -1]
[ 0 1 0 0 -1 0 1 1 0 0 0]
[ 0 0 1 -1 0 1 0 0 0 0 1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 5 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 565
Image of polytope 565 PALP id: 565
grdb id: 516500
Integer points: [ 1 0 0 0 0 -2 -1 0 -1 0 -1]
[ 0 1 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 0 1 -1 1 0 1 0 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 8 1 none
Polytope 566
Image of polytope 566 PALP id: 566
grdb id: 516492
Integer points: [ 1 0 0 0 0 -1 -2 0 -1 0 -1]
[ 0 1 0 -1 -1 0 1 -1 0 0 1]
[ 0 0 1 -1 1 1 0 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 8 1 none
Polytope 567
Image of polytope 567 PALP id: 567
grdb id: 516491
Integer points: [ 1 0 0 1 -1 -1 1 0 0 0 -1]
[ 0 1 0 -1 0 0 -2 -1 -1 0 0]
[ 0 0 1 0 -1 1 -1 0 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
55 rank 2, number 19 x + y + z + x*y-1 + x-1*z + 2*y-1 + 2*x-1 + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 568
Image of polytope 568 PALP id: 568
grdb id: 516761
Integer points: [ 1 0 0 1 1 -1 -1 0 0 -1 -1]
[ 0 1 0 1 0 1 -2 -1 0 -1 0]
[ 0 0 1 -1 -1 0 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
128 ? x*y*z-1 + x + y + z + x*z-1 + x-1*y + 2*y-1 + 3*x-1 + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Polytope 569
Image of polytope 569 PALP id: 569
grdb id: 516530
Integer points: [ 1 0 1 -2 0 -2 -1 -1 0 -1 0]
[ 0 1 -1 -1 0 -1 0 -1 -1 0 0]
[ 0 0 0 0 1 -1 1 0 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 6 1 none
Polytope 570
Image of polytope 570 PALP id: 570
grdb id: 516544
Integer points: [ 1 0 1 -2 0 0 -1 0 -1 0 -1]
[ 0 1 -1 1 0 -2 -1 -1 0 0 1]
[ 0 0 0 0 1 -1 -1 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Polytope 571
Image of polytope 571 PALP id: 571
grdb id: 516463
Integer points: [ 1 0 1 -2 0 1 0 0 -1 0 -1]
[ 0 1 -1 1 0 -2 -2 -1 0 0 1]
[ 0 0 0 0 1 -1 -1 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 4 1 none
Polytope 572
Image of polytope 572 PALP id: 572
grdb id: 516459
Integer points: [ 1 0 1 -1 0 -1 -2 -1 -1 0 0]
[ 0 1 -1 1 0 -2 -2 -1 0 -1 0]
[ 0 0 0 0 1 -1 -1 0 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 4 1 none
Polytope 573
Image of polytope 573 PALP id: 573
grdb id: 516714
Integer points: [ 1 0 1 0 -1 -1 -2 -1 0 -1 0]
[ 0 1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 0 0 1 -1 1 0 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 5 1 none
Polytope 574
Image of polytope 574 PALP id: 574
grdb id: 516748
Integer points: [ 1 0 1 0 0 -1 -2 0 -1 0 -1]
[ 0 1 -1 0 1 0 -1 0 0 -1 -1]
[ 0 0 0 1 -1 1 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 6 1 none
Polytope 575
Image of polytope 575 PALP id: 575
grdb id: 516556
Integer points: [ 1 0 -1 0 -2 -1 -2 -1 -2 -1 0]
[ 0 1 -1 0 0 1 2 1 1 0 0]
[ 0 0 0 1 -1 -1 -1 0 -1 0 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
130 rank 3, number 24 x + y + z + 2*x-1*y + x-1*y*z-1 + x-2*y2*z-1 + 2*x-1 + 2*x-2*y*z-1 + x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 576
Image of polytope 576 PALP id: 576
grdb id: 516693
Integer points: [ 1 0 0 -2 0 2 1 1 -1 0 -1]
[ 0 1 -1 1 0 -2 -2 -1 0 0 1]
[ 0 0 0 0 1 -1 -1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
100 ? x + y + z + 2*x*y-1 + 2*x-1*y + x2*y-2*z-1 + y-1 + 2*x-1 + x-2*y + x*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 577
Image of polytope 577 PALP id: 577
grdb id: 516786
Integer points: [ 1 0 0 -1 0 0 -1 -1 0 0 0]
[ 0 1 -1 0 0 -2 2 1 -1 0 1]
[ 0 0 0 0 1 1 -2 -1 1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
3 ? x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 2*x-1*y*z-1 + y-1 + x-1 + y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 578
Image of polytope 578 PALP id: 578
grdb id: 516789
Integer points: [ 1 0 0 0 -2 1 2 1 -1 0 -1]
[ 0 1 -1 0 1 -1 -2 -1 0 0 1]
[ 0 0 0 1 0 -1 -1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
134 ? x + y + z + 2*x*y-1 + 2*x-1*y + x2*y-2*z-1 + x*y-1*z-1 + y-1 + 2*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 5 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 579
Image of polytope 579 PALP id: 579
grdb id: 516550
Integer points: [ 1 0 0 0 -1 -2 -2 -1 -1 -2 0]
[ 0 1 -1 0 1 0 2 0 1 1 0]
[ 0 0 0 1 -1 -1 -1 0 0 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
69 ? x + y + z + 2*x-1*y + x-1*y*z-1 + x-2*y2*z-1 + y-1 + 2*x-1 + 2*x-2*y*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 580
Image of polytope 580 PALP id: 580
grdb id: 516713
Integer points: [ 1 -1 0 0 -1 -2 -3 -2 -1 0 -1]
[ 0 0 1 0 0 -2 -2 -1 -1 0 -1]
[ 0 0 0 1 -1 -1 -2 -1 0 0 -1]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
79 ? x + y + z + x-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 581
Image of polytope 581 PALP id: 581
grdb id: 516368
Integer points: [ 1 0 -1 -1 0 -2 -2 -1 -2 0 0]
[ 0 1 0 -2 0 -1 -3 -1 -2 -1 0]
[ 0 0 0 0 1 -1 -1 0 -1 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
140 ? x + y + z + 2*y-1 + x-1 + 3*x-1*y-1 + x-1*y-2 + x-2*y-1*z-1 + 2*x-2*y-2*z-1 + x-2*y-3*z-1
123 ? x + y + z + 2*y-1 + x-1 + 2*x-1*y-1 + x-1*y-2 + x-2*y-1*z-1 + 2*x-2*y-2*z-1 + x-2*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 582
Image of polytope 582 PALP id: 582
grdb id: 516762
Integer points: [ 1 0 -1 0 -1 -2 -3 -2 -1 -1 0]
[ 0 1 -1 0 1 -1 0 0 0 0 0]
[ 0 0 0 1 -1 -1 -2 -1 0 -1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
104 ? x + y + z + x-1*y*z-1 + 3*x-1 + 2*x-1*z-1 + x-1*y-1 + 3*x-2*z-1 + x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Polytope 583
Image of polytope 583 PALP id: 583
grdb id: 516501
Integer points: [ 1 0 -1 0 -1 -1 -3 -2 -1 -2 0]
[ 0 1 -1 0 1 1 1 1 0 0 0]
[ 0 0 0 1 0 -1 -2 -1 0 -1 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
86 ? x + y + z + x-1*y + x-1*y*z-1 + 2*x-1 + 2*x-2*y*z-1 + x-1*y-1 + 2*x-2*z-1 + x-3*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 584
Image of polytope 584 PALP id: 584
grdb id: 516502
Integer points: [ 1 0 0 -2 0 -3 -1 -2 -1 -1 0]
[ 0 1 0 -1 -1 -1 -1 -1 0 -1 0]
[ 0 0 1 -1 1 -1 1 0 0 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 8 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 585
Image of polytope 585 PALP id: 585
grdb id: 516766
Integer points: [ 1 0 0 -1 -1 -3 -2 -2 -1 -1 0]
[ 0 1 0 -1 0 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 1 0 1 0 0 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
92 ? x + y + z + x-1*z + 3*x-1 + 2*x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + 3*x-2*y-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Polytope 586
Image of polytope 586 PALP id: 586
grdb id: 516712
Integer points: [ 1 0 0 -1 0 -2 -2 -1 -1 0 -1]
[ 0 1 -1 0 0 -2 -3 -1 -2 0 -1]
[ 0 0 0 0 1 -1 -2 0 -1 0 -1]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
37 rank 3, number 17 x + y + z + y-1 + x-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-1*y-2*z-1 + x-2*y-2*z-1 + x-2*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 587
Image of polytope 587 PALP id: 587
grdb id: 516423
Integer points: [ 1 0 0 0 -3 0 -1 -2 -1 -1 0]
[ 0 1 -1 0 1 1 1 1 1 0 0]
[ 0 0 0 1 -1 1 1 0 0 0 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 8 2 none
Polytope 588
Image of polytope 588 PALP id: 588
grdb id: 516605
Integer points: [ 1 0 0 0 -2 -3 -1 -2 -1 -1 0]
[ 0 1 -1 0 -2 -2 0 -1 -1 0 0]
[ 0 0 0 1 -1 -1 1 0 0 0 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 4 1 none
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 589
Image of polytope 589 PALP id: 589
grdb id: 516777
Integer points: [ 1 0 0 0 -1 -2 -3 -1 -2 0 -1]
[ 0 1 -1 0 1 1 0 0 0 0 0]
[ 0 0 0 1 0 -1 -2 0 -1 0 -1]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
95 ? x + y + z + x-1*y + y-1 + 3*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 3*x-2*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Polytope 590
Image of polytope 590 PALP id: 590
grdb id: 516776
Integer points: [ 1 0 0 0 -1 -1 -3 -2 -1 -1 0]
[ 0 1 0 1 -1 0 -2 -1 0 -1 0]
[ 0 0 1 1 0 -1 -2 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
103 ? y*z + x + y + z + 3*x-1 + x-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*y-1*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Polytope 591
Image of polytope 591 PALP id: 591
grdb id: 516764
Integer points: [ 1 0 0 1 0 -1 -3 -1 -2 0 -1]
[ 0 1 -1 1 0 1 0 0 0 0 0]
[ 0 0 0 0 1 -1 -2 0 -1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x*y + x + y + z + x-1*y*z-1 + y-1 + 3*x-1 + 2*x-1*z-1 + 3*x-2*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Polytope 592
Image of polytope 592 PALP id: 592
grdb id: 515479
Integer points: [ 1 0 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 1 0 0 1 -2 -1 0 -1 0]
[ 0 0 0 1 -1 -1 0 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
129 ? x + y + z + x-1*y + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*z-1 + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Polytope 593
Image of polytope 593 PALP id: 593
grdb id: 515561
Integer points: [ 1 0 -1 0 -1 -1 0 -1 -1 0 0]
[ 0 1 1 0 -1 -2 -1 -1 0 -1 0]
[ 0 0 0 1 -1 0 1 0 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
106 ? x + y + z + x-1*y + y-1*z + 2*y-1 + 3*x-1 + 3*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Polytope 594
Image of polytope 594 PALP id: 594
grdb id: 515566
Integer points: [ 1 0 0 -1 -1 0 -1 -1 -1 0 0]
[ 0 1 0 1 0 -1 -2 0 -1 0 -1]
[ 0 0 1 0 -1 1 0 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
132 ? x + y + z + x-1*y + y-1*z + 2*y-1 + 3*x-1 + x-1*z-1 + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Polytope 595
Image of polytope 595 PALP id: 595
grdb id: 515145
Integer points: [ 1 0 0 -1 0 -2 -2 -1 -2 -1 0]
[ 0 1 -1 1 0 0 -2 -1 -1 0 0]
[ 0 0 0 0 1 -1 -1 0 -1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
87 ? x + y + z + x-1*y + y-1 + 2*x-1 + 2*x-1*y-1 + x-2*z-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 596
Image of polytope 596 PALP id: 596
grdb id: 515083
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 0 -2 0 -1 -1 0]
[ 0 0 1 -1 1 1 1 0 1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
160 ? x + y + z + y-1*z + x-1*z + 2*x-1 + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 597
Image of polytope 597 PALP id: 597
grdb id: 515076
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 0 -2 -1 -1 0 0]
[ 0 0 0 1 -1 1 -1 0 -1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + x-1*z + y-1 + 2*x-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 598
Image of polytope 598 PALP id: 598
grdb id: 515609
Integer points: [ 1 0 0 0 -1 -1 0 0 -1 0 0]
[ 0 1 0 0 1 -1 -2 -1 0 0 -1]
[ 0 0 1 -1 0 0 -1 0 0 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
159 ? x + y + z + x-1*y + z-1 + 2*y-1 + 2*x-1 + 2*y-1*z-1 + x-1*y-1 + y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 599
Image of polytope 599 PALP id: 599
grdb id: 515587
Integer points: [ 1 0 0 0 -1 0 -1 -1 -1 0 0]
[ 0 1 0 0 1 -1 -2 0 -1 0 -1]
[ 0 0 1 -1 0 1 0 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
82 ? x + y + z + x-1*y + y-1*z + z-1 + 2*y-1 + 3*x-1 + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Polytope 600
Image of polytope 600 PALP id: 600
grdb id: 515611
Integer points: [ 1 0 0 0 0 -2 -2 -1 -1 -1 0]
[ 0 1 -1 0 -1 -1 -1 -1 0 -1 0]
[ 0 0 0 1 -1 0 -1 0 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
126 ? x + y + z + y-1 + 2*x-1 + y-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 601
Image of polytope 601 PALP id: 601
grdb id: 515517
Integer points: [ 1 0 0 0 0 -1 -1 0 0 -1 -1]
[ 0 1 0 0 1 1 -2 -1 0 -1 0]
[ 0 0 1 -1 -1 0 0 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
88 ? x + y + z + y*z-1 + x-1*y + z-1 + 2*y-1 + 3*x-1 + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Polytope 602
Image of polytope 602 PALP id: 602
grdb id: 515147
Integer points: [ 1 0 1 -1 0 -2 0 0 -1 -1 0]
[ 0 1 -1 1 0 0 -2 -1 0 -1 0]
[ 0 0 0 0 1 -1 -1 0 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
32 ? x + y + z + x*y-1 + x-1*y + 2*y-1 + 2*x-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 603
Image of polytope 603 PALP id: 603
grdb id: 425465
Integer points: [ 1 0 0 0 -1 -2 -2 -1 -1 -1 0]
[ 0 1 -1 0 0 -1 -1 -1 0 -1 0]
[ 0 0 0 1 -1 0 -1 1 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 6 1 none
Polytope 604
Image of polytope 604 PALP id: 604
grdb id: 425463
Integer points: [ 1 0 0 0 -1 -1 -2 -2 -1 -1 0]
[ 0 1 -1 0 -1 1 0 1 0 1 0]
[ 0 0 0 1 -1 1 -1 0 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
164 ? x + y + z + x-1*y*z + 2*x-1*y + y-1 + 3*x-1 + x-2*y + x-1*y-1*z-1 + x-2*z-1
76 ? x + y + z + x-1*y*z + 2*x-1*y + y-1 + 2*x-1 + x-2*y + x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Polytope 605
Image of polytope 605 PALP id: 605
grdb id: 425466
Integer points: [ 1 0 0 0 -1 1 -1 1 0 1 0]
[ 0 1 0 0 1 -1 0 -2 -1 -1 0]
[ 0 0 1 -1 1 -1 0 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
25 ? x + y + z + x-1*y*z + 2*x*y-1 + x*y-1*z-1 + z-1 + x*y-2 + 2*y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 606
Image of polytope 606 PALP id: 606
grdb id: 425467
Integer points: [ 1 0 0 0 0 -1 -1 -2 -1 -1 0]
[ 0 1 0 0 -1 -1 -1 -1 0 -1 0]
[ 0 0 1 -1 0 -1 1 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 5 1 none
Polytope 607
Image of polytope 607 PALP id: 607
grdb id: 425462
Integer points: [ 1 0 0 0 1 0 -1 -2 -1 0 -1]
[ 0 1 -1 0 0 -1 -1 -1 -1 0 0]
[ 0 0 0 1 -1 -1 1 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 6 1 none
Polytope 608
Image of polytope 608 PALP id: 608
grdb id: 425464
Integer points: [ 1 -1 0 0 1 0 2 2 1 1 0]
[ 0 0 1 0 0 -1 -1 -2 -1 -1 0]
[ 0 0 0 1 -1 -1 -1 -1 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 6 1 none
Polytope 609
Image of polytope 609 PALP id: 609
grdb id: 425459
Integer points: [ 1 0 0 -1 0 -1 -1 2 -1 0 1]
[ 0 1 -1 0 0 1 -1 0 0 0 0]
[ 0 0 0 0 1 -1 -1 1 -1 0 1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
3 ? x2*z + 2*x*z + x + y + z + x-1*y*z-1 + y-1 + x-1 + 2*x-1*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Polytope 610
Image of polytope 610 PALP id: 610
grdb id: 425446
Integer points: [ 1 0 -1 0 0 -1 -2 -2 -1 -1 0]
[ 0 1 -1 0 1 1 -1 0 0 0 0]
[ 0 0 0 1 -1 0 1 1 0 1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
152 rank 3, number 22 x + y + z + y*z-1 + x-1*y + 2*x-1*z + x-1 + x-2*z + x-1*y-1 + x-2*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 611
Image of polytope 611 PALP id: 611
grdb id: 425441
Integer points: [ 1 0 0 0 -1 -2 -1 -2 -1 0 -1]
[ 0 1 -1 0 -1 -1 0 -2 -1 0 0]
[ 0 0 0 1 -1 0 1 -1 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
98 rank 3, number 21 x + y + z + x-1*z + y-1 + 2*x-1 + x-1*y-1 + x-1*y-1*z-1 + x-2*y-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 612
Image of polytope 612 PALP id: 612
grdb id: 425445
Integer points: [ 1 0 0 0 -1 -1 -2 -2 -1 -1 0]
[ 0 1 -1 0 0 0 1 1 0 1 0]
[ 0 0 0 1 -1 1 0 -1 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
160 ? x + y + z + 2*x-1*y + x-1*z + y-1 + x-1 + x-2*y + x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 613
Image of polytope 613 PALP id: 613
grdb id: 425454
Integer points: [ 1 0 0 0 -1 -1 -2 -2 -1 -1 0]
[ 0 1 0 -1 -1 0 -1 -1 0 -1 0]
[ 0 0 1 -1 0 1 0 -1 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 6 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 614
Image of polytope 614 PALP id: 614
grdb id: 425453
Integer points: [ 1 0 0 0 -1 -1 -2 -2 -1 -1 0]
[ 0 1 0 -1 0 -1 0 -1 0 -1 0]
[ 0 0 1 -1 -1 0 -1 -1 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? x + y + z + 2*x-1 + y-1*z-1 + x-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 615
Image of polytope 615 PALP id: 615
grdb id: 425450
Integer points: [ 1 0 0 0 0 -1 -2 -1 -1 0 -1]
[ 0 1 -1 0 -1 0 -1 -2 -1 0 0]
[ 0 0 0 1 -1 1 0 -1 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
47 ? x + y + z + x-1*z + y-1 + 2*x-1 + y-1*z-1 + x-1*y-1 + x-2*y-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 616
Image of polytope 616 PALP id: 616
grdb id: 425457
Integer points: [ 1 0 0 0 0 -1 -1 -2 -1 -1 0]
[ 0 1 -1 0 -1 1 0 1 0 1 0]
[ 0 0 0 1 -1 1 -1 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
77 ? x + y + z + x-1*y*z + 2*x-1*y + y-1 + 2*x-1 + x-2*y + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 617
Image of polytope 617 PALP id: 617
grdb id: 425448
Integer points: [ 1 0 0 0 0 -1 -1 -2 -1 -1 0]
[ 0 1 -1 0 1 0 0 -1 0 -1 0]
[ 0 0 0 1 -1 -1 1 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
66 rank 2, number 24 x + y + z + y*z-1 + x-1*z + y-1 + x-1 + x-1*z-1 + 2*x-1*y-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 618
Image of polytope 618 PALP id: 618
grdb id: 425458
Integer points: [ 1 0 0 0 0 -1 1 -2 -1 -1 0]
[ 0 1 0 0 -1 1 -1 0 0 0 0]
[ 0 0 1 -1 0 0 -1 1 0 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y + 2*x-1*z + x*y-1*z-1 + z-1 + y-1 + 2*x-1 + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 619
Image of polytope 619 PALP id: 619
grdb id: 425438
Integer points: [ 1 0 0 0 1 0 -1 -2 -1 0 -1]
[ 0 1 -1 0 -1 -1 0 1 0 0 1]
[ 0 0 0 1 -1 -1 1 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 6 1 none
Polytope 620
Image of polytope 620 PALP id: 620
grdb id: 425197
Integer points: [ 1 0 -1 0 -1 -1 0 -1 -1 -1 0]
[ 0 1 -1 0 1 0 1 1 1 0 0]
[ 0 0 0 1 -1 1 1 1 0 0 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 621
Image of polytope 621 PALP id: 621
grdb id: 425267
Integer points: [ 1 0 -1 0 0 -1 0 -1 0 -1 0]
[ 0 1 1 0 -1 -1 -1 -1 -1 0 0]
[ 0 0 0 1 -1 0 1 -1 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? x + y + z + x-1*y + y-1*z + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 622
Image of polytope 622 PALP id: 622
grdb id: 425119
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 -1 1 0 0 0]
[ 0 0 1 -1 0 0 1 1 1 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
123 ? x + y + z + x-1*y*z + x-1*y + 2*x-1*z + 3*x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
102 ? x + y + z + x-1*y*z + x-1*y + 2*x-1*z + 2*x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 623
Image of polytope 623 PALP id: 623
grdb id: 425176
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 1 -1 0 -1 -1 0 0]
[ 0 0 1 -1 0 -1 1 1 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? x + y + z + x-1*y + x-1*z + 2*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
65 ? x + y + z + x-1*y + x-1*z + 3*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 624
Image of polytope 624 PALP id: 624
grdb id: 425123
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 -1 0]
[ 0 1 -1 1 0 -1 0 -1 -1 0 0]
[ 0 0 0 0 1 -1 1 1 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Polytope 625
Image of polytope 625 PALP id: 625
grdb id: 425410
Integer points: [ 1 0 0 -1 0 -1 0 -1 -1 0 0]
[ 0 1 0 1 -1 0 -1 0 0 -1 0]
[ 0 0 1 0 -1 -1 1 1 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + x-1*y + y-1*z + x-1*z + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 626
Image of polytope 626 PALP id: 626
grdb id: 425359
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 1 -1 0 0 -1 0 -1 0]
[ 0 0 1 1 -1 -1 1 1 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
28 rank 2, number 25 y*z + x + y + z + x-1*z + 2*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 627
Image of polytope 627 PALP id: 627
grdb id: 425408
Integer points: [ 1 0 0 0 -1 -1 1 1 1 0 -1]
[ 0 1 -1 0 1 -1 -1 1 0 0 0]
[ 0 0 0 1 0 0 -1 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
60 rank 2, number 18 x*y*z-1 + x + y + z + 2*x*z-1 + x-1*y + x*y-1*z-1 + y-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 628
Image of polytope 628 PALP id: 628
grdb id: 425407
Integer points: [ 1 0 0 0 -1 1 -1 -1 -1 0 0]
[ 0 1 -1 0 1 -1 -1 -1 0 -1 0]
[ 0 0 0 1 0 -1 0 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
80 ? x + y + z + x-1*y + x*y-1*z-1 + y-1 + 2*x-1 + 2*y-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 629
Image of polytope 629 PALP id: 629
grdb id: 425411
Integer points: [ 1 0 1 -1 0 1 1 -1 0 0 -1]
[ 0 1 -1 1 0 1 0 -1 -1 0 0]
[ 0 0 0 0 1 -1 -1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x*y*z-1 + x + y + z + x*z-1 + x*y-1 + x-1*y + 2*y-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 630
Image of polytope 630 PALP id: 630
grdb id: 425337
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 1 -1 2 0 1 0]
[ 0 0 0 0 1 0 -1 -1 -1 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
66 rank 2, number 24 x + y + z + x-1*y2*z-1 + x-1*y + 3*x-1*y*z-1 + y-1 + x-1 + 3*x-1*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Polytope 631
Image of polytope 631 PALP id: 631
grdb id: 425271
Integer points: [ 1 0 1 -1 0 -1 -1 -1 -1 0 0]
[ 0 1 -1 1 0 1 -1 2 0 0 -1]
[ 0 0 0 0 1 -1 0 -1 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + x-1*y2*z-1 + x*y-1 + x-1*y + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 632
Image of polytope 632 PALP id: 632
grdb id: 425325
Integer points: [ 1 0 -1 -1 0 -2 0 -2 -1 0 0]
[ 0 1 0 -2 0 -1 -1 -2 -1 0 -1]
[ 0 0 0 0 1 -1 1 -1 0 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
123 ? x + y + z + y-1*z + 2*y-1 + x-1 + 2*x-1*y-1 + x-1*y-2 + x-2*y-1*z-1 + x-2*y-2*z-1
140 ? x + y + z + y-1*z + 2*y-1 + x-1 + 3*x-1*y-1 + x-1*y-2 + x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Polytope 633
Image of polytope 633 PALP id: 633
grdb id: 425104
Integer points: [ 1 0 -1 0 -2 1 -2 0 -1 -1 0]
[ 0 1 -1 0 0 1 1 1 1 0 0]
[ 0 0 0 1 -1 1 -1 1 0 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
86 ? x*y*z + y*z + x + y + z + 2*x-1*y + 2*x-1 + x-2*y*z-1 + x-1*y-1 + x-2*z-1
142 ? x*y*z + y*z + x + y + z + 2*x-1*y + 3*x-1 + x-2*y*z-1 + x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 634
Image of polytope 634 PALP id: 634
grdb id: 425236
Integer points: [ 1 0 -1 0 -1 -1 -2 -2 -2 -1 0]
[ 0 1 -1 0 -1 0 -1 -1 -1 0 0]
[ 0 0 0 1 -1 1 -1 1 0 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 635
Image of polytope 635 PALP id: 635
grdb id: 425353
Integer points: [ 1 0 -1 0 -1 -1 0 -1 -1 0 0]
[ 0 1 0 0 1 0 -1 -2 -1 0 -1]
[ 0 0 0 1 -1 -1 1 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + y-1*z + x-1*y*z-1 + 2*y-1 + x-1 + x-1*z-1 + 2*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 636
Image of polytope 636 PALP id: 636
grdb id: 425280
Integer points: [ 1 0 0 -2 0 -2 0 -1 -1 -1 0]
[ 0 1 -1 -1 0 -1 -1 -1 0 -1 0]
[ 0 0 0 0 1 -1 1 1 0 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
142 ? x + y + z + y-1*z + y-1 + 2*x-1 + x-1*y-1*z + x-1*y-1 + x-2*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 637
Image of polytope 637 PALP id: 637
grdb id: 425381
Integer points: [ 1 0 0 -1 -2 -1 -1 -2 -1 -1 0]
[ 0 1 0 -1 -1 0 -1 -1 -1 0 0]
[ 0 0 1 -1 0 1 1 1 0 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
102 ? x + y + z + x-1*z + 2*x-1 + x-1*y-1*z + 2*x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 638
Image of polytope 638 PALP id: 638
grdb id: 425315
Integer points: [ 1 0 0 -1 0 -2 -1 -2 -1 -1 0]
[ 0 1 0 0 -1 -1 -1 -1 0 -1 0]
[ 0 0 1 -1 1 0 1 -1 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
160 ? x + y + z + y-1*z + 2*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-2*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 639
Image of polytope 639 PALP id: 639
grdb id: 425388
Integer points: [ 1 0 0 -1 0 -1 -2 -2 0 -1 -1]
[ 0 1 -1 0 0 1 1 1 0 0 1]
[ 0 0 0 0 1 0 -1 -2 0 -1 -1]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? x + y + z + x-1*y + 2*x-1*y*z-1 + y-1 + x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 640
Image of polytope 640 PALP id: 640
grdb id: 425133
Integer points: [ 1 0 0 -1 0 -1 -2 -2 -1 -1 0]
[ 0 1 -1 1 0 -2 -1 -2 -1 0 0]
[ 0 0 0 0 1 -1 -1 -1 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 641
Image of polytope 641 PALP id: 641
grdb id: 425340
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 0 1 0 -2 -1 0 -1]
[ 0 0 0 0 1 0 -1 -2 -1 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
66 rank 2, number 24 x + y + z + x-1*y + y-1 + x-1 + 2*y-1*z-1 + x-1*z-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 642
Image of polytope 642 PALP id: 642
grdb id: 425220
Integer points: [ 1 0 0 -1 0 -1 0 -2 -1 -1 0]
[ 0 1 -1 1 0 -1 -1 -1 -1 0 0]
[ 0 0 0 0 1 -1 1 -1 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 643
Image of polytope 643 PALP id: 643
grdb id: 425274
Integer points: [ 1 0 0 0 -2 -2 0 -1 -1 -1 0]
[ 0 1 -1 0 0 1 1 1 1 0 0]
[ 0 0 0 1 -1 0 1 1 0 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
102 ? y*z + x + y + z + x-1*y*z + 2*x-1*y + y-1 + x-1 + x-2*y + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 644
Image of polytope 644 PALP id: 644
grdb id: 425324
Integer points: [ 1 0 0 0 -1 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 -1 -1 0 -1 -1 0 0]
[ 0 0 0 1 -1 0 1 -1 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 6 1 none
Polytope 645
Image of polytope 645 PALP id: 645
grdb id: 425296
Integer points: [ 1 0 0 0 -1 -2 0 -2 -1 -1 0]
[ 0 1 -1 0 1 0 1 1 1 0 0]
[ 0 0 0 1 -1 -1 1 -1 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
47 ? y*z + x + y + z + 2*x-1*y + x-1*y*z-1 + y-1 + 2*x-1 + x-2*y*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 646
Image of polytope 646 PALP id: 646
grdb id: 425362
Integer points: [ 1 0 0 0 -1 -2 0 -1 -1 0 -1]
[ 0 1 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 0 0 1 -1 0 1 1 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
98 rank 3, number 21 x + y + z + y-1*z + y-1 + 2*x-1 + x-1*y-1*z + x-1*y-1 + x-1*y-1*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 647
Image of polytope 647 PALP id: 647
grdb id: 425378
Integer points: [ 1 0 0 0 -1 -1 -2 -2 -1 -1 0]
[ 0 1 0 -1 0 -1 -1 -1 -1 0 0]
[ 0 0 1 -1 1 -1 0 1 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? x + y + z + x-1*z + 2*x-1 + y-1*z-1 + 2*x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 648
Image of polytope 648 PALP id: 648
grdb id: 425367
Integer points: [ 1 0 0 0 -1 0 -1 -2 -1 -1 0]
[ 0 1 -1 0 0 -1 0 1 0 1 0]
[ 0 0 0 1 -1 1 1 0 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? x + y + z + 2*x-1*y + y-1*z + x-1*z + y-1 + x-1 + x-2*y + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 649
Image of polytope 649 PALP id: 649
grdb id: 425303
Integer points: [ 1 0 0 0 0 -1 -1 -2 -1 -1 0]
[ 0 1 -1 0 1 1 -1 1 0 1 0]
[ 0 0 0 1 -1 0 0 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 6 1 none
Polytope 650
Image of polytope 650 PALP id: 650
grdb id: 425384
Integer points: [ 1 0 0 0 0 -1 -1 -2 -1 -1 0]
[ 0 1 0 -1 0 1 -1 0 0 0 0]
[ 0 0 1 0 -1 0 -1 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
147 ? x + y + z + x-1*y + z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 651
Image of polytope 651 PALP id: 651
grdb id: 425405
Integer points: [ 1 0 0 0 0 -1 -1 -2 -1 0 -1]
[ 0 1 0 0 -1 0 0 -1 0 0 -1]
[ 0 0 1 -1 0 -1 1 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 5 1 none
Polytope 652
Image of polytope 652 PALP id: 652
grdb id: 425387
Integer points: [ 1 0 0 0 0 -1 0 -2 -1 -1 0]
[ 0 1 0 -1 0 0 1 -1 0 -1 0]
[ 0 0 1 0 -1 0 1 -2 -1 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 y*z + x + y + z + z-1 + y-1 + x-1 + 2*x-1*z-1 + 2*x-1*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 653
Image of polytope 653 PALP id: 653
grdb id: 425383
Integer points: [ 1 0 0 0 0 1 -1 -2 -1 0 -1]
[ 0 1 0 0 -1 0 -1 -1 -1 0 0]
[ 0 0 1 -1 0 1 -1 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x*z + x + y + z + z-1 + y-1 + 2*x-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 654
Image of polytope 654 PALP id: 654
grdb id: 425396
Integer points: [ 1 0 0 0 0 1 1 -2 -1 -1 0]
[ 0 1 0 -1 0 0 -1 1 0 1 0]
[ 0 0 1 0 -1 -1 -1 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x*z-1 + 2*x-1*y + x*y-1*z-1 + z-1 + y-1 + 2*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 655
Image of polytope 655 PALP id: 655
grdb id: 425293
Integer points: [ 1 0 0 0 1 -1 0 -2 -1 0 -1]
[ 0 1 -1 0 0 -1 -1 -1 -1 0 0]
[ 0 0 0 1 -1 1 1 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + x*z-1 + y-1*z + y-1 + 2*x-1 + x-1*y-1*z + 2*x-1*y-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 656
Image of polytope 656 PALP id: 656
grdb id: 425394
Integer points: [ 1 0 0 1 0 -1 -1 -2 -1 0 -1]
[ 0 1 -1 1 0 -1 1 0 0 0 0]
[ 0 0 0 0 1 -1 -1 -1 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x*y + x + y + z + x-1*y*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 657
Image of polytope 657 PALP id: 657
grdb id: 425356
Integer points: [ 1 0 1 -1 -1 0 -2 -2 -1 0 0]
[ 0 1 -1 1 -1 0 0 -1 0 -1 0]
[ 0 0 0 0 0 1 -1 -1 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
145 ? x + y + z + x*y-1 + x-1*y + 2*y-1 + x-1 + x-1*y-1 + x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 658
Image of polytope 658 PALP id: 658
grdb id: 425329
Integer points: [ 1 0 1 -1 -1 0 -2 -2 -1 0 0]
[ 0 1 -1 1 -1 0 1 0 0 0 -1]
[ 0 0 0 0 0 1 -1 -1 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? x + y + z + x*y-1 + x-1*y + 2*y-1 + x-1 + x-2*y*z-1 + x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 659
Image of polytope 659 PALP id: 659
grdb id: 425263
Integer points: [ 1 0 1 -1 -1 0 -1 -2 -1 0 0]
[ 0 1 -1 1 -1 0 -1 -1 0 -1 0]
[ 0 0 0 0 0 1 -1 -1 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 6 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 660
Image of polytope 660 PALP id: 660
grdb id: 425265
Integer points: [ 1 0 1 -1 0 -1 -2 -2 -1 0 0]
[ 0 1 -1 -1 0 -1 0 -1 0 -1 0]
[ 0 0 0 0 1 -1 -1 -1 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
147 ? x + y + z + x*y-1 + 2*y-1 + 2*x-1 + x-1*y-1 + x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 661
Image of polytope 661 PALP id: 661
grdb id: 425395
Integer points: [ 1 0 1 -1 0 -1 -1 -2 -1 0 0]
[ 0 1 -1 1 0 0 -1 0 0 0 -1]
[ 0 0 0 0 1 -1 0 -1 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 5 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 662
Image of polytope 662 PALP id: 662
grdb id: 425350
Integer points: [ 1 0 1 -1 0 -1 -1 -2 -1 0 0]
[ 0 1 -1 1 0 1 -1 1 0 0 -1]
[ 0 0 0 0 1 -1 0 -1 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 6 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 663
Image of polytope 663 PALP id: 663
grdb id: 425399
Integer points: [ 1 0 1 -1 0 0 -1 -1 -1 0 0]
[ 0 1 -1 1 0 -2 1 -1 0 -1 0]
[ 0 0 0 0 1 -1 1 -1 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
32 ? x + y + z + x-1*y*z + x*y-1 + x-1*y + 2*y-1 + 2*x-1 + y-2*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 664
Image of polytope 664 PALP id: 664
grdb id: 425403
Integer points: [ 1 0 1 0 -1 -1 -1 -2 -1 0 0]
[ 0 1 -1 0 1 0 -1 0 0 -1 0]
[ 0 0 0 1 -1 -1 0 -1 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + x*y-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*z-1 + x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 665
Image of polytope 665 PALP id: 665
grdb id: 425397
Integer points: [ 1 -1 0 0 -2 2 1 2 -1 0 1]
[ 0 0 1 0 0 -1 -1 -1 0 0 0]
[ 0 0 0 1 1 -1 -1 -2 1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x2*y-1*z-1 + 2*x*z-1 + 2*x-1*z + x2*y-1*z-2 + x*y-1*z-1 + x-1 + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 666
Image of polytope 666 PALP id: 666
grdb id: 425307
Integer points: [ 1 0 0 -1 -1 -1 -2 -3 -1 -2 0]
[ 0 1 0 0 -1 -1 0 -1 0 -1 0]
[ 0 0 1 -1 0 -1 -1 -2 0 -1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
63 ? x + y + z + 2*x-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1 + x-2*z-1 + 2*x-2*y-1*z-1 + x-3*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 667
Image of polytope 667 PALP id: 667
grdb id: 254764
Integer points: [ 1 0 0 -1 1 0 1 -1 -1 0 0]
[ 0 1 0 1 -1 0 0 -1 0 0 -1]
[ 0 0 1 0 0 -1 -1 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
88 ? x + y + z + x*z-1 + x*y-1 + x-1*y + z-1 + 2*y-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 668
Image of polytope 668 PALP id: 668
grdb id: 254757
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 -1 0 -1 -1 0 0]
[ 0 0 0 1 -1 -1 1 1 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
65 ? x + y + z + x-1*z + y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 669
Image of polytope 669 PALP id: 669
grdb id: 254772
Integer points: [ 1 0 0 0 -1 0 0 -1 0 0 -1]
[ 0 1 0 0 1 -1 -1 -1 -1 0 0]
[ 0 0 1 -1 0 1 -1 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
159 ? x + y + z + x-1*y + y-1*z + z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 670
Image of polytope 670 PALP id: 670
grdb id: 254738
Integer points: [ 1 0 0 1 -1 0 0 -1 0 0 -1]
[ 0 1 0 -1 1 0 -1 -1 -1 0 0]
[ 0 0 1 0 0 -1 -1 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
82 ? x + y + z + x*y-1 + x-1*y + z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 671
Image of polytope 671 PALP id: 671
grdb id: 254742
Integer points: [ 1 0 1 -1 0 0 -1 -1 -1 0 0]
[ 0 1 -1 1 0 -1 -1 -1 0 -1 0]
[ 0 0 0 0 1 -1 0 -1 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
129 ? x + y + z + x*y-1 + x-1*y + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 672
Image of polytope 672 PALP id: 672
grdb id: 254736
Integer points: [ 1 0 1 -1 0 1 0 -1 0 -1 0]
[ 0 1 -1 1 0 -1 -1 -1 -1 0 0]
[ 0 0 0 0 1 -1 -1 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
114 ? x + y + z + x*y-1 + x-1*y + x*y-1*z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 673
Image of polytope 673 PALP id: 673
grdb id: 254766
Integer points: [ 1 0 1 -1 0 1 1 -1 0 0 -1]
[ 0 1 -1 1 0 0 -1 -1 -1 0 0]
[ 0 0 0 0 1 -1 -1 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
143 ? x + y + z + x*z-1 + x*y-1 + x-1*y + x*y-1*z-1 + 2*y-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 674
Image of polytope 674 PALP id: 674
grdb id: 427168
Integer points: [ 1 0 0 -1 -1 0 -2 -2 -1 -2 0]
[ 0 1 -1 -1 1 0 1 -1 0 0 0]
[ 0 0 0 0 0 1 -1 -1 0 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
69 ? x + y + z + x-1*y + y-1 + 2*x-1 + x-2*y*z-1 + x-1*y-1 + 2*x-2*z-1 + x-2*y-1*z-1
43 ? x + y + z + x-1*y + y-1 + 3*x-1 + x-2*y*z-1 + x-1*y-1 + 2*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 675
Image of polytope 675 PALP id: 675
grdb id: 427137
Integer points: [ 1 0 0 -1 0 -2 0 -2 -1 -1 0]
[ 0 1 -1 1 0 0 -1 -1 -1 0 0]
[ 0 0 0 0 1 -1 1 -1 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
131 ? x + y + z + x-1*y + y-1*z + y-1 + 3*x-1 + 2*x-1*y-1 + x-2*z-1 + x-2*y-1*z-1
87 ? x + y + z + x-1*y + y-1*z + y-1 + 2*x-1 + 2*x-1*y-1 + x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 676
Image of polytope 676 PALP id: 676
grdb id: 427481
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 1 0 -1 -2 0 -1 0]
[ 0 0 0 1 0 -1 0 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + x-1*y + y-1 + 2*x-1 + x-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 677
Image of polytope 677 PALP id: 677
grdb id: 254744
Integer points: [ 1 0 0 0 -1 0 -2 -1 -1 -1 0]
[ 0 1 -1 0 0 1 1 1 1 0 0]
[ 0 0 0 1 -1 1 0 1 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
87 ? y*z + x + y + z + x-1*y*z + 2*x-1*y + y-1 + 2*x-1 + x-2*y + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 678
Image of polytope 678 PALP id: 678
grdb id: 254743
Integer points: [ 1 0 0 0 0 -1 -1 -2 -1 -1 0]
[ 0 1 -1 0 -1 -1 0 -1 -1 0 0]
[ 0 0 0 1 -1 -1 1 0 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
126 ? x + y + z + x-1*z + y-1 + 2*x-1 + y-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 679
Image of polytope 679 PALP id: 679
grdb id: 254752
Integer points: [ 1 0 0 0 0 0 -1 -2 -1 -1 0]
[ 0 1 0 0 -1 -1 0 1 0 1 0]
[ 0 0 1 -1 0 1 1 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? x + y + z + 2*x-1*y + y-1*z + x-1*z + z-1 + y-1 + 2*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 680
Image of polytope 680 PALP id: 680
grdb id: 254750
Integer points: [ 1 0 0 0 0 0 -1 -2 -1 0 -1]
[ 0 1 0 0 -1 1 1 1 1 0 0]
[ 0 0 1 -1 0 1 1 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
147 ? y*z + x + y + z + x-1*y*z + 2*x-1*y + z-1 + y-1 + 2*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 681
Image of polytope 681 PALP id: 681
grdb id: 254751
Integer points: [ 1 0 0 1 -1 0 0 -2 -1 0 -1]
[ 0 1 0 0 0 0 -1 -1 0 0 -1]
[ 0 0 1 -1 1 -1 0 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
159 ? x + y + z + x*z-1 + x-1*z + z-1 + y-1 + 2*x-1 + 2*x-1*y-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 682
Image of polytope 682 PALP id: 682
grdb id: 426422
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 1 -1 1 0 0 0]
[ 0 0 0 1 0 0 -1 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
103 ? x + y + z + x-1*y + x-1*y*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 683
Image of polytope 683 PALP id: 683
grdb id: 426420
Integer points: [ 1 0 0 0 -1 0 -1 0 0 0 -1]
[ 0 1 0 0 0 -1 0 -1 -1 0 0]
[ 0 0 1 -1 -1 1 1 -1 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
32 ? x + y + z + y-1*z + x-1*z + z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 684
Image of polytope 684 PALP id: 684
grdb id: 254010
Integer points: [ 1 0 0 -1 0 0 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 -1 0 -1 -1 -1 0]
[ 0 0 0 0 1 -1 -1 -1 1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
28 rank 2, number 25 x + y + z + y-1 + x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 685
Image of polytope 685 PALP id: 685
grdb id: 254013
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 -1 1 0 1 0 -1 0 0]
[ 0 0 1 -1 1 -1 0 1 -1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
148 ? x + y + z + x-1*y*z + x-1*y + x-1*z + x-1 + y-1*z-1 + x-1*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Polytope 686
Image of polytope 686 PALP id: 686
grdb id: 254017
Integer points: [ 1 0 0 0 -1 1 -1 0 -1 -1 0]
[ 0 1 -1 0 1 -1 0 -1 -1 0 0]
[ 0 0 0 1 0 -1 1 -1 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
80 ? x + y + z + x-1*y + x-1*z + x*y-1*z-1 + y-1 + 2*x-1 + y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 5 Lattice Minkowski decompositions of facet 3
Polytope 687
Image of polytope 687 PALP id: 687
grdb id: 254009
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 1 1 -1 1 0 0 0]
[ 0 0 0 1 -1 0 0 -1 1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 6 1 none
Polytope 688
Image of polytope 688 PALP id: 688
grdb id: 254019
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 0 1 0 0 0]
[ 0 0 1 -1 0 0 1 0 -1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 5 1 none
Polytope 689
Image of polytope 689 PALP id: 689
grdb id: 254015
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 0 -1 1 0 0]
[ 0 0 1 -1 0 0 1 1 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
29 rank 2, number 23 x + y + z + x-1*y + x-1*z + z-1 + x-1*y*z-1 + y-1 + 2*x-1 + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 690
Image of polytope 690 PALP id: 690
grdb id: 254018
Integer points: [ 1 0 0 0 0 1 0 -1 -1 -1 0]
[ 0 1 0 0 -1 0 1 -1 1 0 0]
[ 0 0 1 -1 0 1 1 -1 1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
55 rank 2, number 19 x*z + y*z + x + y + z + x-1*y*z + z-1 + y-1 + 2*x-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 691
Image of polytope 691 PALP id: 691
grdb id: 254713
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 0 1 1 0 0]
[ 0 0 1 -1 0 -1 1 0 1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
37 rank 3, number 17 x + y + z + x-1*y*z + x-1*y + x-1*z + 2*x-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
69 ? x + y + z + x-1*y*z + x-1*y + x-1*z + 3*x-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 692
Image of polytope 692 PALP id: 692
grdb id: 254719
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 1 0 1 0 0]
[ 0 0 1 -1 0 1 -1 1 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
63 ? x + y + z + x-1*y + x-1*z + x-1*y*z-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
105 ? x + y + z + x-1*y + x-1*z + x-1*y*z-1 + 3*x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 693
Image of polytope 693 PALP id: 693
grdb id: 254721
Integer points: [ 1 0 0 -1 -1 -1 -1 0 -1 -1 0]
[ 0 1 0 0 -1 1 0 1 1 0 0]
[ 0 0 1 -1 0 0 1 1 1 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
158 ? y*z + x + y + z + x-1*y*z + x-1*y + x-1*z + x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 694
Image of polytope 694 PALP id: 694
grdb id: 254682
Integer points: [ 1 0 0 -1 -1 0 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 1 0 -1 0 0]
[ 0 0 1 -1 0 1 0 1 1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
57 ? x + y + z + x-1*y + y-1*z + x-1*z + x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 695
Image of polytope 695 PALP id: 695
grdb id: 254728
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 1 -1 1 0 0 0]
[ 0 0 0 1 -1 0 0 -1 1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? x + y + z + x-1*y + x-1*z + x-1*y*z-1 + y-1 + x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 696
Image of polytope 696 PALP id: 696
grdb id: 61980
Integer points: [ 1 0 0 0 -1 0 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 1 -1 0 0 0 0]
[ 0 0 0 1 1 -1 0 -1 1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + y*z-1 + x-1*z + y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 697
Image of polytope 697 PALP id: 697
grdb id: 61978
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 1 1 0 0 1 0 0]
[ 0 0 0 1 -1 0 -1 1 -1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + y*z-1 + x-1*y + x-1*z + x-1*y*z-1 + y-1 + 2*x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 698
Image of polytope 698 PALP id: 698
grdb id: 61971
Integer points: [ 1 0 0 0 0 -1 0 -1 -1 -1 0]
[ 0 1 0 -1 0 0 1 1 -1 0 0]
[ 0 0 1 0 -1 0 -1 -1 -1 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + y*z-1 + z-1 + x-1*y*z-1 + y-1 + x-1 + 2*x-1*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 699
Image of polytope 699 PALP id: 699
grdb id: 61968
Integer points: [ 1 0 0 0 0 -1 1 0 -1 -1 0]
[ 0 1 0 0 -1 1 -1 -1 -1 0 0]
[ 0 0 1 -1 0 0 -1 -1 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + x-1*y + x*y-1*z-1 + z-1 + y-1 + 2*x-1 + y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 700
Image of polytope 700 PALP id: 700
grdb id: 61969
Integer points: [ 1 0 0 0 0 1 0 -1 -1 -1 0]
[ 0 1 0 -1 0 -1 1 0 0 0 0]
[ 0 0 1 0 -1 0 -1 1 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + y*z-1 + x*y-1 + x-1*z + z-1 + y-1 + 2*x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 701
Image of polytope 701 PALP id: 701
grdb id: 61975
Integer points: [ 1 0 0 0 0 1 1 -1 -1 0 -1]
[ 0 1 -1 0 1 0 -1 -1 1 0 0]
[ 0 0 0 1 1 -1 -1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
60 rank 2, number 18 y*z + x + y + z + x*z-1 + x-1*y + x*y-1*z-1 + y-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 702
Image of polytope 702 PALP id: 702
grdb id: 61981
Integer points: [ 1 0 1 0 -1 0 -1 -1 -1 -1 0]
[ 0 1 -1 -1 1 0 0 1 -1 0 0]
[ 0 0 0 0 0 1 -1 1 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + x-1*y*z + x*y-1 + x-1*y + y-1 + 2*x-1 + x-1*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 703
Image of polytope 703 PALP id: 703
grdb id: 61970
Integer points: [ 1 0 1 0 -1 0 -1 -1 -1 -1 0]
[ 0 1 -1 -1 1 0 1 0 0 0 0]
[ 0 0 0 0 0 1 -1 -1 1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + x*y-1 + x-1*y + x-1*z + x-1*y*z-1 + y-1 + 2*x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 704
Image of polytope 704 PALP id: 704
grdb id: 61974
Integer points: [ 1 0 1 0 0 0 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 -1 1 0 0 0 0]
[ 0 0 0 1 -1 0 0 1 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
159 ? x + y + z + x*y-1 + x-1*y + x-1*z + z-1 + y-1 + 2*x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Polytope 705
Image of polytope 705 PALP id: 705
grdb id: 61967
Integer points: [ 1 0 0 -1 0 0 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 -1 0 1 2 1 0]
[ 0 0 0 0 1 1 -1 0 -1 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
66 rank 2, number 24 x + y + z + x-1*y2*z-1 + x-1*y + y-1*z + 2*x-1*y*z-1 + y-1 + x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 706
Image of polytope 706 PALP id: 706
grdb id: 254720
Integer points: [ 1 0 0 -1 -1 0 -1 -2 -2 -1 0]
[ 0 1 -1 1 -1 0 1 0 1 0 0]
[ 0 0 0 0 0 1 -1 -1 -1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
37 rank 3, number 17 x + y + z + x-1*y + x-1*y*z-1 + y-1 + x-1 + x-2*y*z-1 + x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 707
Image of polytope 707 PALP id: 707
grdb id: 61982
Integer points: [ 1 0 0 -1 0 -1 0 -1 -2 -1 0]
[ 0 1 -1 0 0 1 1 0 1 1 0]
[ 0 0 0 0 1 0 -1 -1 -1 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? x + y + z + y*z-1 + x-1*y + 2*x-1*y*z-1 + y-1 + x-1 + x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 708
Image of polytope 708 PALP id: 708
grdb id: 61983
Integer points: [ 1 0 0 -1 0 -1 0 -1 -1 -1 0]
[ 0 1 -1 0 0 0 -1 -1 -2 -1 0]
[ 0 0 0 0 1 -1 1 1 1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
160 ? x + y + z + y-1*z + y-1 + x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 709
Image of polytope 709 PALP id: 709
grdb id: 254716
Integer points: [ 1 0 0 0 -1 -1 -1 -2 -2 -1 0]
[ 0 1 -1 0 0 -1 1 0 1 0 0]
[ 0 0 0 1 -1 0 0 -1 -1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
160 ? x + y + z + x-1*y + y-1 + x-1 + x-1*z-1 + x-2*y*z-1 + x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 710
Image of polytope 710 PALP id: 710
grdb id: 254688
Integer points: [ 1 0 0 0 -1 -1 -1 -2 -2 -1 0]
[ 0 1 -1 0 0 1 -1 0 1 0 0]
[ 0 0 0 1 -1 0 -1 -1 -1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
47 ? x + y + z + x-1*y + y-1 + 2*x-1 + x-1*z-1 + x-2*y*z-1 + x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 711
Image of polytope 711 PALP id: 711
grdb id: 61979
Integer points: [ 1 0 0 0 0 -1 -1 -1 -2 -1 0]
[ 0 1 -1 0 1 -1 0 1 0 0 0]
[ 0 0 0 1 -1 0 -1 -1 -1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + y*z-1 + x-1*y*z-1 + y-1 + 2*x-1 + x-1*z-1 + x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 712
Image of polytope 712 PALP id: 712
grdb id: 254701
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 1 -1 -1 -2 0 0]
[ 0 0 0 1 -1 0 0 -1 -1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + x-1*y + y-1 + 2*x-1 + y-1*z-1 + x-1*y-1 + x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 713
Image of polytope 713 PALP id: 713
grdb id: 61976
Integer points: [ 1 0 0 1 0 0 -1 -1 -2 -1 0]
[ 0 1 -1 -1 0 -1 0 -1 0 0 0]
[ 0 0 0 0 1 -1 -1 -1 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + x*y-1 + y-1 + 2*x-1 + y-1*z-1 + x-1*z-1 + x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 714
Image of polytope 714 PALP id: 714
grdb id: 254575
Integer points: [ 1 0 0 -1 0 -1 0 -1 -1 -1 0]
[ 0 1 -1 0 0 -1 -1 0 -1 -1 0]
[ 0 0 0 0 1 -1 1 1 1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
63 ? x + y + z + y-1*z + x-1*z + y-1 + x-1 + x-1*y-1*z + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 715
Image of polytope 715 PALP id: 715
grdb id: 254612
Integer points: [ 1 0 0 -1 0 -1 0 -1 -1 -1 0]
[ 0 1 -1 0 0 0 -1 -1 -1 -1 0]
[ 0 0 0 0 1 -1 1 -1 1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? x + y + z + y-1*z + y-1 + x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 716
Image of polytope 716 PALP id: 716
grdb id: 254572
Integer points: [ 1 0 0 0 -1 -1 -1 0 -1 -1 0]
[ 0 1 -1 0 0 1 -1 -1 -1 0 0]
[ 0 0 0 1 -1 0 0 1 -1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + x-1*y + y-1*z + y-1 + 2*x-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 717
Image of polytope 717 PALP id: 717
grdb id: 254626
Integer points: [ 1 0 0 0 -1 -1 0 -1 -1 -1 0]
[ 0 1 -1 0 0 1 1 0 1 0 0]
[ 0 0 0 1 -1 0 1 1 1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
69 ? y*z + x + y + z + x-1*y*z + x-1*y + x-1*z + y-1 + 2*x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 718
Image of polytope 718 PALP id: 718
grdb id: 254610
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 1 1 0 0 0 0]
[ 0 0 0 1 1 -1 0 -1 1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + x-1*y + y-1*z + x-1*z + x-1*y*z-1 + y-1 + 2*x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 719
Image of polytope 719 PALP id: 719
grdb id: 254640
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 1 -1 1 0 1 0 0]
[ 0 0 0 1 -1 0 0 -1 -1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
103 ? x + y + z + y*z-1 + x-1*y + x-1*y*z-1 + y-1 + 2*x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 720
Image of polytope 720 PALP id: 720
grdb id: 254619
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 0 0 -1 -1 0 0]
[ 0 0 1 -1 0 -1 1 0 1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
147 ? x + y + z + x-1*z + z-1 + y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 721
Image of polytope 721 PALP id: 721
grdb id: 254615
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 -1 1 0 0 0]
[ 0 0 1 -1 0 1 0 0 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? y*z + x + y + z + x-1*y + z-1 + y-1 + 2*x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 722
Image of polytope 722 PALP id: 722
grdb id: 254624
Integer points: [ 1 0 0 0 0 1 0 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 -1 0 0 0 0]
[ 0 0 1 -1 0 0 1 1 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + x*y-1 + y-1*z + x-1*z + z-1 + y-1 + 2*x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 723
Image of polytope 723 PALP id: 723
grdb id: 254611
Integer points: [ 1 0 1 -1 0 -1 0 1 -1 0 0]
[ 0 1 -1 1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 1 -1 -1 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + x*y-1 + x-1*y + x*y-1*z-1 + y-1 + x-1 + 2*y-1*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 724
Image of polytope 724 PALP id: 724
grdb id: 254603
Integer points: [ 1 0 0 -1 -1 0 -2 -2 0 -1 0]
[ 0 1 -1 -1 1 0 0 -1 1 0 0]
[ 0 0 0 0 0 1 -1 -1 1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
43 ? y*z + x + y + z + x-1*y + y-1 + 3*x-1 + x-1*y-1 + x-2*z-1 + x-2*y-1*z-1
69 ? y*z + x + y + z + x-1*y + y-1 + 2*x-1 + x-1*y-1 + x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 10 irreducible and admissible
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Polytope 725
Image of polytope 725 PALP id: 725
grdb id: 254633
Integer points: [ 1 0 1 -1 0 0 -1 -2 -2 -1 0]
[ 0 1 -1 1 -1 0 0 1 0 0 0]
[ 0 0 0 0 0 1 -1 -1 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? x + y + z + x*y-1 + x-1*y + y-1 + 2*x-1 + x-1*z-1 + x-2*y*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 726
Image of polytope 726 PALP id: 726
grdb id: 254352
Integer points: [ 1 0 0 0 -1 -1 0 -1 -1 -1 0]
[ 0 1 -1 0 0 -1 1 1 -1 0 0]
[ 0 0 0 1 -1 -1 1 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
103 ? y*z + x + y + z + x-1*y + y-1 + 2*x-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 10 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 727
Image of polytope 727 PALP id: 727
grdb id: 254351
Integer points: [ 1 0 0 0 0 0 0 -1 -1 0 -1]
[ 0 1 0 1 -1 0 -1 1 -1 0 0]
[ 0 0 1 -1 1 -1 0 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
32 ? x + y + z + y*z-1 + x-1*y + y-1*z + z-1 + y-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 10 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 728
Image of polytope 728 PALP id: 728
grdb id: 674686
Integer points: [ 1 0 0 0 0 -1 0 -1 -1 -1 0]
[ 0 1 0 0 -1 0 1 1 0 -1 0]
[ 0 0 1 -1 0 0 -1 0 1 1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + y*z-1 + x-1*y + x-1*z + z-1 + y-1 + x-1 + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 5 Lattice Minkowski decompositions of facet 3
Polytope 729
Image of polytope 729 PALP id: 729
grdb id: 674687
Integer points: [ 1 0 0 0 0 -1 0 -1 1 1 0]
[ 0 1 0 0 -1 0 -1 0 1 1 0]
[ 0 0 1 -1 0 0 1 1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x*y + x*y*z-1 + x + y + z + y-1*z + x-1*z + z-1 + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 5 Lattice Minkowski decompositions of facet 3
Polytope 730
Image of polytope 730 PALP id: 730
grdb id: 674688
Integer points: [ 1 0 0 1 0 -1 0 -1 1 0 0]
[ 0 1 0 -1 0 1 -1 0 0 1 0]
[ 0 0 1 1 -1 -1 0 0 1 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x*z + x + y + x*y-1*z + z + y*z-1 + z-1 + x-1*y*z-1 + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 5 Lattice Minkowski decompositions of facet 3
Polytope 731
Image of polytope 731 PALP id: 731
grdb id: 674684
Integer points: [ 1 0 1 -1 -1 0 0 1 -1 0 0]
[ 0 1 -1 1 0 -1 0 -1 0 -1 0]
[ 0 0 0 0 0 0 1 -1 1 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + x*y-1 + x-1*y + x-1*z + x*y-1*z-1 + y-1 + x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 5 Lattice Minkowski decompositions of facet 3
Polytope 732
Image of polytope 732 PALP id: 732
grdb id: 674685
Integer points: [ 1 0 1 -1 0 0 0 -1 -1 0 0]
[ 0 1 -1 1 0 0 -1 0 0 -1 0]
[ 0 0 0 0 1 -1 0 0 -1 1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + x*y-1 + x-1*y + y-1*z + z-1 + y-1 + x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 5 Lattice Minkowski decompositions of facet 3
Polytope 733
Image of polytope 733 PALP id: 733
grdb id: 674683
Integer points: [ 1 0 0 0 0 -1 -1 0 -1 -1 0]
[ 0 1 0 0 -1 0 0 -1 -1 -1 0]
[ 0 0 1 -1 0 0 -1 -1 -1 -2 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
47 ? x + y + z + z-1 + y-1 + x-1 + y-1*z-1 + x-1*z-1 + x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 5 Lattice Minkowski decompositions of facet 3
Polytope 734
Image of polytope 734 PALP id: 734
grdb id: 674679
Integer points: [ 1 0 0 -1 1 -1 1 0 0 -1 0]
[ 0 1 0 1 0 0 -1 0 -1 0 0]
[ 0 0 1 1 -1 1 -1 -1 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
32 ? x + y + z + x-1*y*z + x*z-1 + x-1*z + x*y-1*z-1 + z-1 + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Polytope 735
Image of polytope 735 PALP id: 735
grdb id: 674677
Integer points: [ 1 0 0 0 0 -1 0 -1 -1 -1 0]
[ 0 1 0 0 -1 0 -1 0 -1 -1 0]
[ 0 0 1 -1 0 0 1 -1 0 1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + y-1*z + z-1 + y-1 + x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Polytope 736
Image of polytope 736 PALP id: 736
grdb id: 674673
Integer points: [ 1 0 0 0 0 -1 0 -1 -1 -1 0]
[ 0 1 0 0 -1 0 -1 1 0 1 0]
[ 0 0 1 -1 0 0 -1 0 1 1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + x-1*y*z + x-1*y + x-1*z + z-1 + y-1 + x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Polytope 737
Image of polytope 737 PALP id: 737
grdb id: 674680
Integer points: [ 1 0 0 0 0 0 0 -1 1 -1 0]
[ 0 1 0 1 -1 0 -1 0 0 1 0]
[ 0 0 1 -1 1 -1 0 0 1 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x*z + x + y + z + y*z-1 + y-1*z + z-1 + x-1*y*z-1 + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Polytope 738
Image of polytope 738 PALP id: 738
grdb id: 674678
Integer points: [ 1 0 1 -1 -1 0 0 0 -1 -1 0]
[ 0 1 -1 1 0 -1 0 -1 0 -1 0]
[ 0 0 0 0 0 0 1 -1 -1 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + x*y-1 + x-1*y + y-1 + x-1 + y-1*z-1 + x-1*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Polytope 739
Image of polytope 739 PALP id: 739
grdb id: 674658
Integer points: [ 1 0 0 0 0 -1 -1 0 -1 -1 0]
[ 0 1 0 0 -1 0 -1 -1 0 -1 0]
[ 0 0 1 -1 0 0 0 -1 -1 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
65 ? x + y + z + z-1 + y-1 + x-1 + y-1*z-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 10 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Polytope 740
Image of polytope 740 PALP id: 740
grdb id: 674662
Integer points: [ 1 0 0 0 0 0 0 -1 -1 -1 0]
[ 0 1 0 1 -1 0 -1 0 0 1 0]
[ 0 0 1 -1 1 -1 0 0 1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? x + y + z + y*z-1 + x-1*y + y-1*z + x-1*z + z-1 + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 10 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Polytope 741
Image of polytope 741 PALP id: 741
grdb id: 547501
Integer points: [ 1 0 0 -3 -2 -1 -2 -1 0 -1 0 0]
[ 0 1 1 -2 -1 0 -1 0 1 0 1 0]
[ 0 0 3 -3 -1 1 -2 0 2 -1 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
0 rank 1, B3 y*z3 + 3*y*z2 + 3*y*z + x + y + 3*x-1*z + 6*x-1 + 3*x-1*z-1 + 3*x-2*y-1*z-1 + 3*x-2*y-1*z-2 + x-3*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 9 3 irreducible and admissible
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Polytope 742
Image of polytope 742 PALP id: 742
grdb id: 547505
Integer points: [ 1 0 0 -2 -1 -1 0 0 -1 0 0 0]
[ 0 1 1 -3 -1 -2 0 -1 -1 1 0 1]
[ 0 0 3 -3 0 -2 1 -1 -1 2 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 9 2 irreducible and admissible
Image of facet 14 2 none
Polytope 743
Image of polytope 743 PALP id: 743
grdb id: 547504
Integer points: [ 1 0 2 -4 1 0 -1 -2 -3 1 0 -1]
[ 0 1 2 -4 1 0 -1 -2 -3 1 0 -1]
[ 0 0 3 -3 2 1 0 -1 -2 1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 2 2 none
Image of facet 53 2 irreducible and admissible
Polytope 744
Image of polytope 744 PALP id: 744
grdb id: 547506
Integer points: [ 1 1 0 -4 -2 -1 0 -1 0 1 0 1]
[ 0 3 0 -6 -3 -1 1 -2 0 2 -1 1]
[ 0 0 1 -1 0 0 0 0 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 9 2 irreducible and admissible
Image of facet 12 2 none
Polytope 745
Image of polytope 745 PALP id: 745
grdb id: 547500
Integer points: [ 1 0 0 -9 -6 -3 -5 -2 -1 -4 -1 0]
[ 0 1 0 -6 -4 -2 -3 -1 0 -3 -1 0]
[ 0 0 1 -2 -1 0 -1 0 0 -1 0 0]
Degree: 54
Hilbert function: 1 + 30 t + 140 t2 + 385 t3 + 819 t4 + 1496 t5 + 2470 t6 + 3795 t7 + 5525 t8 + 7714 t9 + 10416 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 14 1 none
Image of facet 54 1 none
Polytope 746
Image of polytope 746 PALP id: 746
grdb id: 546975
Integer points: [ 1 0 0 -3 -3 -3 -2 -2 -1 -1 -1 0]
[ 0 1 0 -2 0 -1 -1 0 0 -1 0 0]
[ 0 0 1 0 -2 -1 0 -1 0 0 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 55 1 none
Polytope 747
Image of polytope 747 PALP id: 747
grdb id: 546970
Integer points: [ 1 0 0 -3 -3 -3 -2 -2 -1 -1 -1 0]
[ 0 1 0 -1 -3 -2 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 1 0 1 0 1 0 0 0]
Degree: 48
Hilbert function: 1 + 27 t + 125 t2 + 343 t3 + 729 t4 + 1331 t5 + 2197 t6 + 3375 t7 + 4913 t8 + 6859 t9 + 9261 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 4 1 none
Image of facet 56 1 Lattice Minkowski decompositions of facet 56
Polytope 748
Image of polytope 748 PALP id: 748
grdb id: 546971
Integer points: [ 1 0 0 -1 -3 -2 -2 -1 -1 -1 0 0]
[ 0 1 0 -2 -2 -2 -1 -1 0 -1 -1 0]
[ 0 0 1 -2 0 -1 0 -1 0 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 14 1 none
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 9 1 irreducible and admissible
Polytope 749
Image of polytope 749 PALP id: 749
grdb id: 546946
Integer points: [ 1 0 0 -3 -1 -2 -1 -2 -1 0 -1 0]
[ 0 1 0 -2 2 0 1 -1 0 1 -1 0]
[ 0 0 1 0 -2 -1 -1 0 0 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 57 1 none
Polytope 750
Image of polytope 750 PALP id: 750
grdb id: 546965
Integer points: [ 1 0 0 -3 1 -2 -1 -1 0 -1 0 1]
[ 0 1 0 0 -2 0 0 -1 -1 0 0 -1]
[ 0 0 1 -2 2 -1 0 0 1 -1 0 1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Image of facet 9 1 irreducible and admissible
Polytope 751
Image of polytope 751 PALP id: 751
grdb id: 546981
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -3 2 1 0 -1 -2 1 0 -1]
[ 0 0 1 2 -3 -2 -1 0 1 -1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 2 2 none
Image of facet 43 1 irreducible and admissible
Image of facet 58 1 Lattice Minkowski decompositions of facet 58
Polytope 752
Image of polytope 752 PALP id: 752
grdb id: 546984
Integer points: [ 1 0 0 -1 -1 0 -1 -1 -1 0 0 0]
[ 0 1 1 -1 -1 1 -1 -1 -1 0 0 0]
[ 0 0 2 1 -3 1 0 -1 -2 1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 2 2 none
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 13 1 irreducible and admissible
Polytope 753
Image of polytope 753 PALP id: 753
grdb id: 546985
Integer points: [ 1 0 -1 0 -1 -1 -1 0 0 0 0 0]
[ 0 1 -1 1 -1 -1 -1 1 1 0 0 0]
[ 0 0 0 3 -3 -2 -1 1 2 -1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 9 2 irreducible and admissible
Image of facet 2 2 none
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 754
Image of polytope 754 PALP id: 754
grdb id: 546986
Integer points: [ 1 0 -1 1 -2 -1 0 -1 0 1 0 1]
[ 0 1 -1 0 0 0 0 0 0 0 0 0]
[ 0 0 0 3 -3 -1 1 -2 0 2 -1 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 9 4 irreducible and admissible
Image of facet 18 1 none
Polytope 755
Image of polytope 755 PALP id: 755
grdb id: 546982
Integer points: [ 1 1 -2 0 0 0 -1 1 0 -1 1 0]
[ 0 3 -3 0 2 1 -1 2 0 -2 1 -1]
[ 0 0 0 1 -1 0 0 0 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 9 4 irreducible and admissible
Image of facet 19 1 none
Polytope 756
Image of polytope 756 PALP id: 756
grdb id: 546977
Integer points: [ 1 0 1 -4 -1 -2 0 -3 -1 -2 1 0]
[ 0 1 0 -1 -1 -1 0 -1 0 0 0 0]
[ 0 0 2 -2 1 0 1 -1 0 -1 1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x*z2 + 2*x*z + x + y + 3*z + 3*x-1 + x-1*y-1*z + 2*x-2*z-1 + 3*x-2*y-1 + 3*x-3*y-1*z-1 + x-4*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 56 1 Lattice Minkowski decompositions of facet 56
Image of facet 1 3 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Polytope 757
Image of polytope 757 PALP id: 757
grdb id: 546966
Integer points: [ 1 0 0 -3 -5 -2 -1 -4 -3 -1 0 -2]
[ 0 1 0 -2 -4 -1 0 -3 -2 -1 0 -2]
[ 0 0 1 0 -2 0 0 -1 -1 0 0 -1]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 14 1 none
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 9 1 irreducible and admissible
Polytope 758
Image of polytope 758 PALP id: 758
grdb id: 546962
Integer points: [ 1 0 0 -3 -5 -4 -2 -3 -1 -1 -2 0]
[ 0 1 0 -2 -2 -2 -1 -1 0 -1 -1 0]
[ 0 0 1 0 -2 -1 0 -1 0 0 -1 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 61 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 759
Image of polytope 759 PALP id: 759
grdb id: 546980
Integer points: [ 1 1 -2 0 1 0 -1 1 0 -1 1 0]
[ 0 3 -3 0 4 1 -1 2 0 -2 1 -1]
[ 0 0 0 1 -1 0 0 0 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 9 4 irreducible and admissible
Image of facet 21 1 none
Polytope 760
Image of polytope 760 PALP id: 760
grdb id: 546953
Integer points: [ 1 1 0 -5 -1 -3 -2 -1 0 -1 0 1]
[ 0 2 0 -3 -1 -2 -1 0 1 -1 0 1]
[ 0 0 1 -1 1 0 0 0 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 4 1 none
Image of facet 62 1 none
Polytope 761
Image of polytope 761 PALP id: 761
grdb id: 546972
Integer points: [ 1 0 0 -2 -6 -2 -4 -1 -3 -1 -3 0]
[ 0 1 0 -2 -3 -1 -2 0 -1 -1 -2 0]
[ 0 0 1 -1 -2 0 -1 0 -1 0 -1 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 2 none
Polytope 762
Image of polytope 762 PALP id: 762
grdb id: 546956
Integer points: [ 1 0 -3 0 -7 -5 -2 -4 -1 -1 -3 0]
[ 0 1 -2 0 -4 -3 -1 -2 0 -1 -2 0]
[ 0 0 0 1 -2 -1 0 -1 0 0 -1 0]
Degree: 48
Hilbert function: 1 + 27 t + 125 t2 + 343 t3 + 729 t4 + 1331 t5 + 2197 t6 + 3375 t7 + 4913 t8 + 6859 t9 + 9261 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 63 1 none
Polytope 763
Image of polytope 763 PALP id: 763
grdb id: 546951
Integer points: [ 1 0 0 -5 -8 -6 -4 -2 -3 -1 -2 0]
[ 0 1 0 -2 -4 -3 -2 -1 -1 0 -1 0]
[ 0 0 1 -2 -3 -2 -1 0 -1 0 -1 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 64 1 none
Polytope 764
Image of polytope 764 PALP id: 764
grdb id: 546751
Integer points: [ 1 0 0 -2 -2 -1 -2 -1 -2 -1 -2 0]
[ 0 1 0 -2 2 1 1 0 0 -1 -1 0]
[ 0 0 1 -1 -1 0 -1 0 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
29 rank 2, number 23 x + y + z + 2*x-1*y + x-2*y2*z-1 + 4*x-1 + 4*x-2*y*z-1 + 2*x-1*y-1 + 6*x-2*z-1 + 4*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 765
Image of polytope 765 PALP id: 765
grdb id: 546813
Integer points: [ 1 0 0 -3 -3 -2 -1 -3 -2 -1 0 -1]
[ 0 1 0 -2 -2 -1 0 -2 -1 -1 0 -1]
[ 0 0 1 0 -2 0 0 -1 -1 0 0 -1]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 14 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Polytope 766
Image of polytope 766 PALP id: 766
grdb id: 546827
Integer points: [ 1 0 0 -2 0 -1 0 -1 0 0 -1 0]
[ 0 1 0 1 -3 -1 -2 0 -1 -1 1 0]
[ 0 0 1 0 -2 -1 -1 0 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 14 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Polytope 767
Image of polytope 767 PALP id: 767
grdb id: 546826
Integer points: [ 1 0 0 -1 -3 -2 -1 -2 -1 -1 0 0]
[ 0 1 0 -2 0 0 0 -1 -1 0 0 -1]
[ 0 0 1 0 -2 -1 0 -1 0 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 14 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Polytope 768
Image of polytope 768 PALP id: 768
grdb id: 546850
Integer points: [ 1 -1 0 0 0 0 0 0 0 0 0 0]
[ 0 0 1 1 -2 -1 0 -1 0 1 0 1]
[ 0 0 0 3 -3 -1 1 -2 0 2 -1 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
45 ? y*z3 + 3*y*z2 + 3*y*z + x + y + 3*z + 3*z-1 + x-1 + 3*y-1*z-1 + 3*y-1*z-2 + y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 9 6 irreducible and admissible
Polytope 769
Image of polytope 769 PALP id: 769
grdb id: 546852
Integer points: [ 1 0 0 -2 1 0 -1 1 0 -1 1 0]
[ 0 1 0 3 -3 -1 1 -2 0 2 -1 1]
[ 0 0 1 3 -3 -1 1 -2 0 2 -1 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
141 ? x-2*y3*z3 + 3*x-1*y2*z2 + 3*y*z + x + y + z + 3*x-1*y*z + 3*x*y-1*z-1 + 3*y-1*z-1 + 3*x*y-2*z-2 + x*y-3*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 9 6 irreducible and admissible
Polytope 770
Image of polytope 770 PALP id: 770
grdb id: 546851
Integer points: [ 1 1 -2 0 1 1 1 0 0 0 -1 -1]
[ 0 3 -3 0 0 1 2 -1 0 1 -2 -1]
[ 0 0 0 1 -1 0 0 0 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
116 ? x*y3 + 3*x*y2 + 3*x*y + x + 3*y + z + x*z-1 + 3*y-1 + 3*x-1*y-1 + 3*x-1*y-2 + x-2*y-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 9 6 irreducible and admissible
Polytope 771
Image of polytope 771 PALP id: 771
grdb id: 546830
Integer points: [ 1 0 0 0 -6 -4 -2 -3 -1 -3 -1 0]
[ 0 1 -1 0 3 2 1 1 0 2 1 0]
[ 0 0 0 1 -2 -1 0 -1 0 -1 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 14 2 none
Polytope 772
Image of polytope 772 PALP id: 772
grdb id: 541770
Integer points: [ 1 0 0 -1 0 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 -3 -2 -1 0 -2 -1 -1 0]
[ 0 0 1 1 -2 -2 -1 0 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 9 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 5 1 none
Polytope 773
Image of polytope 773 PALP id: 773
grdb id: 541768
Integer points: [ 1 0 0 -2 2 -1 -1 0 1 -1 0 1]
[ 0 1 0 2 -3 0 1 -1 -2 1 0 -1]
[ 0 0 1 1 -1 -1 1 -1 -1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 2 2 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 774
Image of polytope 774 PALP id: 774
grdb id: 541766
Integer points: [ 1 0 0 -1 2 -2 -1 0 1 -1 0 1]
[ 0 1 0 1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 1 1 -3 1 0 -1 -2 1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 49 2 Lattice Minkowski decompositions of facet 49
Image of facet 2 2 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 775
Image of polytope 775 PALP id: 775
grdb id: 541769
Integer points: [ 1 1 0 -1 0 -1 0 0 -1 0 1 0]
[ 0 2 0 -3 2 -1 1 1 -2 0 1 -1]
[ 0 0 1 -1 1 -1 0 1 -1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 2 2 none
Image of facet 15 3 Lattice Minkowski decompositions of facet 15
Polytope 776
Image of polytope 776 PALP id: 776
grdb id: 541681
Integer points: [ 1 0 0 -2 -2 -1 -1 -1 -1 -2 0 0]
[ 0 1 0 0 -2 2 1 0 -1 -1 1 0]
[ 0 0 1 -1 1 -2 -1 0 1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + 2*y*z-1 + x-1*y2*z-2 + 3*x-1*y*z-1 + 3*x-1 + 2*x-1*y-1*z + x-2*z-1 + 2*x-2*y-1 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Polytope 777
Image of polytope 777 PALP id: 777
grdb id: 541758
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -2 2 2 -1 0 1 -1 0 1]
[ 0 0 1 -2 1 2 -1 0 1 -1 0 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 5 1 none
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Polytope 778
Image of polytope 778 PALP id: 778
grdb id: 541751
Integer points: [ 1 0 0 0 -1 -2 -1 -1 0 -1 0 0]
[ 0 1 0 2 -2 -2 0 -1 1 -1 0 -1]
[ 0 0 1 1 -2 -1 0 -1 1 0 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 8 1 none
Polytope 779
Image of polytope 779 PALP id: 779
grdb id: 541757
Integer points: [ 1 0 1 0 -1 -1 0 0 0 -1 -1 -1]
[ 0 1 -1 0 2 -2 1 0 -1 1 0 -1]
[ 0 0 0 1 -2 2 -1 0 1 -1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 6 1 none
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Polytope 780
Image of polytope 780 PALP id: 780
grdb id: 541741
Integer points: [ 1 1 -2 0 1 0 0 -1 0 1 -1 0]
[ 0 2 -1 0 -1 -2 -1 -1 0 1 0 1]
[ 0 0 0 1 -1 -1 0 0 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 4 1 none
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Polytope 781
Image of polytope 781 PALP id: 781
grdb id: 541749
Integer points: [ 1 1 -1 0 -1 -2 -1 0 -1 0 1 0]
[ 0 2 -2 0 1 0 0 1 -1 0 1 -1]
[ 0 0 0 1 -1 -1 0 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 1 none
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 4 1 none
Polytope 782
Image of polytope 782 PALP id: 782
grdb id: 541692
Integer points: [ 1 0 0 -2 -3 -3 -1 -2 -1 -2 0 -1]
[ 0 1 0 0 -2 -3 0 -1 -1 -2 0 -1]
[ 0 0 1 -1 -2 -2 0 -1 0 -1 0 -1]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? x + y + z + 2*x-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + 3*x-2*y-1*z-1 + 3*x-2*y-2*z-1 + x-3*y-2*z-2 + x-3*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 9 1 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 783
Image of polytope 783 PALP id: 783
grdb id: 541745
Integer points: [ 1 0 0 -1 -3 -3 -2 -1 -2 -1 -1 0]
[ 0 1 0 0 -2 -3 -1 0 -2 -1 -1 0]
[ 0 0 1 -1 0 1 0 0 1 1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 6 1 none
Polytope 784
Image of polytope 784 PALP id: 784
grdb id: 541629
Integer points: [ 1 0 0 0 -1 -3 -2 -1 -2 -1 -1 0]
[ 0 1 0 -1 1 -3 -1 0 -2 -1 -1 0]
[ 0 0 1 -1 0 -2 -1 0 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 8 1 none
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 14 1 none
Polytope 785
Image of polytope 785 PALP id: 785
grdb id: 541661
Integer points: [ 1 0 0 1 -2 1 0 0 -1 -1 1 0]
[ 0 1 0 -2 0 -3 -1 -2 0 -1 -1 0]
[ 0 0 1 0 -1 -1 0 -1 0 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
25 ? x + y + z + 2*x*y-1 + x*y-2 + 3*y-1 + 2*x-1 + x*y-3*z-1 + 3*y-2*z-1 + 3*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 786
Image of polytope 786 PALP id: 786
grdb id: 541686
Integer points: [ 1 0 0 -2 -1 -2 -2 -1 -2 -1 0 0]
[ 0 1 0 0 -2 -3 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 2 2 1 1 0 0 1 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 66 1 none
Image of facet 9 1 irreducible and admissible
Polytope 787
Image of polytope 787 PALP id: 787
grdb id: 541694
Integer points: [ 1 0 0 -2 0 -3 -1 0 -1 -2 0 -1]
[ 0 1 0 0 2 -2 1 1 0 -1 0 -1]
[ 0 0 1 -1 1 -2 0 1 0 -1 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 37 1 none
Polytope 788
Image of polytope 788 PALP id: 788
grdb id: 541725
Integer points: [ 1 0 1 -3 -2 1 0 -1 -2 1 0 -1]
[ 0 1 0 0 -1 1 0 0 0 0 0 0]
[ 0 0 2 -2 0 1 1 0 -1 1 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 67 1 none
Polytope 789
Image of polytope 789 PALP id: 789
grdb id: 541719
Integer points: [ 1 1 -3 0 -3 -1 -2 -1 0 -1 0 1]
[ 0 2 -2 0 -2 -1 -1 0 1 -1 0 1]
[ 0 0 0 1 -1 1 0 0 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 6 1 none
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Polytope 790
Image of polytope 790 PALP id: 790
grdb id: 541662
Integer points: [ 1 1 -3 0 -1 1 0 -1 -2 1 0 -1]
[ 0 2 -2 0 1 1 1 0 -1 1 0 -1]
[ 0 0 0 1 -1 1 0 0 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 68 1 none
Polytope 791
Image of polytope 791 PALP id: 791
grdb id: 541576
Integer points: [ 1 1 -3 0 0 1 0 -1 -2 1 0 -1]
[ 0 2 -2 0 2 1 1 0 -1 1 0 -1]
[ 0 0 0 1 -1 1 0 0 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 69 1 none
Polytope 792
Image of polytope 792 PALP id: 792
grdb id: 541672
Integer points: [ 1 0 0 -4 0 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 -2 -1 -2 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 1 1 1 0 0 0 0 0]
Degree: 54
Hilbert function: 1 + 30 t + 140 t2 + 385 t3 + 819 t4 + 1496 t5 + 2470 t6 + 3795 t7 + 5525 t8 + 7714 t9 + 10416 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 37 1 none
Image of facet 8 1 none
Polytope 793
Image of polytope 793 PALP id: 793
grdb id: 541695
Integer points: [ 1 0 0 -1 -3 -4 -3 -2 -2 -1 -1 0]
[ 0 1 0 1 -2 -2 -1 -1 0 0 -1 0]
[ 0 0 1 -1 0 -1 -1 0 -1 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
37 rank 3, number 17 x + y + z + x-1*y*z-1 + 2*x-1 + 2*x-1*y-1 + 3*x-2*z-1 + 2*x-2*y-1 + 3*x-3*y-1*z-1 + x-3*y-2 + x-4*y-2*z-1
43 ? x + y + z + x-1*y*z-1 + 4*x-1 + 2*x-1*y-1 + 3*x-2*z-1 + 3*x-2*y-1 + 3*x-3*y-1*z-1 + x-3*y-2 + x-4*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Image of facet 9 1 irreducible and admissible
Polytope 794
Image of polytope 794 PALP id: 794
grdb id: 541630
Integer points: [ 1 0 0 0 -1 -4 -2 -3 -1 -2 -1 0]
[ 0 1 -1 0 -1 2 1 1 0 0 1 0]
[ 0 0 0 1 -1 -1 0 -1 0 -1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 4 1 none
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 795
Image of polytope 795 PALP id: 795
grdb id: 541660
Integer points: [ 1 0 1 0 -3 -4 -2 -1 0 -1 0 1]
[ 0 1 -2 0 1 2 1 0 -1 1 0 -1]
[ 0 0 0 1 -1 -1 0 0 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 26 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 4 1 none
Polytope 796
Image of polytope 796 PALP id: 796
grdb id: 541737
Integer points: [ 1 0 0 -4 -4 -5 -3 -2 -2 -1 -2 0]
[ 0 1 0 -1 -2 -2 -1 -1 0 0 -1 0]
[ 0 0 1 -2 -1 -2 -1 0 -1 0 -1 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
74 ? x + y + z + x-1 + 2*x-2*z-1 + 2*x-2*y-1 + 2*x-2*y-1*z-1 + 2*x-3*y-1*z-1 + x-4*y-1*z-2 + x-4*y-2*z-1 + x-5*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 71 1 Lattice Minkowski decompositions of facet 71
Polytope 797
Image of polytope 797 PALP id: 797
grdb id: 541647
Integer points: [ 1 0 0 -3 -1 -5 -3 -2 -4 -1 -1 0]
[ 0 1 0 -1 -1 -3 -2 -1 -2 0 -1 0]
[ 0 0 1 -1 1 -1 0 0 -1 0 0 0]
Degree: 48
Hilbert function: 1 + 27 t + 125 t2 + 343 t3 + 729 t4 + 1331 t5 + 2197 t6 + 3375 t7 + 4913 t8 + 6859 t9 + 9261 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 4 1 none
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Polytope 798
Image of polytope 798 PALP id: 798
grdb id: 541690
Integer points: [ 1 0 0 -2 -3 -5 -2 -4 -1 -3 -1 0]
[ 0 1 0 0 -2 -3 -1 -2 0 -1 -1 0]
[ 0 0 1 -1 0 -1 0 -1 0 -1 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
155 ? x + y + z + 2*x-1 + 2*x-1*y-1 + x-2*z-1 + 2*x-2*y-1 + 3*x-3*y-1*z-1 + x-3*y-2 + 3*x-4*y-2*z-1 + x-5*y-3*z-1
139 ? x + y + z + 3*x-1 + 2*x-1*y-1 + x-2*z-1 + 4*x-2*y-1 + 3*x-3*y-1*z-1 + x-3*y-2 + 3*x-4*y-2*z-1 + x-5*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Image of facet 9 1 irreducible and admissible
Polytope 799
Image of polytope 799 PALP id: 799
grdb id: 541753
Integer points: [ 1 -1 0 0 3 4 2 1 2 3 0 1]
[ 0 0 1 0 -2 -4 -1 -1 -2 -3 0 -1]
[ 0 0 0 1 -2 -3 -1 0 -1 -2 0 -1]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 13 1 irreducible and admissible
Image of facet 6 1 none
Polytope 800
Image of polytope 800 PALP id: 800
grdb id: 541196
Integer points: [ 1 0 -1 0 -2 0 -1 0 -1 -1 0 0]
[ 0 1 1 0 -2 -2 -2 -1 -1 0 -1 0]
[ 0 0 0 1 -1 1 0 1 0 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 4 1 none
Image of facet 37 1 none
Polytope 801
Image of polytope 801 PALP id: 801
grdb id: 541398
Integer points: [ 1 0 0 0 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 -1 0 1 -1 0 -1 0 0 1 0]
[ 0 0 0 1 0 -2 -1 -1 0 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + 2*x-1*y + y-1 + 2*x-1 + x-2*y + 2*x-1*z-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 802
Image of polytope 802 PALP id: 802
grdb id: 541397
Integer points: [ 1 0 -2 0 2 0 0 1 1 -1 0 -1]
[ 0 1 1 0 -2 -2 -1 -1 -2 0 0 1]
[ 0 0 0 1 -1 -1 0 0 -1 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 4 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 803
Image of polytope 803 PALP id: 803
grdb id: 541393
Integer points: [ 1 0 -1 0 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 -1 0 2 -2 1 0 -1 1 0 -1]
[ 0 0 0 1 -2 2 -1 0 1 -1 0 1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
124 ? x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 4*x-1*y*z-1 + 6*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Polytope 804
Image of polytope 804 PALP id: 804
grdb id: 540968
Integer points: [ 1 0 0 -2 -1 -2 -1 -1 -2 -1 0 0]
[ 0 1 0 0 -2 2 1 0 1 -1 0 -1]
[ 0 0 1 -1 0 -1 0 0 -1 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 37 1 none
Polytope 805
Image of polytope 805 PALP id: 805
grdb id: 541365
Integer points: [ 1 0 0 -2 0 -2 -1 0 -1 -2 -1 0]
[ 0 1 0 2 -2 0 1 -1 0 1 -1 0]
[ 0 0 1 -1 1 -1 0 1 0 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
29 rank 2, number 23 x + y + z + 2*x-1*y + 2*y-1*z + x-2*y2*z-1 + 4*x-1 + y-2*z + 2*x-2*y*z-1 + 2*x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Polytope 806
Image of polytope 806 PALP id: 806
grdb id: 541058
Integer points: [ 1 0 0 0 -2 -2 -1 -2 -1 -2 -1 0]
[ 0 1 0 -1 -1 2 1 1 0 0 -1 0]
[ 0 0 1 1 -1 -1 0 -1 0 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
29 rank 2, number 23 x + y + z + 2*x-1*y + y-1*z + x-2*y2*z-1 + 4*x-1 + 3*x-2*y*z-1 + 2*x-1*y-1 + 3*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 9 1 irreducible and admissible
Polytope 807
Image of polytope 807 PALP id: 807
grdb id: 541378
Integer points: [ 1 0 0 0 -2 2 1 -1 0 0 1 -1]
[ 0 1 -1 0 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 0 1 0 -2 -1 0 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
60 rank 2, number 18 x + y + z + 2*x*z-1 + x2*y-1*z-2 + 2*x*y-1*z-1 + y-1 + 2*x-1 + 2*y-1*z-1 + 2*x-1*y-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 808
Image of polytope 808 PALP id: 808
grdb id: 541389
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 -1 0 2 -2 1 0 -1 1 0 -1]
[ 0 0 0 1 -2 2 -1 0 1 -1 0 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
91 ? x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 4*x-1*y*z-1 + y-1 + 6*x-1 + 4*x-1*y-1*z + x-1*y-2*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Polytope 809
Image of polytope 809 PALP id: 809
grdb id: 541429
Integer points: [ 1 0 0 0 0 -2 -1 -1 0 -1 0 0]
[ 0 1 0 0 -2 2 0 1 -1 1 -1 0]
[ 0 0 1 -1 1 -1 0 -1 0 0 1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + 2*x-1*y + 2*y-1*z + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 2*x-1 + y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 810
Image of polytope 810 PALP id: 810
grdb id: 541067
Integer points: [ 1 0 0 -2 -1 -2 -1 -1 -2 -2 0 0]
[ 0 1 0 0 -2 -3 0 -1 -1 -2 0 -1]
[ 0 0 1 -1 0 -1 0 0 -1 -1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
95 ? x + y + z + 2*y-1 + 2*x-1 + 3*x-1*y-1 + x-2*z-1 + x-1*y-2 + 3*x-2*y-1*z-1 + 3*x-2*y-2*z-1 + x-2*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 811
Image of polytope 811 PALP id: 811
grdb id: 541431
Integer points: [ 1 0 0 0 -3 -3 -2 -1 -2 -1 -1 0]
[ 0 1 0 -1 0 -1 0 0 -1 -1 0 0]
[ 0 0 1 1 -2 -2 -1 0 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
77 ? x + y + z + y-1*z + 3*x-1 + 2*x-1*z-1 + 3*x-1*y-1 + 3*x-2*z-1 + 3*x-2*y-1*z-1 + x-3*z-2 + x-3*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 9 2 irreducible and admissible
Polytope 812
Image of polytope 812 PALP id: 812
grdb id: 541418
Integer points: [ 1 0 0 0 -2 -2 -1 -1 -2 0 -1 -1]
[ 0 1 -1 0 -1 -3 -2 -1 -2 0 -1 0]
[ 0 0 0 1 0 -2 -1 0 -1 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
76 ? x + y + z + y-1 + 2*x-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + 2*x-1*y-2*z-1 + 2*x-2*y-2*z-1 + x-2*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 813
Image of polytope 813 PALP id: 813
grdb id: 541011
Integer points: [ 1 0 0 0 -1 -3 -1 -1 -2 -2 0 -1]
[ 0 1 -1 0 -2 0 -1 0 -1 0 0 0]
[ 0 0 0 1 -1 1 0 1 0 1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 4 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 814
Image of polytope 814 PALP id: 814
grdb id: 541434
Integer points: [ 1 0 0 0 2 -3 1 -1 -2 1 0 -1]
[ 0 1 -1 0 -1 0 -1 0 0 0 0 0]
[ 0 0 0 1 2 -2 1 0 -1 1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
94 ? x2*y-1*z2 + 2*x*z + x + y + 2*x*y-1*z + z + y-1 + 3*x-1 + 2*x-1*z-1 + 3*x-2*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 5 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 9 1 irreducible and admissible
Polytope 815
Image of polytope 815 PALP id: 815
grdb id: 541386
Integer points: [ 1 0 0 1 -3 1 0 -1 -2 1 0 -1]
[ 0 1 0 2 -2 2 1 0 -1 1 0 -1]
[ 0 0 1 2 -2 1 1 0 -1 1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
162 ? x*y2*z2 + x*y2*z + 2*x*y*z + 4*y*z + x + y + z + 6*x-1 + 2*x-1*y-1*z-1 + 4*x-2*y-1*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Polytope 816
Image of polytope 816 PALP id: 816
grdb id: 541377
Integer points: [ 1 0 0 -2 0 -4 -3 -1 -2 -1 -2 0]
[ 0 1 -1 -1 0 -3 -2 -1 -2 0 -1 0]
[ 0 0 0 0 1 -2 -1 0 -1 0 -1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
105 ? x + y + z + y-1 + 2*x-1 + 2*x-1*y-1 + x-2*y-1 + 2*x-2*y-1*z-1 + 2*x-2*y-2*z-1 + 2*x-3*y-2*z-1 + x-4*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 817
Image of polytope 817 PALP id: 817
grdb id: 541066
Integer points: [ 1 0 0 -1 -2 -4 -3 -2 -1 -2 -1 0]
[ 0 1 0 0 -2 -3 -2 -1 -1 -1 0 0]
[ 0 0 1 1 -1 -2 -1 0 0 -1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 14 1 none
Polytope 818
Image of polytope 818 PALP id: 818
grdb id: 541426
Integer points: [ 1 0 0 0 -2 -4 -3 -1 -2 -1 -2 0]
[ 0 1 -1 0 1 1 1 0 0 1 1 0]
[ 0 0 0 1 0 -2 -1 0 -1 0 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
69 ? x + y + z + 2*x-1*y + y-1 + 2*x-1 + x-2*y + 2*x-2*y*z-1 + 2*x-2*z-1 + 2*x-3*y*z-1 + x-4*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 819
Image of polytope 819 PALP id: 819
grdb id: 540304
Integer points: [ 1 0 0 0 -2 -2 -1 -1 -2 0 -1 -1]
[ 0 1 -1 0 1 1 0 1 1 0 0 1]
[ 0 0 0 1 0 -2 0 0 -1 0 -1 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
103 ? x + y + z + 2*x-1*y + 2*x-1*y*z-1 + y-1 + 2*x-1 + x-2*y + 2*x-1*z-1 + 2*x-2*y*z-1 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 820
Image of polytope 820 PALP id: 820
grdb id: 540280
Integer points: [ 1 0 0 0 -2 0 0 -1 -1 0 0 -1]
[ 0 1 0 0 0 -2 -1 -1 0 -1 0 0]
[ 0 0 1 -1 1 -1 0 0 1 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + 2*x-1*z + z-1 + 2*y-1 + 2*x-1 + x-2*z + 2*y-1*z-1 + 2*x-1*y-1 + y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 821
Image of polytope 821 PALP id: 821
grdb id: 540271
Integer points: [ 1 0 0 0 0 -2 -1 -1 0 -1 0 0]
[ 0 1 0 0 -2 0 -1 0 -1 0 -1 0]
[ 0 0 1 -1 1 1 1 0 0 1 1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
32 ? x + y + z + 2*y-1*z + 2*x-1*z + z-1 + 2*y-1 + 2*x-1 + y-2*z + 2*x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 822
Image of polytope 822 PALP id: 822
grdb id: 513290
Integer points: [ 1 0 0 0 -1 0 -1 0 -1 -1 0 0]
[ 0 1 0 0 1 -2 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 -1 1 2 0 1 0 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 5 1 none
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 823
Image of polytope 823 PALP id: 823
grdb id: 513288
Integer points: [ 1 0 0 -1 1 1 -1 0 0 -1 1 0]
[ 0 1 0 1 -2 -3 -1 -1 -2 0 -1 0]
[ 0 0 1 1 0 -1 -1 0 -1 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
25 ? x + y + z + x-1*y*z + 2*x*y-1 + x*y-2 + 3*y-1 + 2*x-1 + x*y-3*z-1 + 2*y-2*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 824
Image of polytope 824 PALP id: 824
grdb id: 513286
Integer points: [ 1 0 0 0 -1 -1 -3 -2 -2 -1 -1 0]
[ 0 1 -1 0 -1 1 1 1 0 0 1 0]
[ 0 0 0 1 -1 1 -1 0 -1 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 4 1 none
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 825
Image of polytope 825 PALP id: 825
grdb id: 513259
Integer points: [ 1 0 0 -1 -2 -1 -2 -1 -2 -1 0 0]
[ 0 1 0 -1 0 -2 -2 0 -1 -1 0 -1]
[ 0 0 1 -1 -1 0 -1 0 -1 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
164 ? x + y + z + 2*y-1 + 2*x-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-2*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 826
Image of polytope 826 PALP id: 826
grdb id: 513240
Integer points: [ 1 0 0 -1 -2 -1 -2 -1 -1 -1 0 0]
[ 0 1 0 0 -1 -2 -2 -1 0 -1 0 -1]
[ 0 0 1 1 0 -2 -1 0 0 -1 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 8 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 827
Image of polytope 827 PALP id: 827
grdb id: 513250
Integer points: [ 1 0 0 -1 -1 -2 -2 -2 -1 -1 -1 0]
[ 0 1 0 -1 1 -2 0 -1 0 0 -1 0]
[ 0 0 1 -1 1 -1 1 0 0 1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
69 ? x + y + z + x-1*y*z + 2*x-1*z + 3*x-1 + x-2*z + 2*x-1*y-1 + x-1*y-1*z-1 + 2*x-2*y-1 + x-2*y-2*z-1
37 rank 3, number 17 x + y + z + x-1*y*z + 2*x-1*z + 2*x-1 + x-2*z + 2*x-1*y-1 + x-1*y-1*z-1 + 2*x-2*y-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 828
Image of polytope 828 PALP id: 828
grdb id: 513257
Integer points: [ 1 0 0 -1 -1 -1 -1 0 -1 -1 0 -1]
[ 0 1 0 1 -1 -1 -2 -1 0 -1 0 0]
[ 0 0 1 -1 -1 1 0 0 -1 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 829
Image of polytope 829 PALP id: 829
grdb id: 513211
Integer points: [ 1 0 0 -1 0 -2 -2 -2 -1 -1 -1 0]
[ 0 1 0 0 -1 0 -2 -1 0 -1 -1 0]
[ 0 0 1 -1 -1 -1 -1 -1 0 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 830
Image of polytope 830 PALP id: 830
grdb id: 513201
Integer points: [ 1 0 0 0 -2 -1 -2 -1 -1 -1 0 0]
[ 0 1 -1 0 0 -2 -1 -1 0 0 -1 0]
[ 0 0 0 1 -1 -2 -2 -1 0 -1 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + y-1 + 2*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1*z-1 + x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
50 ? x + y + z + y-1 + 2*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1*z-1 + x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 831
Image of polytope 831 PALP id: 831
grdb id: 513207
Integer points: [ 1 0 0 0 -1 -2 -2 -1 -1 -2 0 -1]
[ 0 1 -1 0 -1 -2 0 0 -1 -1 0 0]
[ 0 0 0 1 -1 -1 1 1 0 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 8 1 none
Polytope 832
Image of polytope 832 PALP id: 832
grdb id: 513258
Integer points: [ 1 0 0 1 -2 -1 -2 -1 0 -1 -1 0]
[ 0 1 0 -1 1 -1 0 0 -1 0 1 0]
[ 0 0 1 -1 0 1 1 0 0 1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 8 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 833
Image of polytope 833 PALP id: 833
grdb id: 513268
Integer points: [ 1 0 0 1 1 -1 -2 0 -1 0 -1 0]
[ 0 1 0 1 -1 1 -1 1 0 0 -1 -1]
[ 0 0 1 -1 0 -1 0 -1 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 6 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 834
Image of polytope 834 PALP id: 834
grdb id: 513253
Integer points: [ 1 0 1 -2 0 -1 0 0 -1 1 0 -1]
[ 0 1 -2 1 0 -1 -2 -1 0 -1 0 1]
[ 0 0 0 0 1 -1 -1 0 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 28 1 none
Polytope 835
Image of polytope 835 PALP id: 835
grdb id: 513263
Integer points: [ 1 0 1 0 -1 0 -1 0 -1 -1 0 0]
[ 0 1 -1 0 1 -2 -2 -1 -1 0 -1 0]
[ 0 0 0 1 1 -1 -2 0 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y*z + x*y-1 + 2*y-1 + 3*x-1 + 2*y-1*z-1 + y-2*z-1 + 3*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 836
Image of polytope 836 PALP id: 836
grdb id: 513242
Integer points: [ 1 0 -2 0 2 -1 1 0 1 -1 0 -1]
[ 0 1 1 0 -2 0 -2 -1 -1 0 0 1]
[ 0 0 0 1 -1 1 -1 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 4 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 837
Image of polytope 837 PALP id: 837
grdb id: 513035
Integer points: [ 1 0 -1 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -2 0 2 -1 0 1 0 -1 0 -1]
[ 0 0 0 1 -1 1 1 0 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 26 1 none
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 838
Image of polytope 838 PALP id: 838
grdb id: 513271
Integer points: [ 1 0 0 -1 0 -2 1 0 -1 -1 0 1]
[ 0 1 -1 0 0 -1 2 1 0 -1 0 1]
[ 0 0 0 0 1 -2 2 1 -1 -1 0 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x*y2*z2 + 2*x*y*z + 2*y*z + x + y + z + y-1 + x-1 + 2*x-1*z-1 + 2*x-1*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 839
Image of polytope 839 PALP id: 839
grdb id: 513231
Integer points: [ 1 0 0 0 -2 -1 -2 -1 -1 -2 0 -1]
[ 0 1 -1 0 2 -1 0 0 1 1 0 0]
[ 0 0 0 1 -1 1 1 1 0 0 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 8 1 none
Polytope 840
Image of polytope 840 PALP id: 840
grdb id: 513276
Integer points: [ 1 0 0 1 0 -1 -2 1 0 -1 0 -1]
[ 0 1 0 -2 1 2 1 -1 0 1 -1 0]
[ 0 0 1 0 -1 -1 0 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 6 1 none
Image of facet 9 1 irreducible and admissible
Polytope 841
Image of polytope 841 PALP id: 841
grdb id: 513274
Integer points: [ 1 0 1 0 -1 -2 -2 0 -1 1 0 -1]
[ 0 1 -2 0 1 1 2 -1 0 -1 0 1]
[ 0 0 0 1 -1 0 -1 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 5 1 none
Image of facet 9 1 irreducible and admissible
Polytope 842
Image of polytope 842 PALP id: 842
grdb id: 513277
Integer points: [ 1 1 -1 -1 0 -1 -2 -1 0 0 0 1]
[ 0 2 -2 0 0 -1 -2 -1 1 0 -1 1]
[ 0 0 0 0 1 -1 -1 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 5 1 none
Polytope 843
Image of polytope 843 PALP id: 843
grdb id: 513261
Integer points: [ 1 -1 0 0 -2 -2 -3 -2 -1 -1 0 -1]
[ 0 0 1 0 -2 -1 -2 -1 -1 0 0 -1]
[ 0 0 0 1 -1 -2 -2 -1 0 -1 0 -1]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 6 1 none
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 844
Image of polytope 844 PALP id: 844
grdb id: 513266
Integer points: [ 1 -1 0 0 -1 -3 -3 -2 -1 -2 0 -1]
[ 0 0 1 0 0 -2 -3 -1 -1 -2 0 -1]
[ 0 0 0 1 -1 -2 -2 -1 0 -1 0 -1]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 6 1 none
Polytope 845
Image of polytope 845 PALP id: 845
grdb id: 513167
Integer points: [ 1 0 -1 0 -1 -3 -3 -2 -2 -1 -1 0]
[ 0 1 -1 0 0 -2 -2 -1 -1 0 -1 0]
[ 0 0 0 1 1 -1 -2 0 -1 0 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 27 1 none
Polytope 846
Image of polytope 846 PALP id: 846
grdb id: 513216
Integer points: [ 1 0 -1 0 0 -1 -3 -2 -1 -2 -1 0]
[ 0 1 -1 0 1 1 1 1 0 0 1 0]
[ 0 0 0 1 -1 0 -2 -1 0 -1 -1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 847
Image of polytope 847 PALP id: 847
grdb id: 513090
Integer points: [ 1 0 0 -3 -3 0 -2 -1 -2 -1 -1 0]
[ 0 1 0 -1 -2 -1 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 0 1 1 1 0 0 0 0]
Degree: 48
Hilbert function: 1 + 27 t + 125 t2 + 343 t3 + 729 t4 + 1331 t5 + 2197 t6 + 3375 t7 + 4913 t8 + 6859 t9 + 9261 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
117 ? x + y + z + y-1*z + 2*x-1 + 2*x-1*y-1*z + 2*x-1*y-1 + x-2*y-1 + x-2*y-2*z + x-3*y-1*z-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 47 1 Lattice Minkowski decompositions of facet 47
Polytope 848
Image of polytope 848 PALP id: 848
grdb id: 513225
Integer points: [ 1 0 0 -2 0 -3 -2 -1 -2 -1 -1 0]
[ 0 1 0 -1 -1 -2 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 1 0 1 1 0 0 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
142 ? x + y + z + y-1*z + 3*x-1 + 2*x-1*y-1*z + x-1*y-1 + 3*x-2*y-1 + x-2*y-2*z + x-2*y-1*z-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 9 1 irreducible and admissible
Polytope 849
Image of polytope 849 PALP id: 849
grdb id: 513187
Integer points: [ 1 0 0 -2 0 -3 -2 -1 -2 -1 -1 0]
[ 0 1 0 0 -1 -2 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 1 0 1 1 0 0 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
158 ? x + y + z + y-1*z + x-1 + 2*x-1*y-1*z + 2*x-1*y-1 + x-2*z-1 + x-2*y-1 + x-2*y-2*z + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 48 1 Lattice Minkowski decompositions of facet 48
Polytope 850
Image of polytope 850 PALP id: 850
grdb id: 513081
Integer points: [ 1 0 0 -1 -2 -2 -3 -2 -1 -1 -1 0]
[ 0 1 0 1 0 -2 -2 -1 0 -1 -1 0]
[ 0 0 1 0 -1 -1 -2 -1 0 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 46 1 none
Polytope 851
Image of polytope 851 PALP id: 851
grdb id: 513218
Integer points: [ 1 0 0 -1 -1 -3 -3 -2 -1 -2 -1 0]
[ 0 1 0 0 -1 -2 -2 -1 0 -1 -1 0]
[ 0 0 1 -1 1 0 -1 0 0 -1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 6 1 none
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 852
Image of polytope 852 PALP id: 852
grdb id: 513119
Integer points: [ 1 0 0 -1 -1 -3 -3 -2 -2 -1 -1 0]
[ 0 1 0 1 -1 -1 -2 -1 0 0 -1 0]
[ 0 0 1 -1 1 -1 0 0 -1 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
43 ? x + y + z + x-1*y*z-1 + 4*x-1 + x-1*y-1*z + 2*x-1*y-1 + 2*x-2*z-1 + 3*x-2*y-1 + x-3*y-1*z-1 + x-3*y-2
37 rank 3, number 17 x + y + z + x-1*y*z-1 + 2*x-1 + x-1*y-1*z + 2*x-1*y-1 + 2*x-2*z-1 + 2*x-2*y-1 + x-3*y-1*z-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Polytope 853
Image of polytope 853 PALP id: 853
grdb id: 513181
Integer points: [ 1 0 0 -1 0 -2 -3 -1 -2 -1 -1 0]
[ 0 1 0 -1 1 1 0 1 0 0 0 0]
[ 0 0 1 0 1 -1 -2 0 -1 0 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
79 ? y*z + x + y + z + 2*x-1*y + x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + 2*x-2*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 47 1 Lattice Minkowski decompositions of facet 47
Polytope 854
Image of polytope 854 PALP id: 854
grdb id: 513217
Integer points: [ 1 0 0 0 -1 -1 -3 -2 -1 -1 -2 0]
[ 0 1 -1 0 0 0 -2 -1 -1 0 -1 0]
[ 0 0 0 1 -1 1 -1 0 0 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 855
Image of polytope 855 PALP id: 855
grdb id: 513267
Integer points: [ 1 0 0 0 0 -2 -3 -1 -2 -1 -1 0]
[ 0 1 -1 0 1 -1 -2 0 -1 0 -1 0]
[ 0 0 0 1 -1 0 -1 0 -1 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 6 1 none
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 856
Image of polytope 856 PALP id: 856
grdb id: 513273
Integer points: [ 1 0 0 0 0 -2 -3 -1 -2 -1 -1 0]
[ 0 1 -1 0 1 1 0 1 0 0 0 0]
[ 0 0 0 1 -1 -2 -2 -1 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
29 rank 2, number 23 x + y + z + y*z-1 + 2*x-1*y*z-1 + y-1 + 3*x-1 + x-1*z-1 + x-2*y*z-2 + 3*x-2*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 9 1 irreducible and admissible
Polytope 857
Image of polytope 857 PALP id: 857
grdb id: 513223
Integer points: [ 1 0 0 1 -1 1 -3 1 0 -1 -1 -2]
[ 0 1 0 -1 0 -1 1 -1 0 1 0 1]
[ 0 0 1 -1 1 1 0 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 8 1 none
Image of facet 9 1 irreducible and admissible
Polytope 858
Image of polytope 858 PALP id: 858
grdb id: 513117
Integer points: [ 1 0 1 -2 0 0 1 0 -1 1 0 -1]
[ 0 1 -2 1 0 -2 -3 -1 0 -1 0 1]
[ 0 0 0 0 1 -1 -1 0 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 29 1 none
Polytope 859
Image of polytope 859 PALP id: 859
grdb id: 513038
Integer points: [ 1 0 1 0 -3 0 -1 -2 -1 0 -1 0]
[ 0 1 -1 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 0 0 1 -1 1 1 0 0 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 8 1 none
Image of facet 26 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 860
Image of polytope 860 PALP id: 860
grdb id: 513112
Integer points: [ 1 0 -1 0 -2 -2 -3 -1 -2 -1 -1 0]
[ 0 1 -1 0 0 2 2 1 1 0 1 0]
[ 0 0 0 1 -1 -1 -2 0 -1 0 -1 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 46 1 none
Polytope 861
Image of polytope 861 PALP id: 861
grdb id: 513246
Integer points: [ 1 0 0 0 -2 -2 -3 -1 -1 -2 0 -1]
[ 0 1 -1 0 0 2 2 1 0 1 0 1]
[ 0 0 0 1 -1 -1 -2 0 0 -1 0 -1]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
76 ? x + y + z + 2*x-1*y + 2*x-1*y*z-1 + x-2*y2*z-1 + y-1 + 2*x-1 + 2*x-2*y*z-1 + x-3*y2*z-2 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 862
Image of polytope 862 PALP id: 862
grdb id: 513234
Integer points: [ 1 0 0 2 -3 -2 -1 -1 -2 1 0 -1]
[ 0 1 0 2 -2 -1 0 0 -1 1 0 -1]
[ 0 0 1 -1 0 1 1 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
100 ? x2*y2*z-1 + 2*x*y + x + y + z + x-1*z + 3*x-1 + 2*x-1*y-1 + x-2*y-1*z + 3*x-2*y-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Polytope 863
Image of polytope 863 PALP id: 863
grdb id: 513227
Integer points: [ 1 0 1 -2 0 -2 -3 -1 0 -1 0 1]
[ 0 1 -2 1 0 1 2 0 -1 1 0 -1]
[ 0 0 0 0 1 -1 -1 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 6 1 none
Image of facet 9 1 irreducible and admissible
Polytope 864
Image of polytope 864 PALP id: 864
grdb id: 513262
Integer points: [ 1 1 -1 -1 0 -2 -2 -1 0 0 0 1]
[ 0 2 -2 0 0 -2 -3 -1 -1 0 1 1]
[ 0 0 0 0 1 -1 -1 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
94 ? x*y2 + 2*x*y + x + 2*y + z + 2*y-1 + x-1 + x-1*y-1 + x-1*y-2 + x-2*y-2*z-1 + x-2*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 5 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 865
Image of polytope 865 PALP id: 865
grdb id: 513265
Integer points: [ 1 1 -1 -1 0 -1 -2 -1 0 0 0 1]
[ 0 2 -2 0 0 -2 -3 -1 -1 0 1 1]
[ 0 0 0 0 1 -1 -1 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 6 1 none
Polytope 866
Image of polytope 866 PALP id: 866
grdb id: 513050
Integer points: [ 1 0 0 -3 -1 -4 -2 -3 -2 -1 -1 0]
[ 0 1 0 -2 0 -3 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 1 -1 1 0 0 0 0 0]
Degree: 50
Hilbert function: 1 + 28 t + 130 t2 + 357 t3 + 759 t4 + 1386 t5 + 2288 t6 + 3515 t7 + 5117 t8 + 7144 t9 + 9646 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 8 1 none
Image of facet 45 1 none
Polytope 867
Image of polytope 867 PALP id: 867
grdb id: 513115
Integer points: [ 1 0 0 -2 -1 -3 -4 -2 -3 -1 -1 0]
[ 0 1 0 0 -1 -2 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 1 0 -1 0 -1 0 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
139 ? x + y + z + 3*x-1 + x-1*y-1*z + 2*x-1*y-1 + x-2*z-1 + 4*x-2*y-1 + 2*x-3*y-1*z-1 + x-3*y-2 + x-4*y-2*z-1
155 ? x + y + z + 2*x-1 + x-1*y-1*z + 2*x-1*y-1 + x-2*z-1 + 2*x-2*y-1 + 2*x-3*y-1*z-1 + x-3*y-2 + x-4*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Polytope 868
Image of polytope 868 PALP id: 868
grdb id: 511646
Integer points: [ 1 0 -1 0 -1 0 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 1 1 1 1 1 0 0 0]
[ 0 0 0 1 -1 1 2 0 1 0 1 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 14 1 none
Polytope 869
Image of polytope 869 PALP id: 869
grdb id: 511652
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 1 -1 -1 0 -1 0 -1 0]
[ 0 0 1 -1 0 -1 2 1 1 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + x-1*y + 2*x-1*z + x-1*y-1*z2 + 3*x-1 + 3*x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 870
Image of polytope 870 PALP id: 870
grdb id: 512540
Integer points: [ 1 0 -1 0 -2 -1 0 0 -1 -1 0 0]
[ 0 1 1 0 0 -2 -2 -1 0 -1 0 -1]
[ 0 0 0 1 -1 0 1 1 0 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
65 ? x + y + z + x-1*y + 2*y-1*z + 2*y-1 + x-1 + y-2*z + x-1*y-1 + x-2*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 48 1 Lattice Minkowski decompositions of facet 48
Polytope 871
Image of polytope 871 PALP id: 871
grdb id: 512161
Integer points: [ 1 0 -1 0 -1 -2 -2 -1 -2 -1 0 0]
[ 0 1 1 0 -2 1 -1 0 0 -1 0 -1]
[ 0 0 0 1 0 -1 -1 0 -1 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
103 ? x + y + z + x-1*y + 2*y-1 + x-1 + x-2*y*z-1 + 2*x-1*y-1 + 2*x-2*z-1 + x-1*y-2 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 47 1 Lattice Minkowski decompositions of facet 47
Polytope 872
Image of polytope 872 PALP id: 872
grdb id: 512882
Integer points: [ 1 0 -1 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 -2 -2 -1 0 -1 0 -1]
[ 0 0 0 1 -1 0 -1 0 -1 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
80 ? x + y + z + x-1*y*z-1 + 2*y-1 + x-1 + 3*x-1*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 9 1 irreducible and admissible
Polytope 873
Image of polytope 873 PALP id: 873
grdb id: 511781
Integer points: [ 1 0 0 -2 -1 -2 0 -1 -1 -1 0 0]
[ 0 1 0 0 -2 1 1 1 0 -1 0 -1]
[ 0 0 1 -1 0 -1 1 0 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 45 1 none
Polytope 874
Image of polytope 874 PALP id: 874
grdb id: 512805
Integer points: [ 1 0 0 -2 -1 0 -2 -1 -1 -2 0 0]
[ 0 1 0 0 -2 -1 -2 0 -1 -1 0 -1]
[ 0 0 1 -1 0 1 -1 0 0 -1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
95 ? x + y + z + y-1*z + 2*y-1 + 2*x-1 + 3*x-1*y-1 + x-2*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 875
Image of polytope 875 PALP id: 875
grdb id: 512727
Integer points: [ 1 0 0 -2 0 -1 -2 -1 -2 -1 -1 0]
[ 0 1 0 -1 -1 0 -1 -1 -1 0 -1 0]
[ 0 0 1 -1 1 1 1 1 0 0 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 8 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 876
Image of polytope 876 PALP id: 876
grdb id: 512861
Integer points: [ 1 0 0 -2 0 -1 1 0 -1 1 0 -1]
[ 0 1 0 1 -1 0 -2 -1 0 -1 0 1]
[ 0 0 1 0 -1 -1 0 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
135 ? x + y + z + 2*x*y-1 + 2*x-1*y + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Polytope 877
Image of polytope 877 PALP id: 877
grdb id: 512853
Integer points: [ 1 0 0 -2 0 1 1 0 -1 1 0 -1]
[ 0 1 0 1 -1 -2 -2 -1 0 -1 0 1]
[ 0 0 1 0 -1 0 -1 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
136 ? x + y + z + 2*x*y-1 + 2*x-1*y + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Polytope 878
Image of polytope 878 PALP id: 878
grdb id: 512841
Integer points: [ 1 0 0 -1 -2 -1 -2 -1 -2 -1 -1 0]
[ 0 1 0 -1 0 1 -2 0 -1 -1 0 0]
[ 0 0 1 -1 -1 -1 -1 0 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
28 rank 2, number 25 x + y + z + x-1*y*z-1 + 2*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-2*z-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 879
Image of polytope 879 PALP id: 879
grdb id: 512646
Integer points: [ 1 0 0 -1 0 0 -2 -1 -1 0 -1 0]
[ 0 1 0 1 -1 -1 -1 -1 0 -1 -1 0]
[ 0 0 1 0 -1 1 -1 0 0 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 8 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 880
Image of polytope 880 PALP id: 880
grdb id: 512603
Integer points: [ 1 0 0 0 -1 -2 -2 -2 -1 -1 0 -1]
[ 0 1 0 -1 0 -1 -1 -1 0 -1 0 -1]
[ 0 0 1 -1 1 -1 1 0 0 0 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 8 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 881
Image of polytope 881 PALP id: 881
grdb id: 512900
Integer points: [ 1 0 0 0 1 -2 -2 -1 0 -1 0 -1]
[ 0 1 0 0 -1 0 -1 -1 -1 0 0 0]
[ 0 0 1 -1 0 1 0 0 0 0 0 1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 5 1 none
Image of facet 9 1 irreducible and admissible
Polytope 882
Image of polytope 882 PALP id: 882
grdb id: 512859
Integer points: [ 1 0 0 0 1 -2 1 0 -1 1 0 -1]
[ 0 1 0 0 -1 1 -2 -1 0 -1 0 1]
[ 0 0 1 -1 -1 0 0 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
91 ? x + y + z + 2*x*y-1 + 2*x-1*y + x*y-1*z-1 + z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Polytope 883
Image of polytope 883 PALP id: 883
grdb id: 512876
Integer points: [ 1 0 0 0 1 -2 1 1 0 -1 0 -1]
[ 0 1 0 1 0 1 -2 -1 0 1 -1 0]
[ 0 0 1 -1 -1 0 0 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
101 ? x + y + z + x*z-1 + y*z-1 + 2*x*y-1 + 2*x-1*y + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Polytope 884
Image of polytope 884 PALP id: 884
grdb id: 512673
Integer points: [ 1 0 1 -2 0 0 -2 0 -1 -1 0 -1]
[ 0 1 -1 1 0 -2 0 -1 -1 0 0 1]
[ 0 0 0 0 1 -1 -1 0 -1 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
88 ? x + y + z + x*y-1 + 2*x-1*y + 2*y-1 + 2*x-1 + x-2*y + y-2*z-1 + 2*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 885
Image of polytope 885 PALP id: 885
grdb id: 512657
Integer points: [ 1 0 1 -1 0 0 -2 -1 -1 0 -1 0]
[ 0 1 -1 1 0 -2 -2 -1 0 -1 -2 0]
[ 0 0 0 0 1 -1 -1 0 0 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 4 1 none
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 886
Image of polytope 886 PALP id: 886
grdb id: 512851
Integer points: [ 1 0 1 0 -1 -2 -2 -1 0 -1 -1 0]
[ 0 1 -1 0 -1 -1 0 -1 -1 0 0 0]
[ 0 0 0 1 -1 0 1 0 0 1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 6 1 none
Image of facet 9 1 irreducible and admissible
Polytope 887
Image of polytope 887 PALP id: 887
grdb id: 512725
Integer points: [ 1 0 0 -1 -2 -1 -2 -2 -1 -1 -1 0]
[ 0 1 0 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 0 1 2 1 0 0 1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
63 ? x + y + z + 2*x-1*z + 2*x-1 + x-1*y-1*z + x-2*y-1*z2 + 2*x-1*y-1 + 2*x-2*y-1*z + x-1*y-1*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 888
Image of polytope 888 PALP id: 888
grdb id: 512866
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 -2 -2 -1 0 -1 -1 0]
[ 0 0 1 -1 -1 1 2 1 0 0 1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
77 ? x + y + z + 2*y-1*z + x-1*y*z-1 + 3*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 889
Image of polytope 889 PALP id: 889
grdb id: 512668
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 0 -2 2 -1 0 1 -1 0]
[ 0 0 1 0 -1 0 -1 0 0 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + x-1*y2*z-1 + x-1*y + 2*x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*z-1 + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 9 1 irreducible and admissible
Polytope 890
Image of polytope 890 PALP id: 890
grdb id: 512904
Integer points: [ 1 0 0 0 -1 0 -1 -1 0 0 0 0]
[ 0 1 0 0 0 -2 2 1 -1 0 1 -1]
[ 0 0 1 -1 0 1 -2 -1 1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
94 ? x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + z-1 + 2*x-1*y*z-1 + 2*y-1 + x-1 + y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 5 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 891
Image of polytope 891 PALP id: 891
grdb id: 512868
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 0 0 0]
[ 0 1 -1 0 -2 -1 2 0 1 -1 0 1]
[ 0 0 0 1 1 1 -2 0 -1 1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
94 ? x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 3*x-1*y*z-1 + y-1 + 3*x-1 + y-2*z + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Polytope 892
Image of polytope 892 PALP id: 892
grdb id: 512907
Integer points: [ 1 0 0 0 0 -1 -1 0 0 0 0 0]
[ 0 1 1 -1 -1 0 1 0 -1 0 1 0]
[ 0 0 2 -2 0 0 1 -1 -1 0 1 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
91 ? y*z2 + 2*y*z + x + y + 2*z + x-1*y*z + 2*z-1 + y-1 + x-1 + 2*y-1*z-1 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 6 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 893
Image of polytope 893 PALP id: 893
grdb id: 512906
Integer points: [ 1 1 -1 -1 0 1 1 1 0 0 0 -1]
[ 0 2 -2 0 0 1 0 1 -1 0 1 -1]
[ 0 0 0 0 1 -1 -1 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
127 ? x*y2 + 2*x*y + x*y*z-1 + x + 2*y + z + x*z-1 + 2*y-1 + x-1 + 2*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 6 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 894
Image of polytope 894 PALP id: 894
grdb id: 512481
Integer points: [ 1 0 -1 -1 0 -2 -2 -1 -2 -1 0 0]
[ 0 1 1 -2 0 -1 -3 -1 -2 0 -1 0]
[ 0 0 0 0 1 -1 -1 0 -1 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
131 ? x + y + z + x-1*y + 2*y-1 + 2*x-1 + x-1*y-1 + x-1*y-2 + x-2*y-1*z-1 + 2*x-2*y-2*z-1 + x-2*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 47 1 Lattice Minkowski decompositions of facet 47
Polytope 895
Image of polytope 895 PALP id: 895
grdb id: 511491
Integer points: [ 1 0 -1 0 -2 -2 0 -1 -1 -1 0 0]
[ 0 1 1 0 -2 -3 -1 -2 -1 0 -1 0]
[ 0 0 0 1 -1 -1 1 0 0 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 4 1 none
Image of facet 45 1 none
Polytope 896
Image of polytope 896 PALP id: 896
grdb id: 511645
Integer points: [ 1 0 -1 0 -1 0 -3 -1 -2 -1 -2 0]
[ 0 1 -1 0 1 1 1 1 1 0 0 0]
[ 0 0 0 1 -1 1 -2 0 -1 0 -1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
98 rank 3, number 21 y*z + x + y + z + 3*x-1*y + x-1*y*z-1 + 3*x-1 + 3*x-2*y*z-1 + x-1*y-1 + 2*x-2*z-1 + x-3*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 897
Image of polytope 897 PALP id: 897
grdb id: 512864
Integer points: [ 1 0 0 -1 0 -3 -2 -2 -1 -1 -1 0]
[ 0 1 0 0 -1 -2 -2 -1 0 -1 -1 0]
[ 0 0 1 -1 1 0 1 0 0 1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
87 ? x + y + z + y-1*z + 3*x-1 + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + 3*x-2*y-1 + x-2*y-2*z + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 9 1 irreducible and admissible
Polytope 898
Image of polytope 898 PALP id: 898
grdb id: 512610
Integer points: [ 1 0 0 0 -1 -1 -3 -2 -1 -2 -1 0]
[ 0 1 -1 0 -2 0 -2 -1 -1 -2 0 0]
[ 0 0 0 1 -1 1 -1 0 0 -1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 4 1 none
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 899
Image of polytope 899 PALP id: 899
grdb id: 512887
Integer points: [ 1 0 0 0 0 -2 -3 -1 -2 -1 -1 0]
[ 0 1 -1 0 1 1 0 1 0 0 0 0]
[ 0 0 0 1 -1 0 1 0 1 1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 6 1 none
Image of facet 9 1 irreducible and admissible
Polytope 900
Image of polytope 900 PALP id: 900
grdb id: 512863
Integer points: [ 1 0 0 0 0 -2 -3 -1 -2 -1 -1 0]
[ 0 1 -1 0 1 1 0 1 0 0 0 0]
[ 0 0 0 1 1 -1 -2 0 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? y*z + x + y + z + 2*x-1*y + y-1 + 3*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 3*x-2*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 9 1 irreducible and admissible
Polytope 901
Image of polytope 901 PALP id: 901
grdb id: 510711
Integer points: [ 1 0 -1 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 1 0 0 -2 -2 -1 0 -1 -1 0]
[ 0 0 0 1 -1 0 -1 0 0 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
129 ? x + y + z + x-1*y + 2*y-1 + 3*x-1 + x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 9 1 irreducible and admissible
Polytope 902
Image of polytope 902 PALP id: 902
grdb id: 510714
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 1 -1 -2 -1 0 0 -1 0]
[ 0 0 1 0 -1 -1 0 0 0 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
114 ? x + y + z + x-1*y + x-1*y*z-1 + 2*y-1 + 3*x-1 + 2*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 9 1 irreducible and admissible
Polytope 903
Image of polytope 903 PALP id: 903
grdb id: 508945
Integer points: [ 1 0 0 -1 0 -2 -2 -1 -2 -1 -2 0]
[ 0 1 -1 1 0 1 -2 -1 -1 0 0 0]
[ 0 0 0 0 1 -1 -1 0 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
147 ? x + y + z + x-1*y + y-1 + 3*x-1 + x-2*y*z-1 + 2*x-1*y-1 + 3*x-2*z-1 + 3*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 904
Image of polytope 904 PALP id: 904
grdb id: 510713
Integer points: [ 1 0 0 0 -1 0 -1 -1 -1 0 0 0]
[ 0 1 0 -1 0 -1 0 0 0 0 0 -1]
[ 0 0 1 1 1 -1 -2 0 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
100 ? x + y + z + y-1*z + x-1*z + 2*z-1 + 2*y-1 + 3*x-1 + y-1*z-1 + 3*x-1*z-1 + x-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 9 1 irreducible and admissible
Polytope 905
Image of polytope 905 PALP id: 905
grdb id: 420934
Integer points: [ 1 0 0 -1 1 0 -1 -2 0 -1 0 -1]
[ 0 1 0 1 -1 0 -1 0 -1 0 0 0]
[ 0 0 1 1 -1 -1 1 1 0 1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 5 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 906
Image of polytope 906 PALP id: 906
grdb id: 420926
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 1 0 -2 -1 0 -1 0]
[ 0 0 1 -1 0 0 1 -2 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 31 1 none
Polytope 907
Image of polytope 907 PALP id: 907
grdb id: 420929
Integer points: [ 1 0 0 0 0 -1 -2 -2 -1 -1 -1 0]
[ 0 1 -1 0 1 -1 -1 -1 0 0 -1 0]
[ 0 0 0 1 -1 1 0 -1 0 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 6 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 908
Image of polytope 908 PALP id: 908
grdb id: 420931
Integer points: [ 1 0 0 0 0 1 -2 -2 -1 -1 0 -1]
[ 0 1 0 -1 0 -1 0 1 0 0 0 1]
[ 0 0 1 0 -1 -1 1 0 0 1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
60 rank 2, number 18 x + y + z + 2*x-1*y + 2*x-1*z + x*y-1*z-1 + z-1 + y-1 + x-1 + x-2*y + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 909
Image of polytope 909 PALP id: 909
grdb id: 420832
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 1 -1 0 1 0 0]
[ 0 0 1 -1 0 -1 1 1 0 0 1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + z-1 + x-1*y*z-1 + y-1 + 2*x-1 + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 910
Image of polytope 910 PALP id: 910
grdb id: 420831
Integer points: [ 1 0 0 0 1 -1 -1 1 0 0 0 -1]
[ 0 1 0 1 0 -1 1 -1 0 -1 0 0]
[ 0 0 1 -1 -1 1 -1 -1 -1 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
35 rank 2, number 15 x + y + z + x*z-1 + y*z-1 + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 911
Image of polytope 911 PALP id: 911
grdb id: 420731
Integer points: [ 1 0 -1 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 1 -2 0 -2 0 -1 -1 0 -1 0]
[ 0 0 0 0 1 -1 1 1 0 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 29 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 912
Image of polytope 912 PALP id: 912
grdb id: 420837
Integer points: [ 1 0 -1 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 1 0 -1 -2 0 -1 -1 0 -1 0]
[ 0 0 0 1 -1 0 1 1 0 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 28 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 913
Image of polytope 913 PALP id: 913
grdb id: 420759
Integer points: [ 1 0 -1 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 1 0 1 -1 -2 0 0 -1 0 -1]
[ 0 0 0 1 -1 1 0 1 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 29 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 914
Image of polytope 914 PALP id: 914
grdb id: 420811
Integer points: [ 1 0 -1 0 -1 1 -2 0 -1 -1 0 0]
[ 0 1 1 0 -1 -1 -1 -1 -1 0 -1 0]
[ 0 0 0 1 -1 1 -1 1 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 915
Image of polytope 915 PALP id: 915
grdb id: 420801
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 0 0 -2 -1 0 -1 0 -1]
[ 0 0 1 0 -1 1 0 1 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 28 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 916
Image of polytope 916 PALP id: 916
grdb id: 420820
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 0 -2 -1 0 -1 0 -1]
[ 0 0 1 -1 1 1 0 1 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 917
Image of polytope 917 PALP id: 917
grdb id: 420911
Integer points: [ 1 0 0 -1 0 -1 -1 0 0 -1 0 0]
[ 0 1 0 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 0 1 0 0 1 -1 -2 -1 0 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + 2*z-1 + y-1 + x-1 + x-1*y-1*z + 2*y-1*z-1 + 2*x-1*y-1 + y-1*z-2 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 918
Image of polytope 918 PALP id: 918
grdb id: 420861
Integer points: [ 1 0 0 0 -2 -1 -1 -2 -2 -1 -1 0]
[ 0 1 -1 0 -1 0 -1 -1 -1 0 -1 0]
[ 0 0 0 1 -1 1 1 1 0 0 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 8 2 none
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 919
Image of polytope 919 PALP id: 919
grdb id: 420898
Integer points: [ 1 0 0 0 -1 -2 -1 -2 -1 -1 -1 0]
[ 0 1 -1 0 1 1 -1 0 1 0 0 0]
[ 0 0 0 1 -1 0 1 1 0 0 1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
37 rank 3, number 17 x + y + z + 2*x-1*y + 2*x-1*z + x-1*y*z-1 + y-1 + x-1 + x-2*y + x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 920
Image of polytope 920 PALP id: 920
grdb id: 420919
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 1 1 0 -2 0 -1 0 -1]
[ 0 0 0 1 0 1 -1 -2 0 -1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y*z + x-1*y + y-1 + 3*x-1 + 2*y-1*z-1 + x-1*z-1 + 3*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 921
Image of polytope 921 PALP id: 921
grdb id: 420848
Integer points: [ 1 0 0 0 -1 0 -1 -2 0 -1 0 -1]
[ 0 1 0 -1 0 -1 0 1 -1 0 0 1]
[ 0 0 1 -1 -1 1 1 0 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + 2*x-1*y + y-1*z + x-1*z + 2*y-1 + 3*x-1 + x-2*y + y-1*z-1 + x-1*z-1
46 ? x + y + z + 2*x-1*y + y-1*z + x-1*z + 2*y-1 + 2*x-1 + x-2*y + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 922
Image of polytope 922 PALP id: 922
grdb id: 420905
Integer points: [ 1 0 0 0 -1 1 -1 -2 -1 0 -1 0]
[ 0 1 -1 0 1 -1 -1 -1 -1 -1 0 0]
[ 0 0 0 1 0 -1 0 -1 -1 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 6 1 none
Polytope 923
Image of polytope 923 PALP id: 923
grdb id: 420856
Integer points: [ 1 0 0 0 0 -2 -2 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 -1 -1 -1 0 -1 -1 0]
[ 0 0 0 1 -1 0 -1 1 0 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
103 ? x + y + z + y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + x-2*y-1*z-1
112 rank 3, number 15 x + y + z + y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 924
Image of polytope 924 PALP id: 924
grdb id: 420855
Integer points: [ 1 0 0 0 0 -1 -2 -2 -1 -1 -1 0]
[ 0 1 -1 0 -1 0 1 1 0 0 1 0]
[ 0 0 0 1 -1 1 0 -1 0 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + 2*x-1*y + x-1*z + y-1 + 2*x-1 + x-2*y + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1
144 rank 3, number 12 x + y + z + 2*x-1*y + x-1*z + y-1 + 3*x-1 + x-2*y + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 925
Image of polytope 925 PALP id: 925
grdb id: 420902
Integer points: [ 1 0 0 0 0 -1 -2 -2 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 1 0 0 0 1 0]
[ 0 0 1 -1 0 1 0 1 0 1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + 2*x-1*y + 2*x-1*z + z-1 + y-1 + x-1 + x-2*y + x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 926
Image of polytope 926 PALP id: 926
grdb id: 420892
Integer points: [ 1 0 0 0 0 -1 -2 -2 -1 0 -1 -1]
[ 0 1 0 0 -1 0 -1 -2 -1 0 0 -1]
[ 0 0 1 -1 0 1 0 -1 0 0 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
29 rank 2, number 23 x + y + z + x-1*z + z-1 + y-1 + 2*x-1 + x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 927
Image of polytope 927 PALP id: 927
grdb id: 420895
Integer points: [ 1 0 0 0 0 1 -2 -2 -1 -1 0 -1]
[ 0 1 0 0 -1 0 -1 -2 -1 -1 0 0]
[ 0 0 1 -1 0 1 0 -1 0 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
55 rank 2, number 19 x*z + x + y + z + z-1 + y-1 + 2*x-1 + x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 928
Image of polytope 928 PALP id: 928
grdb id: 420923
Integer points: [ 1 0 0 0 0 1 1 -2 -1 1 0 -1]
[ 0 1 0 0 -1 -1 -1 1 0 -1 0 1]
[ 0 0 1 -1 0 -1 1 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
94 ? x + y + x*y-1*z + z + 2*x*y-1 + 2*x-1*y + x*y-1*z-1 + z-1 + y-1 + 2*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 1 4 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 929
Image of polytope 929 PALP id: 929
grdb id: 420909
Integer points: [ 1 0 0 0 1 -1 0 -1 -1 -1 0 0]
[ 0 1 0 -1 -1 0 -1 0 0 0 0 0]
[ 0 0 1 0 1 1 1 -2 0 -1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + x*y-1*z + z + y-1*z + x-1*z + 2*z-1 + y-1 + 3*x-1 + 3*x-1*z-1 + x-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 930
Image of polytope 930 PALP id: 930
grdb id: 420924
Integer points: [ 1 0 0 0 1 -1 0 -1 0 -1 0 0]
[ 0 1 0 0 -1 1 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 0 -1 1 1 0 0 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x*y-1 + 2*y-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + y-2*z + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 931
Image of polytope 931 PALP id: 931
grdb id: 420888
Integer points: [ 1 0 0 0 1 0 -2 1 1 -1 0 -1]
[ 0 1 -1 0 -1 -1 1 -1 -1 0 0 1]
[ 0 0 0 1 -1 -1 0 1 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + x*y-1*z + z + 2*x*y-1 + 2*x-1*y + x*y-1*z-1 + y-1 + 2*x-1 + x-2*y + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 932
Image of polytope 932 PALP id: 932
grdb id: 420899
Integer points: [ 1 0 0 1 -1 -2 0 -2 -1 -1 0 0]
[ 0 1 0 -1 -1 0 -1 -1 0 -1 0 -1]
[ 0 0 1 1 -1 -1 1 -1 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
29 rank 2, number 23 x + y + x*y-1*z + z + y-1*z + 2*y-1 + 2*x-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 933
Image of polytope 933 PALP id: 933
grdb id: 420810
Integer points: [ 1 0 0 1 -1 0 0 -2 0 -1 0 -1]
[ 0 1 0 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 0 1 -1 1 -1 1 0 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 8 1 none
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 934
Image of polytope 934 PALP id: 934
grdb id: 420917
Integer points: [ 1 0 0 1 1 -1 0 -1 0 0 -1 -1]
[ 0 1 0 1 0 1 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 -1 0 1 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 6 1 none
Polytope 935
Image of polytope 935 PALP id: 935
grdb id: 420847
Integer points: [ 1 0 1 -2 0 0 -1 -1 0 -1 0 -1]
[ 0 1 -1 1 0 -2 -1 1 -1 0 0 1]
[ 0 0 0 0 1 -1 -1 1 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
81 ? x + y + z + x-1*y*z + x*y-1 + 2*x-1*y + 2*y-1 + 3*x-1 + x-2*y + y-2*z-1 + x-1*y-1*z-1
88 ? x + y + z + x-1*y*z + x*y-1 + 2*x-1*y + 2*y-1 + 2*x-1 + x-2*y + y-2*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 936
Image of polytope 936 PALP id: 936
grdb id: 420812
Integer points: [ 1 0 1 -1 0 -1 -2 0 -1 -1 0 0]
[ 0 1 -1 1 0 -1 -1 -1 -1 0 -1 0]
[ 0 0 0 0 1 -1 -1 1 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 8 2 none
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 937
Image of polytope 937 PALP id: 937
grdb id: 420799
Integer points: [ 1 0 1 -1 0 0 -1 -1 -1 0 -1 0]
[ 0 1 -1 1 0 -2 -2 0 -1 -1 0 0]
[ 0 0 0 0 1 -1 -1 1 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 4 1 none
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 938
Image of polytope 938 PALP id: 938
grdb id: 420790
Integer points: [ 1 0 1 0 -2 -2 0 -1 -1 0 -1 0]
[ 0 1 -1 0 0 -1 -1 -1 -1 -1 0 0]
[ 0 0 0 1 -1 0 1 1 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
145 ? x + y + z + x*y-1 + y-1*z + 3*y-1 + x-1 + x-1*y-1*z + 3*x-1*y-1 + x-2*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Polytope 939
Image of polytope 939 PALP id: 939
grdb id: 420918
Integer points: [ 1 0 1 0 -1 0 -1 -2 -1 0 -1 0]
[ 0 1 -1 0 1 -1 -1 -1 -1 -1 0 0]
[ 0 0 0 1 -1 1 1 0 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x*y-1 + y-1*z + x-1*y*z-1 + 3*y-1 + x-1 + x-1*y-1*z + 3*x-1*y-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Polytope 940
Image of polytope 940 PALP id: 940
grdb id: 420813
Integer points: [ 1 0 1 0 0 -2 1 -1 0 -1 0 -1]
[ 0 1 -1 0 -1 1 -2 0 -1 0 0 1]
[ 0 0 0 1 -1 0 -1 1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 941
Image of polytope 941 PALP id: 941
grdb id: 420889
Integer points: [ 1 -1 0 0 -1 0 -1 -1 -1 0 0 0]
[ 0 0 1 0 0 2 1 -2 -1 1 0 -1]
[ 0 0 0 1 -1 1 0 -2 -1 1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? y2*z + 2*y*z + x + y + z + x-1*y + x-1 + 2*y-1*z-1 + x-1*z-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 942
Image of polytope 942 PALP id: 942
grdb id: 420863
Integer points: [ 1 0 -1 0 -1 -2 -2 -3 -2 -1 -1 0]
[ 0 1 -1 0 -1 0 -1 -1 -1 0 0 0]
[ 0 0 0 1 -1 1 1 1 0 0 1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 943
Image of polytope 943 PALP id: 943
grdb id: 420747
Integer points: [ 1 0 0 -2 -1 -3 -3 -2 -2 -1 -1 0]
[ 0 1 0 -1 0 -2 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 1 0 -1 1 0 0 0 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
93 ? x + y + z + x-1*z + 2*x-1 + 2*x-1*y-1 + x-2*y-1*z + x-2*y-1 + x-2*y-1*z-1 + x-3*y-2 + x-3*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 51 1 Lattice Minkowski decompositions of facet 51
Polytope 944
Image of polytope 944 PALP id: 944
grdb id: 420858
Integer points: [ 1 0 0 -2 0 -1 -2 -3 -2 -1 -1 0]
[ 0 1 -1 -1 0 -2 -1 -2 -2 -1 0 0]
[ 0 0 0 0 1 -1 -1 -1 -1 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
104 ? x + y + z + y-1 + 2*x-1 + 3*x-1*y-1 + x-2*y-1 + x-1*y-2*z-1 + x-2*y-1*z-1 + 2*x-2*y-2*z-1 + x-3*y-2*z-1
105 ? x + y + z + y-1 + 2*x-1 + 2*x-1*y-1 + x-2*y-1 + x-1*y-2*z-1 + x-2*y-1*z-1 + 2*x-2*y-2*z-1 + x-3*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 945
Image of polytope 945 PALP id: 945
grdb id: 420883
Integer points: [ 1 0 0 -1 -1 -2 -3 -3 -1 -2 0 -1]
[ 0 1 0 0 -1 0 -1 -2 0 -1 0 -1]
[ 0 0 1 -1 0 -1 -2 -2 0 -1 0 -1]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
37 rank 3, number 17 x + y + z + 2*x-1 + x-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + 2*x-2*y-1*z-1 + x-3*y-1*z-2 + x-3*y-2*z-2
111 ? x + y + z + 2*x-1 + x-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + 3*x-2*y-1*z-1 + x-3*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 946
Image of polytope 946 PALP id: 946
grdb id: 420783
Integer points: [ 1 0 0 -1 -1 -2 -3 -2 -2 -1 -1 0]
[ 0 1 0 -1 0 -2 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 1 -1 0 1 0 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
98 rank 3, number 21 x + y + z + x-1*z + 3*x-1 + x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + 3*x-2*y-1 + x-2*y-2*z-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Polytope 947
Image of polytope 947 PALP id: 947
grdb id: 420849
Integer points: [ 1 0 0 -1 -1 -2 -2 -3 -1 -2 0 -1]
[ 0 1 0 -1 1 -1 1 0 0 0 0 0]
[ 0 0 1 0 0 -1 -1 -2 0 -1 0 -1]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
61 rank 2, number 27 x + y + z + x-1*y + x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + x-2*z-1 + x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 50 1 Lattice Minkowski decompositions of facet 50
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 948
Image of polytope 948 PALP id: 948
grdb id: 420667
Integer points: [ 1 0 0 -1 0 -1 -2 -3 -1 -2 0 -1]
[ 0 1 0 -1 -1 1 1 0 0 0 0 0]
[ 0 0 1 0 1 0 -1 -2 0 -1 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
148 ? x + y + z + x-1*y + y-1*z + x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + 2*x-2*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 51 1 Lattice Minkowski decompositions of facet 51
Polytope 949
Image of polytope 949 PALP id: 949
grdb id: 420897
Integer points: [ 1 0 0 0 -2 -2 -2 -3 -1 -1 -1 0]
[ 0 1 0 -1 -1 0 -1 -1 -1 0 0 0]
[ 0 0 1 -1 0 1 1 1 0 1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? x + y + z + 2*x-1*z + 2*x-1 + x-2*z + y-1*z-1 + 2*x-1*y-1 + x-2*y-1*z + x-2*y-1 + x-3*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Polytope 950
Image of polytope 950 PALP id: 950
grdb id: 420807
Integer points: [ 1 0 0 0 -2 0 -1 -3 -2 -1 -1 0]
[ 0 1 -1 0 0 1 1 1 1 1 0 0]
[ 0 0 0 1 -1 1 1 -1 0 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 951
Image of polytope 951 PALP id: 951
grdb id: 420907
Integer points: [ 1 0 0 1 0 -1 -1 -3 -1 -2 0 -1]
[ 0 1 -1 1 0 -1 1 0 0 0 0 0]
[ 0 0 0 0 1 -1 -1 -2 0 -1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
55 rank 2, number 19 x*y + x + y + z + x-1*y*z-1 + y-1 + 3*x-1 + x-1*z-1 + x-1*y-1*z-1 + 3*x-2*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Polytope 952
Image of polytope 952 PALP id: 952
grdb id: 419952
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 -1 1 1 0 0 0]
[ 0 0 1 -1 0 -1 1 1 0 1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
69 ? x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + x-1*y*z-1 + 3*x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 953
Image of polytope 953 PALP id: 953
grdb id: 419976
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 1 -1 0 0 -1 0]
[ 0 0 1 -1 -1 0 1 1 1 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + x-1*y*z + x-1*y + 2*x-1*z + 3*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 954
Image of polytope 954 PALP id: 954
grdb id: 420357
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 1 1 -1 -1 0 -1 0 0]
[ 0 0 1 1 0 -1 1 -1 0 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + x-1*y + x-1*z + x-1*y*z-1 + 3*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 955
Image of polytope 955 PALP id: 955
grdb id: 420626
Integer points: [ 1 0 1 -1 0 1 -1 1 0 1 0 -1]
[ 0 1 -1 1 0 1 -1 -1 -1 0 0 0]
[ 0 0 0 0 1 -1 0 -1 0 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
128 ? x*y*z-1 + x + y + z + 2*x*z-1 + x*y-1 + x-1*y + x*y-1*z-1 + 2*y-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 956
Image of polytope 956 PALP id: 956
grdb id: 420092
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 1 -1 0 0 -1 0]
[ 0 0 1 -1 0 -1 0 2 1 0 1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
47 ? x + y + z + x-1*y + 2*x-1*z + x-1*y-1*z2 + x-1*y*z-1 + 3*x-1 + 2*x-1*y-1*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 957
Image of polytope 957 PALP id: 957
grdb id: 420093
Integer points: [ 1 0 0 -1 -1 -1 0 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 1 1 1 0 0 0]
[ 0 0 1 -1 0 0 1 2 1 0 1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
102 ? y*z + x-1*y*z2 + x + y + z + 2*x-1*y*z + x-1*y + 2*x-1*z + 2*x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 958
Image of polytope 958 PALP id: 958
grdb id: 420501
Integer points: [ 1 0 1 -1 0 -1 -1 -1 0 -1 -1 0]
[ 0 1 -1 1 0 -1 0 2 -1 0 1 0]
[ 0 0 0 0 1 0 -1 -1 0 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*y2*z-1 + x*y-1 + x-1*y + 2*x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 959
Image of polytope 959 PALP id: 959
grdb id: 419682
Integer points: [ 1 0 -1 -1 0 -2 0 -2 -1 -1 0 0]
[ 0 1 1 -2 0 -1 -1 -2 -1 0 -1 0]
[ 0 0 0 0 1 -1 1 -1 0 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
131 ? x + y + z + x-1*y + y-1*z + 2*y-1 + 2*x-1 + x-1*y-1 + x-1*y-2 + x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 51 1 Lattice Minkowski decompositions of facet 51
Polytope 960
Image of polytope 960 PALP id: 960
grdb id: 419214
Integer points: [ 1 0 -1 0 -2 -2 0 -1 -1 -1 0 0]
[ 0 1 1 0 1 0 -1 -2 0 -1 0 -1]
[ 0 0 0 1 -1 -1 1 0 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
103 ? x + y + z + x-1*y + y-1*z + 2*y-1 + x-1 + x-2*y*z-1 + 2*x-1*y-1 + x-2*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 51 1 Lattice Minkowski decompositions of facet 51
Polytope 961
Image of polytope 961 PALP id: 961
grdb id: 420256
Integer points: [ 1 0 -1 0 -2 -1 0 -2 -1 -1 0 0]
[ 0 1 1 0 0 -2 -1 -1 0 -1 0 -1]
[ 0 0 0 1 -1 0 1 -1 0 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
65 ? x + y + z + x-1*y + y-1*z + 2*y-1 + x-1 + x-1*y-1 + x-2*z-1 + x-1*y-2 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 50 1 Lattice Minkowski decompositions of facet 50
Polytope 962
Image of polytope 962 PALP id: 962
grdb id: 419943
Integer points: [ 1 0 -1 0 -1 -1 -1 0 -1 -1 0 0]
[ 0 1 1 0 -1 -2 -2 -1 -1 0 -1 0]
[ 0 0 0 1 -1 0 -1 1 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 6 1 none
Polytope 963
Image of polytope 963 PALP id: 963
grdb id: 419969
Integer points: [ 1 0 -1 0 0 -1 -2 0 -1 -1 0 0]
[ 0 1 1 0 -1 0 0 -2 0 -1 -1 0]
[ 0 0 0 1 -1 -1 -1 -1 0 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + x-1*y + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 964
Image of polytope 964 PALP id: 964
grdb id: 420516
Integer points: [ 1 0 -1 0 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 1 -1 -2 -1 0 -1 0]
[ 0 0 0 1 1 -1 -1 0 0 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
80 ? x + y + z + y-1*z + x-1*y*z-1 + 2*y-1 + x-1 + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 965
Image of polytope 965 PALP id: 965
grdb id: 420475
Integer points: [ 1 0 -1 0 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 1 0 -1 0 -2 -1 -1 0 -1 0]
[ 0 0 0 1 -1 1 0 1 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
129 ? x + y + z + x-1*y + x-1*z + 2*y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 966
Image of polytope 966 PALP id: 966
grdb id: 420000
Integer points: [ 1 0 0 -1 -1 -2 -1 -2 -2 -1 -1 0]
[ 0 1 0 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 0 1 -1 1 -1 1 1 0 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 967
Image of polytope 967 PALP id: 967
grdb id: 420277
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 0 -2 -1 0 -1 0 -1]
[ 0 0 1 -1 -1 1 0 1 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
145 ? x + y + z + x-1*z + 2*y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
147 ? x + y + z + x-1*z + 2*y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 968
Image of polytope 968 PALP id: 968
grdb id: 419980
Integer points: [ 1 0 0 -1 -1 -1 0 -1 -1 -1 0 0]
[ 0 1 0 0 1 1 1 -2 0 -1 0 -1]
[ 0 0 1 -1 0 -1 1 0 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? y*z + x + y + z + x-1*y + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*z-1 + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Polytope 969
Image of polytope 969 PALP id: 969
grdb id: 420582
Integer points: [ 1 0 0 -1 0 -2 -1 -2 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 -2 -2 0 -1 -1 0]
[ 0 0 1 -1 1 0 1 1 0 0 1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
160 ? x + y + z + y-1*z + 2*x-1 + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z + x-2*y-1 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 970
Image of polytope 970 PALP id: 970
grdb id: 419977
Integer points: [ 1 0 0 -1 0 -1 -2 -2 -1 -2 -1 0]
[ 0 1 -1 1 0 -1 0 -2 -1 -1 0 0]
[ 0 0 0 0 1 -1 -1 -1 0 -1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
126 ? x + y + z + x-1*y + y-1 + 2*x-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-2*z-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 971
Image of polytope 971 PALP id: 971
grdb id: 420107
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 0 -2 -1 0 -1 0]
[ 0 0 1 -1 1 0 1 1 1 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? x + y + z + x-1*y + y-1*z + x-1*z + 2*x-1 + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 972
Image of polytope 972 PALP id: 972
grdb id: 420520
Integer points: [ 1 0 0 -1 0 0 -2 -2 -1 -1 0 -1]
[ 0 1 -1 0 0 -1 -1 -1 -1 0 0 -1]
[ 0 0 0 0 1 1 -1 -2 0 -1 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
66 rank 2, number 24 x + y + z + y-1*z + y-1 + x-1 + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 973
Image of polytope 973 PALP id: 973
grdb id: 420086
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 1 0 0 -2 -1 -1 0 0]
[ 0 0 0 1 0 -1 1 -1 0 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + x-1*y + x-1*z + y-1 + 2*x-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 974
Image of polytope 974 PALP id: 974
grdb id: 420461
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 0 -1 -2 0 -1 0 -1]
[ 0 0 1 -1 0 1 1 0 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
82 ? x + y + z + x-1*y + x-1*z + z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 975
Image of polytope 975 PALP id: 975
grdb id: 420522
Integer points: [ 1 0 0 0 -1 -1 -1 0 -1 0 0 0]
[ 0 1 0 0 1 0 -1 -2 0 -1 -1 0]
[ 0 0 1 -1 0 -1 0 1 0 0 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + x-1*y + 2*y-1*z + z-1 + 2*y-1 + 2*x-1 + y-2*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 976
Image of polytope 976 PALP id: 976
grdb id: 420478
Integer points: [ 1 0 0 0 -1 0 -2 -2 -1 -1 -1 0]
[ 0 1 -1 0 -1 1 0 1 0 1 0 0]
[ 0 0 0 1 0 -1 -1 -2 0 -1 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + y*z-1 + 2*x-1*y*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + x-1*y-1 + x-2*y*z-2 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 977
Image of polytope 977 PALP id: 977
grdb id: 420521
Integer points: [ 1 0 0 0 -1 0 0 -1 0 0 -1 -1]
[ 0 1 0 0 1 -1 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 0 -1 1 0 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 5 1 none
Polytope 978
Image of polytope 978 PALP id: 978
grdb id: 420589
Integer points: [ 1 0 0 0 0 -1 -2 -2 -1 -1 -1 0]
[ 0 1 -1 0 -1 0 -1 -1 -1 0 -1 0]
[ 0 0 0 1 -1 1 0 -1 0 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 6 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 979
Image of polytope 979 PALP id: 979
grdb id: 420517
Integer points: [ 1 0 0 0 0 -1 -2 -2 -1 -1 0 -1]
[ 0 1 -1 0 -1 1 1 1 0 1 0 0]
[ 0 0 0 1 1 0 -1 -2 0 -1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + x-1*y + y-1*z + 2*x-1*y*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 980
Image of polytope 980 PALP id: 980
grdb id: 420523
Integer points: [ 1 0 0 0 0 -1 -2 -2 -1 -1 -1 0]
[ 0 1 -1 0 1 0 1 1 0 1 1 0]
[ 0 0 0 1 -1 -1 0 -1 0 -1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
103 ? x + y + z + y*z-1 + 2*x-1*y + 2*x-1*y*z-1 + y-1 + 2*x-1 + x-2*y + x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 981
Image of polytope 981 PALP id: 981
grdb id: 419971
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 0 0 -2 -1 -1 0 0]
[ 0 0 0 1 -1 -1 1 -1 0 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + x-1*z + y-1 + 2*x-1 + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 982
Image of polytope 982 PALP id: 982
grdb id: 420617
Integer points: [ 1 0 0 0 1 -1 -1 -2 -1 -1 0 0]
[ 0 1 0 0 -1 1 -1 0 0 0 -1 0]
[ 0 0 1 -1 0 -1 0 -1 0 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + x*y-1 + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + 2*x-1*z-1 + x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 983
Image of polytope 983 PALP id: 983
grdb id: 420459
Integer points: [ 1 0 0 0 1 -1 0 -1 -1 -1 0 0]
[ 0 1 0 0 0 1 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 -1 0 -1 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
85 rank 3, number 8 x + y + z + x*z-1 + x-1*y + z-1 + 2*y-1 + 3*x-1 + y-1*z-1 + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 984
Image of polytope 984 PALP id: 984
grdb id: 420477
Integer points: [ 1 0 0 1 0 0 -2 -2 -1 -1 0 -1]
[ 0 1 -1 -1 0 -1 0 -1 -1 0 0 0]
[ 0 0 0 0 1 -1 -1 -2 -1 0 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + x*y-1 + y-1 + 2*x-1 + y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 985
Image of polytope 985 PALP id: 985
grdb id: 420534
Integer points: [ 1 0 0 1 1 -1 0 -2 0 -1 0 -1]
[ 0 1 0 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 0 1 -1 0 1 1 0 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
143 ? x + y + z + x*z-1 + x*y-1 + y-1*z + 3*y-1 + 2*x-1 + x-1*y-1*z + 3*x-1*y-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 986
Image of polytope 986 PALP id: 986
grdb id: 420318
Integer points: [ 1 0 1 -1 -1 0 -2 -2 -1 -2 0 0]
[ 0 1 -1 1 -1 0 1 -1 0 0 -1 0]
[ 0 0 0 0 0 1 -1 -1 0 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
159 ? x + y + z + x*y-1 + x-1*y + 2*y-1 + 2*x-1 + x-2*y*z-1 + x-1*y-1 + 2*x-2*z-1 + x-2*y-1*z-1
82 ? x + y + z + x*y-1 + x-1*y + 2*y-1 + 3*x-1 + x-2*y*z-1 + x-1*y-1 + 2*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 987
Image of polytope 987 PALP id: 987
grdb id: 420317
Integer points: [ 1 0 1 -1 0 -1 -2 -2 -1 -1 0 0]
[ 0 1 -1 1 0 -2 -1 -2 -1 0 -1 0]
[ 0 0 0 0 1 -1 -1 -1 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 8 2 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Polytope 988
Image of polytope 988 PALP id: 988
grdb id: 420104
Integer points: [ 1 0 1 -1 0 -1 -1 1 0 0 0 -1]
[ 0 1 -1 1 0 0 0 -2 -1 -1 0 0]
[ 0 0 0 0 1 -1 1 -1 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x*y-1 + x-1*y + x-1*z + 2*y-1 + 2*x-1 + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 989
Image of polytope 989 PALP id: 989
grdb id: 420596
Integer points: [ 1 0 1 -1 0 0 -1 -2 -1 0 -1 0]
[ 0 1 -1 1 0 -1 -1 -1 0 -1 -1 0]
[ 0 0 0 0 1 -1 0 -1 0 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 6 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 990
Image of polytope 990 PALP id: 990
grdb id: 420514
Integer points: [ 1 0 1 -1 0 0 -1 -2 -1 -1 0 0]
[ 0 1 -1 1 0 1 -1 1 0 1 0 -1]
[ 0 0 0 0 1 -1 0 -1 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 6 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 991
Image of polytope 991 PALP id: 991
grdb id: 420106
Integer points: [ 1 0 1 0 0 -2 0 -1 0 -1 0 -1]
[ 0 1 -1 0 -1 1 -1 0 -1 0 0 1]
[ 0 0 0 1 -1 0 1 1 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 992
Image of polytope 992 PALP id: 992
grdb id: 420623
Integer points: [ 1 0 1 0 0 -1 -1 -2 -1 0 0 -1]
[ 0 1 -1 0 0 1 -1 0 0 0 -1 0]
[ 0 0 0 1 -1 0 0 -1 0 0 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 5 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 993
Image of polytope 993 PALP id: 993
grdb id: 420628
Integer points: [ 1 -1 0 0 -2 2 0 2 1 -1 0 1]
[ 0 0 1 0 0 -1 -1 -1 -1 0 0 0]
[ 0 0 0 1 1 -1 -1 -2 -1 1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + x2*y-1*z-1 + 2*x*z-1 + 2*x-1*z + x2*y-1*z-2 + 2*x*y-1*z-1 + x-1 + x-2*z + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 994
Image of polytope 994 PALP id: 994
grdb id: 419984
Integer points: [ 1 0 -1 0 -2 1 1 0 -1 0 -1 0]
[ 0 1 -1 0 0 1 2 2 1 1 0 0]
[ 0 0 0 1 -1 1 1 1 0 1 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
86 ? x*y2*z + x*y*z + y2*z + 2*y*z + x + y + z + 2*x-1*y + 2*x-1 + x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 995
Image of polytope 995 PALP id: 995
grdb id: 420102
Integer points: [ 1 0 0 0 -1 -2 -1 -2 -1 -2 -1 0]
[ 0 1 -1 0 1 0 2 2 1 1 0 0]
[ 0 0 0 1 -1 -1 -1 -1 0 -1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
47 ? x + y + z + x-1*y2*z-1 + 2*x-1*y + x-1*y*z-1 + x-2*y2*z-1 + y-1 + 2*x-1 + 2*x-2*y*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 996
Image of polytope 996 PALP id: 996
grdb id: 420620
Integer points: [ 1 0 0 0 2 -2 1 2 1 0 -1 -1]
[ 0 1 -1 0 -1 1 -1 -2 -1 0 0 1]
[ 0 0 0 1 -1 0 -1 -1 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + x2*y-1*z-1 + 2*x*y-1 + 2*x-1*y + x2*y-2*z-1 + x*y-1*z-1 + y-1 + 2*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 997
Image of polytope 997 PALP id: 997
grdb id: 420335
Integer points: [ 1 0 0 -2 -2 0 -1 -3 -2 -1 -1 0]
[ 0 1 0 0 -1 -1 -1 -1 -1 0 -1 0]
[ 0 0 1 -1 -1 1 1 -1 0 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
105 ? x + y + z + y-1*z + 3*x-1 + x-1*y-1*z + 2*x-1*y-1 + x-2*z-1 + 2*x-2*y-1 + x-2*y-1*z-1 + x-3*y-1*z-1
63 ? x + y + z + y-1*z + 2*x-1 + x-1*y-1*z + 2*x-1*y-1 + x-2*z-1 + 2*x-2*y-1 + x-2*y-1*z-1 + x-3*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 998
Image of polytope 998 PALP id: 998
grdb id: 420039
Integer points: [ 1 0 0 -1 -1 -1 -1 -3 -2 -2 -1 0]
[ 0 1 0 -1 0 -1 1 -1 -1 0 0 0]
[ 0 0 1 0 -1 -1 0 -2 -1 -1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
111 ? x + y + z + x-1*y + 2*x-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1 + 2*x-2*z-1 + 2*x-2*y-1*z-1 + x-3*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 999
Image of polytope 999 PALP id: 999
grdb id: 420480
Integer points: [ 1 0 0 -1 0 -1 -2 -3 -1 -2 0 -1]
[ 0 1 -1 0 0 0 -2 -2 -1 -1 0 -1]
[ 0 0 0 0 1 -1 -1 -2 0 -1 0 -1]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? x + y + z + y-1 + x-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1000
Image of polytope 1000 PALP id: 1000
grdb id: 420060
Integer points: [ 1 0 0 0 -2 0 -3 -1 -2 -1 -1 0]
[ 0 1 -1 0 -1 -1 -1 -1 -1 0 -1 0]
[ 0 0 0 1 -1 1 -1 1 0 0 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 8 1 none
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1001
Image of polytope 1001 PALP id: 1001
grdb id: 420468
Integer points: [ 1 0 0 0 -1 -1 -2 -3 -1 -2 0 -1]
[ 0 1 -1 0 1 -1 1 0 0 0 0 0]
[ 0 0 0 1 0 -1 -1 -2 0 -1 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
147 ? x + y + z + x-1*y + y-1 + 3*x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1*z-1 + 3*x-2*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Polytope 1002
Image of polytope 1002 PALP id: 1002
grdb id: 424846
Integer points: [ 1 0 0 0 0 -1 0 -1 0 0 0 -1]
[ 0 1 0 -1 1 0 -1 0 -1 0 0 0]
[ 0 0 1 1 -1 1 -1 -1 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
100 ? x + y + z + y*z-1 + y-1*z + x-1*z + 2*z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1003
Image of polytope 1003 PALP id: 1003
grdb id: 424844
Integer points: [ 1 0 1 -1 0 1 -1 -1 -1 0 0 0]
[ 0 1 -1 1 0 -1 -1 -1 0 -1 -1 0]
[ 0 0 0 0 1 -1 0 -1 0 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
143 ? x + y + z + x*y-1 + x-1*y + x*y-1*z-1 + 2*y-1 + 2*x-1 + 2*y-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1004
Image of polytope 1004 PALP id: 1004
grdb id: 424124
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 0 2 0 0 1 1 0]
[ 0 0 0 1 1 -1 -1 1 0 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + x-1*y2*z-1 + 2*x-1*y + y-1*z + x-1*z + 2*x-1*y*z-1 + y-1 + 2*x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1005
Image of polytope 1005 PALP id: 1005
grdb id: 424631
Integer points: [ 1 0 0 -1 -1 -1 0 -1 -1 -1 0 0]
[ 0 1 0 1 0 -1 -1 -2 -1 0 -1 0]
[ 0 0 1 0 -1 -1 1 0 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
129 ? x + y + z + x-1*y + y-1*z + 2*y-1 + 3*x-1 + x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Polytope 1006
Image of polytope 1006 PALP id: 1006
grdb id: 424645
Integer points: [ 1 0 0 -1 -1 -1 0 -1 -1 -1 0 0]
[ 0 1 0 1 1 0 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 0 -1 1 0 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
114 ? x + y + z + x-1*y + y-1*z + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*z-1 + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Polytope 1007
Image of polytope 1007 PALP id: 1007
grdb id: 424144
Integer points: [ 1 0 0 -1 0 0 -2 -2 -1 -1 -2 0]
[ 0 1 -1 1 0 -1 1 -1 -1 0 0 0]
[ 0 0 0 0 1 1 -1 -1 0 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
147 ? x + y + z + x-1*y + y-1*z + y-1 + 3*x-1 + x-2*y*z-1 + 2*x-1*y-1 + 2*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 1008
Image of polytope 1008 PALP id: 1008
grdb id: 424582
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 1 -1 1 -2 0 -1 0 0]
[ 0 0 0 1 0 0 -1 -1 0 -1 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + x-1*y + x-1*y*z-1 + y-1 + 2*x-1 + 3*x-1*z-1 + x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 9 1 irreducible and admissible
Polytope 1009
Image of polytope 1009 PALP id: 1009
grdb id: 424127
Integer points: [ 1 0 0 0 -1 0 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 -1 0 -2 0 -1 -1 0]
[ 0 0 0 1 -1 1 1 1 0 0 1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
65 ? x + y + z + y-1*z + x-1*z + y-1 + 2*x-1 + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1010
Image of polytope 1010 PALP id: 1010
grdb id: 424638
Integer points: [ 1 0 0 0 0 0 -1 -1 0 0 -1 -1]
[ 0 1 0 1 0 -1 1 -2 -1 0 -1 0]
[ 0 0 1 -1 -1 1 0 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
100 ? x + y + z + y*z-1 + x-1*y + y-1*z + z-1 + 2*y-1 + 3*x-1 + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Polytope 1011
Image of polytope 1011 PALP id: 1011
grdb id: 251691
Integer points: [ 1 0 0 0 1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 -1 1 0 -1 -1 0 -1 0]
[ 0 0 0 1 -1 0 1 0 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 6 1 none
Polytope 1012
Image of polytope 1012 PALP id: 1012
grdb id: 251690
Integer points: [ 1 0 0 0 -1 -1 -1 -2 -2 -1 -1 0]
[ 0 1 0 -1 0 -1 1 0 -1 0 -1 0]
[ 0 0 1 -1 -1 0 0 -1 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
148 ? x + y + z + x-1*y + x-1 + y-1*z-1 + x-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1013
Image of polytope 1013 PALP id: 1013
grdb id: 251664
Integer points: [ 1 0 0 -1 -1 0 -1 0 -1 -1 0 0]
[ 0 1 0 1 1 -1 0 -1 0 0 -1 0]
[ 0 0 1 1 0 -1 -1 1 1 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
55 rank 2, number 19 x + y + z + x-1*y*z + x-1*y + y-1*z + x-1*z + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1014
Image of polytope 1014 PALP id: 1014
grdb id: 251612
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 1 0 -1 -1 -1 0 0]
[ 0 0 0 1 -1 0 1 -1 1 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1015
Image of polytope 1015 PALP id: 1015
grdb id: 251683
Integer points: [ 1 0 0 0 1 -1 -1 0 0 0 0 -1]
[ 0 1 0 0 1 0 0 -1 -1 -1 0 0]
[ 0 0 1 -1 0 1 -1 -1 1 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x*y + x + y + z + y-1*z + x-1*z + z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1016
Image of polytope 1016 PALP id: 1016
grdb id: 251653
Integer points: [ 1 0 1 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 1 0 0 -1 0 -1 0 -1 0]
[ 0 0 0 0 1 -1 0 1 -1 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + x*y-1 + x-1*y + x-1*z + 2*y-1 + x-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1017
Image of polytope 1017 PALP id: 1017
grdb id: 251657
Integer points: [ 1 0 1 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 1 0 1 0 -1 0 0 -1 0]
[ 0 0 0 0 1 -1 -1 0 1 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x*y-1 + x-1*y + x-1*z + x-1*y*z-1 + 2*y-1 + x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1018
Image of polytope 1018 PALP id: 1018
grdb id: 251643
Integer points: [ 1 0 1 -1 0 0 -1 -1 -1 -1 0 0]
[ 0 1 -1 1 0 -1 -1 0 -1 0 -1 0]
[ 0 0 0 0 1 -1 0 1 -1 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 6 1 none
Polytope 1019
Image of polytope 1019 PALP id: 1019
grdb id: 251674
Integer points: [ 1 0 1 -1 0 0 -1 -1 -1 -1 0 0]
[ 0 1 -1 1 0 1 1 0 -1 0 0 -1]
[ 0 0 0 0 1 -1 -1 1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 6 1 none
Polytope 1020
Image of polytope 1020 PALP id: 1020
grdb id: 251682
Integer points: [ 1 0 1 -1 0 1 1 0 -1 0 0 -1]
[ 0 1 -1 1 0 1 0 -1 -1 -1 0 0]
[ 0 0 0 0 1 -1 -1 1 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
128 ? x*y*z-1 + x + y + z + x*z-1 + x*y-1 + x-1*y + y-1*z + 2*y-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1021
Image of polytope 1021 PALP id: 1021
grdb id: 251679
Integer points: [ 1 0 1 0 -1 0 0 1 -1 0 0 -1]
[ 0 1 -1 0 1 0 1 0 -1 -1 0 0]
[ 0 0 0 1 0 -1 -1 1 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x*z + x + y + z + y*z-1 + x*y-1 + x-1*y + z-1 + 2*y-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1022
Image of polytope 1022 PALP id: 1022
grdb id: 251663
Integer points: [ 1 0 1 0 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 -1 1 0 -1 -1 0 -1 0]
[ 0 0 0 1 1 -1 -1 0 1 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x*y-1 + y-1*z + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 1023
Image of polytope 1023 PALP id: 1023
grdb id: 251681
Integer points: [ 1 0 1 0 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 0 1 0 0 -1 0 0 -1]
[ 0 0 0 1 -1 0 1 -1 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 5 1 none
Polytope 1024
Image of polytope 1024 PALP id: 1024
grdb id: 251677
Integer points: [ 1 0 1 -1 0 -1 0 -1 -1 -1 0 0]
[ 0 1 -1 1 0 2 -1 1 -1 0 0 -1]
[ 0 0 0 0 1 -1 1 -1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*y2*z-1 + x*y-1 + x-1*y + y-1*z + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1025
Image of polytope 1025 PALP id: 1025
grdb id: 251668
Integer points: [ 1 0 -1 0 -1 -1 0 -1 -1 -1 0 0]
[ 0 1 0 0 -1 -2 -1 -1 -2 -1 -1 0]
[ 0 0 0 1 -1 0 1 1 1 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
98 rank 3, number 21 x + y + z + y-1*z + 2*y-1 + x-1 + x-1*y-1*z + x-1*y-1 + x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1026
Image of polytope 1026 PALP id: 1026
grdb id: 251647
Integer points: [ 1 0 0 -1 0 -1 0 -2 -2 -1 0 -1]
[ 0 1 -1 0 0 1 1 1 1 1 0 0]
[ 0 0 0 0 1 0 -1 -1 -2 -1 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
28 rank 2, number 25 x + y + z + y*z-1 + x-1*y + x-1*y*z-1 + y-1 + x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1027
Image of polytope 1027 PALP id: 1027
grdb id: 251680
Integer points: [ 1 0 0 -1 0 1 -1 0 1 0 0 0]
[ 0 1 -1 0 0 1 1 -2 1 1 0 -1]
[ 0 0 0 0 1 0 -1 1 -1 -1 0 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x*y + x*y*z-1 + x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y*z-1 + y-1 + x-1 + y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1028
Image of polytope 1028 PALP id: 1028
grdb id: 251655
Integer points: [ 1 0 0 0 -1 -1 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 0 0 1 1 1 0 1 0]
[ 0 0 0 1 -1 1 0 1 1 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
160 ? x + y + z + x-1*y*z + 2*x-1*y + x-1*z + x-2*y*z + y-1 + x-1 + x-2*y + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1029
Image of polytope 1029 PALP id: 1029
grdb id: 251686
Integer points: [ 1 0 0 0 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 0 0 1 0 -1 -2 -1 0 -1]
[ 0 0 1 -1 0 -1 -1 0 1 0 0 1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + 2*y-1*z + z-1 + x-1*y*z-1 + 2*y-1 + x-1 + y-2*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1030
Image of polytope 1030 PALP id: 1030
grdb id: 251644
Integer points: [ 1 0 0 0 -1 0 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 0 -1 -1 -1 -1 0 -1 0]
[ 0 0 0 1 -1 1 0 1 -1 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
47 ? x + y + z + y-1*z + y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1 + x-2*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1031
Image of polytope 1031 PALP id: 1031
grdb id: 251669
Integer points: [ 1 0 0 0 -1 0 -1 -2 -2 -1 -1 0]
[ 0 1 -1 0 0 -1 0 1 1 0 1 0]
[ 0 0 0 1 -1 1 1 -1 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
147 ? x + y + z + 2*x-1*y + y-1*z + x-1*z + y-1 + 3*x-1 + x-2*y + x-1*z-1 + x-2*y*z-1
112 rank 3, number 15 x + y + z + 2*x-1*y + y-1*z + x-1*z + y-1 + 2*x-1 + x-2*y + x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Polytope 1032
Image of polytope 1032 PALP id: 1032
grdb id: 251675
Integer points: [ 1 0 0 0 -1 0 0 1 -2 -1 0 -1]
[ 0 1 0 0 0 -1 1 0 -2 -1 0 -1]
[ 0 0 1 -1 0 0 1 1 -1 0 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
60 rank 2, number 18 x*z + y*z + x + y + z + z-1 + y-1 + x-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Polytope 1033
Image of polytope 1033 PALP id: 1033
grdb id: 251670
Integer points: [ 1 0 0 0 0 -1 -2 -1 -2 -1 0 -1]
[ 0 1 -1 0 -1 0 -1 -1 -1 -1 0 0]
[ 0 0 0 1 -1 1 0 1 1 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
47 ? x + y + z + x-1*z + y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + x-1*y-1 + x-2*y-1*z + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1034
Image of polytope 1034 PALP id: 1034
grdb id: 251654
Integer points: [ 1 0 0 0 0 -1 -1 -2 -2 -1 0 -1]
[ 0 1 -1 0 1 -1 0 -1 -1 0 0 -1]
[ 0 0 0 1 -1 1 1 0 1 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
66 rank 2, number 24 x + y + z + y*z-1 + x-1*z + y-1 + x-1 + x-1*y-1*z + 2*x-1*y-1 + x-2*y-1*z + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1035
Image of polytope 1035 PALP id: 1035
grdb id: 251645
Integer points: [ 1 0 0 0 0 0 -1 -1 -2 -1 0 -1]
[ 0 1 0 0 -1 1 1 -1 0 0 0 0]
[ 0 0 1 -1 0 -1 -1 -1 -1 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
29 rank 2, number 23 x + y + z + y*z-1 + z-1 + x-1*y*z-1 + y-1 + 2*x-1 + x-1*z-1 + x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1036
Image of polytope 1036 PALP id: 1036
grdb id: 251685
Integer points: [ 1 0 0 1 -1 0 0 0 -2 -1 0 -1]
[ 0 1 0 -1 1 -1 0 1 1 1 0 0]
[ 0 0 1 -1 1 0 -1 1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? y*z + x + y + z + x-1*y*z + 2*x-1*y + x*y-1*z-1 + z-1 + y-1 + 2*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 1037
Image of polytope 1037 PALP id: 1037
grdb id: 251665
Integer points: [ 1 0 1 -1 -1 0 -2 0 -2 -1 0 0]
[ 0 1 -1 1 -1 0 1 -1 0 0 0 -1]
[ 0 0 0 0 0 1 -1 1 -1 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
82 ? x + y + z + x*y-1 + x-1*y + y-1*z + 2*y-1 + 3*x-1 + x-2*y*z-1 + x-1*y-1 + x-2*z-1
159 ? x + y + z + x*y-1 + x-1*y + y-1*z + 2*y-1 + 2*x-1 + x-2*y*z-1 + x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Polytope 1038
Image of polytope 1038 PALP id: 1038
grdb id: 253947
Integer points: [ 1 0 -1 0 0 -1 -1 0 -1 0 -1 0]
[ 0 1 1 0 -1 -1 0 -1 -1 -1 0 0]
[ 0 0 0 1 -1 0 1 1 1 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? x + y + z + x-1*y + y-1*z + x-1*z + 2*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1039
Image of polytope 1039 PALP id: 1039
grdb id: 253620
Integer points: [ 1 0 0 -1 -1 -1 0 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 1 -1 1 0 0 0]
[ 0 0 1 -1 0 0 1 1 1 1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
63 ? y*z + x + y + z + x-1*y*z + x-1*y + 2*x-1*z + 2*x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
105 ? y*z + x + y + z + x-1*y*z + x-1*y + 2*x-1*z + 3*x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1040
Image of polytope 1040 PALP id: 1040
grdb id: 253880
Integer points: [ 1 0 0 -1 -1 1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 1 0 1 1 0 1 0]
[ 0 0 1 -1 0 1 1 0 1 0 1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
57 ? x*y*z + 2*y*z + x + y + z + x-1*y*z + x-1*y + x-1*z + x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1041
Image of polytope 1041 PALP id: 1041
grdb id: 253625
Integer points: [ 1 0 0 -1 0 -1 0 -1 -1 -1 -1 0]
[ 0 1 -1 1 0 -1 -1 0 -1 -1 0 0]
[ 0 0 0 0 1 -1 1 1 1 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1042
Image of polytope 1042 PALP id: 1042
grdb id: 253678
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 1 1 -1 0 0 0 0]
[ 0 0 0 1 0 0 -1 -1 1 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + x-1*y + x-1*z + x-1*y*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
122 ? x + y + z + x-1*y + x-1*z + x-1*y*z-1 + y-1 + 3*x-1 + 2*x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1043
Image of polytope 1043 PALP id: 1043
grdb id: 253688
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 1 -1 0 -1 -1 0 0]
[ 0 0 0 1 -1 0 -1 1 1 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
145 ? x + y + z + x-1*y + x-1*z + y-1 + 3*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
103 ? x + y + z + x-1*y + x-1*z + y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1044
Image of polytope 1044 PALP id: 1044
grdb id: 253986
Integer points: [ 1 0 0 0 -1 1 0 0 -1 0 0 -1]
[ 0 1 0 1 1 -1 0 -1 -1 -1 0 0]
[ 0 0 1 -1 0 0 -1 1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
100 ? x + y + z + y*z-1 + x*y-1 + x-1*y + y-1*z + z-1 + 2*y-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1045
Image of polytope 1045 PALP id: 1045
grdb id: 253900
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 0 0 -1 -1 -1 0 0]
[ 0 0 0 1 -1 -1 1 -1 1 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + x-1*z + y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1046
Image of polytope 1046 PALP id: 1046
grdb id: 253997
Integer points: [ 1 0 0 0 1 -1 0 0 -1 0 -1 0]
[ 0 1 0 0 0 1 -1 -1 -1 -1 0 0]
[ 0 0 1 -1 -1 0 1 -1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x*z-1 + x-1*y + y-1*z + z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 1047
Image of polytope 1047 PALP id: 1047
grdb id: 253987
Integer points: [ 1 0 0 1 -1 0 0 -1 -1 -1 0 0]
[ 0 1 0 -1 1 0 -1 0 -1 0 -1 0]
[ 0 0 1 0 0 -1 1 -1 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
88 ? x + y + z + x*y-1 + x-1*y + y-1*z + z-1 + 2*y-1 + 2*x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1048
Image of polytope 1048 PALP id: 1048
grdb id: 253985
Integer points: [ 1 0 0 1 -1 0 1 0 -1 -1 0 0]
[ 0 1 0 -1 1 0 0 -1 -1 0 -1 0]
[ 0 0 1 0 0 -1 -1 1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
85 rank 3, number 8 x + y + z + x*z-1 + x*y-1 + x-1*y + y-1*z + z-1 + 2*y-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1049
Image of polytope 1049 PALP id: 1049
grdb id: 254003
Integer points: [ 1 0 1 -1 0 0 -1 0 -1 0 -1 0]
[ 0 1 -1 1 0 -1 0 -1 0 -1 0 0]
[ 0 0 0 0 1 -1 -1 1 1 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + x*y-1 + x-1*y + y-1*z + x-1*z + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1050
Image of polytope 1050 PALP id: 1050
grdb id: 253990
Integer points: [ 1 0 1 -1 0 1 0 -1 -1 0 -1 0]
[ 0 1 -1 1 0 -1 -1 0 -1 -1 0 0]
[ 0 0 0 0 1 -1 -1 1 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
143 ? x + y + z + x*y-1 + x-1*y + x-1*z + x*y-1*z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1051
Image of polytope 1051 PALP id: 1051
grdb id: 253840
Integer points: [ 1 0 1 0 -1 0 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 0 -1 -1 0 -1 0 -1 0]
[ 0 0 0 1 -1 -1 0 1 -1 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + x*y-1 + x-1*z + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 1052
Image of polytope 1052 PALP id: 1052
grdb id: 253864
Integer points: [ 1 0 0 -1 0 -1 0 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 -1 -1 0 -1 -1 -1 0]
[ 0 0 0 0 1 -1 1 1 2 0 1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
160 ? x + y + z + y-1*z + x-1*z + x-1*y-1*z2 + y-1 + x-1 + 3*x-1*y-1*z + 3*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Polytope 1053
Image of polytope 1053 PALP id: 1053
grdb id: 253821
Integer points: [ 1 0 0 0 -1 0 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 1 -1 1 2 0 1 0]
[ 0 0 0 1 -1 1 -1 1 1 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? y*z + x-1*y2*z + x + y + z + x-1*y*z + 2*x-1*y + y-1 + 2*x-1 + x-1*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1054
Image of polytope 1054 PALP id: 1054
grdb id: 253914
Integer points: [ 1 0 1 -1 0 0 -1 -1 -1 -1 0 0]
[ 0 1 -1 1 0 1 1 -1 2 0 0 -1]
[ 0 0 0 0 1 -1 -1 0 -1 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + y*z-1 + x-1*y2*z-1 + x*y-1 + x-1*y + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1055
Image of polytope 1055 PALP id: 1055
grdb id: 253608
Integer points: [ 1 0 0 -1 -1 -1 -1 -2 -2 -2 -1 0]
[ 0 1 0 0 -1 -1 1 -1 1 0 0 0]
[ 0 0 1 -1 0 -1 0 -1 -1 -1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
69 ? x + y + z + x-1*y + 3*x-1 + x-1*z-1 + x-2*y*z-1 + x-1*y-1 + x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1*z-1
37 rank 3, number 17 x + y + z + x-1*y + 2*x-1 + x-1*z-1 + x-2*y*z-1 + x-1*y-1 + x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1056
Image of polytope 1056 PALP id: 1056
grdb id: 253766
Integer points: [ 1 0 0 -1 0 -1 -2 0 -2 -1 -1 0]
[ 0 1 -1 1 0 -1 0 -1 -1 -1 0 0]
[ 0 0 0 0 1 -1 -1 1 -1 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
147 ? x + y + z + x-1*y + y-1*z + y-1 + 3*x-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-1
112 rank 3, number 15 x + y + z + x-1*y + y-1*z + y-1 + 2*x-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1057
Image of polytope 1057 PALP id: 1057
grdb id: 253915
Integer points: [ 1 0 0 -1 0 -1 -1 -2 -2 -1 -1 0]
[ 0 1 -1 0 0 0 -2 -1 -2 -1 -1 0]
[ 0 0 0 0 1 -1 -1 -1 -1 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? x + y + z + y-1 + x-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1 + x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 1058
Image of polytope 1058 PALP id: 1058
grdb id: 253965
Integer points: [ 1 0 0 0 -1 -2 0 -2 -1 -1 -1 0]
[ 0 1 -1 0 -1 -1 -1 -1 -1 0 -1 0]
[ 0 0 0 1 -1 0 1 -1 1 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
69 ? x + y + z + y-1*z + y-1 + 2*x-1 + x-1*y-1*z + 2*x-1*y-1 + x-1*y-1*z-1 + x-2*y-1 + x-2*y-1*z-1
87 ? x + y + z + y-1*z + y-1 + 2*x-1 + x-1*y-1*z + 3*x-1*y-1 + x-1*y-1*z-1 + x-2*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Polytope 1059
Image of polytope 1059 PALP id: 1059
grdb id: 253743
Integer points: [ 1 0 0 0 -1 -1 -1 -2 -2 -2 -1 0]
[ 0 1 -1 0 -1 0 1 1 -1 0 0 0]
[ 0 0 0 1 0 -1 0 -1 -1 -1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
65 ? x + y + z + x-1*y + y-1 + 2*x-1 + x-1*z-1 + x-2*y*z-1 + x-1*y-1 + 2*x-2*z-1 + x-2*y-1*z-1
95 ? x + y + z + x-1*y + y-1 + 3*x-1 + x-1*z-1 + x-2*y*z-1 + x-1*y-1 + 2*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1060
Image of polytope 1060 PALP id: 1060
grdb id: 253828
Integer points: [ 1 0 0 0 -1 -1 -1 -2 -2 -1 -1 0]
[ 0 1 -1 0 1 1 -1 0 1 0 0 0]
[ 0 0 0 1 0 -1 -1 -1 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + x-1*y + x-1*y*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 1061
Image of polytope 1061 PALP id: 1061
grdb id: 253819
Integer points: [ 1 0 0 0 -1 0 -2 -2 -1 -1 -1 0]
[ 0 1 -1 0 0 1 0 1 1 1 0 0]
[ 0 0 0 1 -1 1 -1 0 1 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? y*z + x + y + z + x-1*y*z + 2*x-1*y + y-1 + x-1 + x-2*y + x-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1062
Image of polytope 1062 PALP id: 1062
grdb id: 253974
Integer points: [ 1 0 0 0 -1 0 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 1 -1 0 -1 -2 0 -1 0]
[ 0 0 0 1 0 -1 -1 0 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + x-1*y + y-1 + 2*x-1 + y-1*z-1 + x-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1063
Image of polytope 1063 PALP id: 1063
grdb id: 253844
Integer points: [ 1 0 0 0 -1 0 -1 -1 -1 -1 0 0]
[ 0 1 0 0 0 1 0 -1 -2 -1 0 -1]
[ 0 0 1 -1 0 -1 1 1 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + y*z-1 + x-1*z + z-1 + 2*y-1 + x-1 + x-1*y-1*z + 2*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 1064
Image of polytope 1064 PALP id: 1064
grdb id: 253824
Integer points: [ 1 0 0 0 0 -1 -1 -2 -2 -1 -1 0]
[ 0 1 -1 0 -1 1 -1 0 1 0 0 0]
[ 0 0 0 1 -1 0 -1 -1 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + x-1*y + y-1 + 2*x-1 + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Polytope 1065
Image of polytope 1065 PALP id: 1065
grdb id: 253949
Integer points: [ 1 0 0 0 0 -1 -1 -2 -2 -1 -1 0]
[ 0 1 -1 0 1 1 0 0 1 0 1 0]
[ 0 0 0 1 -1 0 -1 -1 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + y*z-1 + x-1*y + 2*x-1*y*z-1 + y-1 + 2*x-1 + x-1*z-1 + x-2*y*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 1066
Image of polytope 1066 PALP id: 1066
grdb id: 253989
Integer points: [ 1 0 0 0 0 -1 -1 -2 -2 -1 -1 0]
[ 0 1 0 0 -1 0 -1 -1 -1 0 -1 0]
[ 0 0 1 -1 0 1 1 0 1 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
147 ? x + y + z + x-1*z + z-1 + y-1 + 2*x-1 + x-1*y-1*z + 2*x-1*y-1 + x-2*y-1*z + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1067
Image of polytope 1067 PALP id: 1067
grdb id: 253992
Integer points: [ 1 0 0 0 0 -1 0 -1 -2 -1 -1 0]
[ 0 1 0 0 -1 0 -1 -1 -1 -1 0 0]
[ 0 0 1 -1 0 0 -1 -2 -2 -1 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + z-1 + y-1 + x-1 + y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1*z-1 + x-1*y-1*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 1068
Image of polytope 1068 PALP id: 1068
grdb id: 253963
Integer points: [ 1 0 0 0 0 0 -1 -1 -2 -1 0 -1]
[ 0 1 0 0 -1 -1 0 0 1 0 0 1]
[ 0 0 1 -1 0 1 1 -1 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + 2*x-1*y + y-1*z + x-1*z + z-1 + y-1 + x-1 + x-2*y + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1069
Image of polytope 1069 PALP id: 1069
grdb id: 253996
Integer points: [ 1 0 0 0 0 0 -1 -1 -2 -1 -1 0]
[ 0 1 0 0 -1 1 1 -1 0 0 0 0]
[ 0 0 1 -1 0 -1 0 1 1 0 1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + y*z-1 + x-1*y + 2*x-1*z + z-1 + y-1 + 2*x-1 + x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 1070
Image of polytope 1070 PALP id: 1070
grdb id: 253984
Integer points: [ 1 0 0 0 0 1 0 -1 -2 -1 -1 0]
[ 0 1 0 0 -1 -1 -1 -1 0 0 0 0]
[ 0 0 1 -1 0 0 -1 -1 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + x*y-1 + z-1 + y-1 + 2*x-1 + y-1*z-1 + 2*x-1*z-1 + x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1071
Image of polytope 1071 PALP id: 1071
grdb id: 253877
Integer points: [ 1 0 1 -1 -1 0 -1 -2 -2 -1 0 0]
[ 0 1 -1 1 -1 0 -1 0 -1 0 -1 0]
[ 0 0 0 0 0 1 -1 -1 -1 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? x + y + z + x*y-1 + x-1*y + 2*y-1 + x-1 + x-1*y-1 + x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1072
Image of polytope 1072 PALP id: 1072
grdb id: 253847
Integer points: [ 1 0 1 -1 -1 0 0 1 -2 0 -1 0]
[ 0 1 -1 1 0 -1 0 -2 1 -1 0 0]
[ 0 0 0 0 0 0 1 -1 -1 -1 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
60 rank 2, number 18 x + y + z + x*y-1 + x-1*y + y-1 + x-1 + x*y-2*z-1 + 3*y-1*z-1 + 3*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Polytope 1073
Image of polytope 1073 PALP id: 1073
grdb id: 253879
Integer points: [ 1 0 1 -1 0 -1 -1 -2 -2 -1 0 0]
[ 0 1 -1 1 0 0 -1 1 0 0 0 -1]
[ 0 0 0 0 1 -1 0 -1 -1 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + x*y-1 + x-1*y + 2*y-1 + x-1 + x-1*z-1 + x-2*y*z-1 + x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1074
Image of polytope 1074 PALP id: 1074
grdb id: 253994
Integer points: [ 1 0 1 0 0 0 -1 0 -2 -1 -1 0]
[ 0 1 -1 0 0 -1 1 1 0 0 0 0]
[ 0 0 0 1 -1 0 0 1 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 y*z + x + y + z + x*y-1 + x-1*y + z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 1075
Image of polytope 1075 PALP id: 1075
grdb id: 253971
Integer points: [ 1 0 0 0 -1 -1 -1 -2 -3 -1 -2 0]
[ 0 1 -1 0 0 1 1 0 1 0 1 0]
[ 0 0 0 1 -1 0 -1 -1 -2 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
47 ? x + y + z + x-1*y + x-1*y*z-1 + y-1 + 2*x-1 + x-1*z-1 + 2*x-2*y*z-1 + x-2*z-1 + x-3*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1076
Image of polytope 1076 PALP id: 1076
grdb id: 253194
Integer points: [ 1 0 0 0 -1 0 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 -1 -1 0 -1 -1 0 0]
[ 0 0 0 1 -1 1 -1 1 1 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + y-1*z + x-1*z + y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1077
Image of polytope 1077 PALP id: 1077
grdb id: 253434
Integer points: [ 1 0 0 0 -1 0 0 -1 -1 -1 0 0]
[ 0 1 0 0 1 -1 -1 0 0 0 -1 0]
[ 0 0 1 -1 0 -1 1 1 -1 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + x-1*y + y-1*z + x-1*z + z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1078
Image of polytope 1078 PALP id: 1078
grdb id: 253196
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 1 1 -1 -1 0 0 0]
[ 0 0 0 1 1 0 -1 0 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + x-1*y + y-1*z + x-1*y*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1079
Image of polytope 1079 PALP id: 1079
grdb id: 253437
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 0 0 -1 -1 -1 0 0]
[ 0 0 1 -1 0 -1 1 1 -1 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? x + y + z + x-1*z + z-1 + y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1080
Image of polytope 1080 PALP id: 1080
grdb id: 253446
Integer points: [ 1 0 0 1 -1 0 1 0 -1 0 -1 0]
[ 0 1 0 -1 1 0 -1 -1 -1 -1 0 0]
[ 0 0 1 0 0 -1 -1 -1 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
88 ? x + y + z + x*y-1 + x-1*y + x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1081
Image of polytope 1081 PALP id: 1081
grdb id: 253431
Integer points: [ 1 0 0 1 -1 0 1 0 -1 -1 0 0]
[ 0 1 0 -1 1 0 0 1 -1 0 -1 0]
[ 0 0 1 0 0 -1 -1 -1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
85 rank 3, number 8 x + y + z + x*z-1 + y*z-1 + x*y-1 + x-1*y + z-1 + 2*y-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1082
Image of polytope 1082 PALP id: 1082
grdb id: 253449
Integer points: [ 1 0 1 -1 0 0 -1 -1 -1 -1 0 0]
[ 0 1 -1 1 0 -1 0 -1 -1 0 -1 0]
[ 0 0 0 0 1 -1 -1 0 -1 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
114 ? x + y + z + x*y-1 + x-1*y + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1083
Image of polytope 1083 PALP id: 1083
grdb id: 253439
Integer points: [ 1 0 0 0 0 0 -1 -1 -2 -1 -1 0]
[ 0 1 0 0 -1 -1 0 -1 -1 0 -1 0]
[ 0 0 1 -1 0 1 -1 1 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? x + y + z + y-1*z + z-1 + y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 1084
Image of polytope 1084 PALP id: 1084
grdb id: 674626
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 -1 1 0 -1 0 -1 1 0 0]
[ 0 0 1 -1 1 -1 0 1 -1 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
66 rank 2, number 24 x + y + z + x-1*y*z + x-1*y + x-1*z + 2*x-1 + y-1*z-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
16 ? x + y + z + x-1*y*z + x-1*y + x-1*z + 3*x-1 + y-1*z-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Polytope 1085
Image of polytope 1085 PALP id: 1085
grdb id: 674625
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 1 -1 -1 1 1 0 0 0]
[ 0 0 0 1 -1 0 1 0 -1 1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
66 rank 2, number 24 x + y + z + y*z-1 + x-1*y + x-1*z + x-1*y*z-1 + y-1 + x-1 + x-1*y-1*z + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Polytope 1086
Image of polytope 1086 PALP id: 1086
grdb id: 674621
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 0 -1 1 0 1 0 0]
[ 0 0 1 -1 0 -1 0 0 1 1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + x-1*y*z + x-1*y + x-1*z + z-1 + y-1 + x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Polytope 1087
Image of polytope 1087 PALP id: 1087
grdb id: 674628
Integer points: [ 1 0 0 0 0 -1 0 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 0 1 0 -1 -1 -1 0]
[ 0 0 1 -1 0 0 1 1 -1 1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 y*z + x + y + z + x-1*z + z-1 + y-1 + x-1 + x-1*y-1*z + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 5 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1088
Image of polytope 1088 PALP id: 1088
grdb id: 674629
Integer points: [ 1 0 0 0 0 -1 1 0 -1 -1 -1 0]
[ 0 1 0 0 -1 1 -1 -1 0 -1 0 0]
[ 0 0 1 -1 0 0 1 1 -1 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + x*y-1*z + z + x-1*y + y-1*z + z-1 + y-1 + 2*x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 5 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1089
Image of polytope 1089 PALP id: 1089
grdb id: 674630
Integer points: [ 1 0 1 -1 0 -1 0 -1 1 -1 0 0]
[ 0 1 -1 1 -1 0 0 1 -2 0 -1 0]
[ 0 0 0 0 0 0 1 1 -1 -1 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
60 rank 2, number 18 x + y + z + x-1*y*z + x*y-1 + x-1*y + y-1 + x-1 + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1090
Image of polytope 1090 PALP id: 1090
grdb id: 674596
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 1 -1 1 -1 0 0 0]
[ 0 0 0 1 -1 0 0 -1 1 1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
147 ? x + y + z + x-1*y + x-1*z + x-1*y*z-1 + y-1 + 3*x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
112 rank 3, number 15 x + y + z + x-1*y + x-1*z + x-1*y*z-1 + y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 1091
Image of polytope 1091 PALP id: 1091
grdb id: 674595
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 1 -1 0 -1 0 1 1 0 0]
[ 0 0 1 1 -1 -1 0 1 0 1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? y*z + x + y + z + x-1*y*z + x-1*y + x-1*z + 2*x-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
65 ? y*z + x + y + z + x-1*y*z + x-1*y + x-1*z + 3*x-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 1092
Image of polytope 1092 PALP id: 1092
grdb id: 674586
Integer points: [ 1 0 0 0 -1 -1 -1 0 -1 -1 -1 0]
[ 0 1 -1 0 0 -1 1 1 0 1 0 0]
[ 0 0 0 1 -1 0 0 1 1 1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? y*z + x + y + z + x-1*y*z + x-1*y + x-1*z + y-1 + x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Polytope 1093
Image of polytope 1093 PALP id: 1093
grdb id: 674579
Integer points: [ 1 0 0 0 0 -1 0 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 0 -1 0 -1 -1 -1 0]
[ 0 0 1 -1 0 0 1 1 1 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + y-1*z + x-1*z + z-1 + y-1 + x-1 + x-1*y-1*z + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1094
Image of polytope 1094 PALP id: 1094
grdb id: 674577
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 1 0 -1 -1 0 0]
[ 0 0 1 -1 0 -1 0 1 0 1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + x-1*y + x-1*z + z-1 + y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1095
Image of polytope 1095 PALP id: 1095
grdb id: 674598
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 1 0 -1 1 0 0]
[ 0 0 1 -1 0 1 0 -1 -1 1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? y*z + x + y + z + x-1*y*z + x-1*y + z-1 + y-1 + 2*x-1 + x-1*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1096
Image of polytope 1096 PALP id: 1096
grdb id: 674606
Integer points: [ 1 0 0 0 0 0 0 1 -1 -1 -1 0]
[ 0 1 0 -1 1 0 -1 0 1 -1 0 0]
[ 0 0 1 1 -1 -1 0 -1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x*z-1 + y*z-1 + x-1*y + y-1*z + z-1 + y-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1097
Image of polytope 1097 PALP id: 1097
grdb id: 674602
Integer points: [ 1 0 0 0 0 1 -1 1 -1 0 -1 0]
[ 0 1 0 0 -1 -1 0 -1 0 -1 0 0]
[ 0 0 1 -1 0 0 1 -1 -1 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x*y-1 + x-1*z + x*y-1*z-1 + z-1 + y-1 + 2*x-1 + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1098
Image of polytope 1098 PALP id: 1098
grdb id: 674610
Integer points: [ 1 0 1 -1 0 0 0 -1 -1 -1 -1 0]
[ 0 1 -1 1 -1 0 -1 1 0 0 0 0]
[ 0 0 0 0 0 1 1 -1 -1 1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x*y-1 + x-1*y + y-1*z + x-1*z + x-1*y*z-1 + y-1 + 2*x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1099
Image of polytope 1099 PALP id: 1099
grdb id: 674600
Integer points: [ 1 0 1 0 0 0 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 -1 1 1 0 0 0 0]
[ 0 0 0 1 -1 0 0 1 -1 1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + x-1*y*z + x*y-1 + x-1*y + x-1*z + z-1 + y-1 + 2*x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1100
Image of polytope 1100 PALP id: 1100
grdb id: 674599
Integer points: [ 1 0 0 0 -1 0 -1 0 -1 -1 -1 0]
[ 0 1 0 0 0 -1 0 -1 -1 -2 -1 0]
[ 0 0 1 -1 0 0 -1 1 1 1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + y-1*z + z-1 + y-1 + x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1101
Image of polytope 1101 PALP id: 1101
grdb id: 674607
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -2 -1 0]
[ 0 1 0 0 -1 -1 0 1 1 1 0 0]
[ 0 0 1 -1 0 -1 1 1 0 1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + x-1*y*z + x-1*y + x-1*z + x-2*y*z + z-1 + y-1 + 2*x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1102
Image of polytope 1102 PALP id: 1102
grdb id: 674578
Integer points: [ 1 0 1 -1 0 0 -1 -1 -2 -2 -1 0]
[ 0 1 -1 1 -1 0 0 -1 1 0 0 0]
[ 0 0 0 0 0 1 -1 -1 -1 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + x*y-1 + x-1*y + y-1 + 2*x-1 + x-1*z-1 + x-2*y*z-1 + x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1103
Image of polytope 1103 PALP id: 1103
grdb id: 674597
Integer points: [ 1 0 1 -1 0 0 -1 -1 -2 -2 -1 0]
[ 0 1 -1 1 -1 0 1 0 1 0 0 0]
[ 0 0 0 0 0 1 -1 -1 -1 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + x*y-1 + x-1*y + x-1*y*z-1 + y-1 + 2*x-1 + x-1*z-1 + x-2*y*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1104
Image of polytope 1104 PALP id: 1104
grdb id: 674529
Integer points: [ 1 0 0 0 -1 0 -1 0 -1 -1 -1 0]
[ 0 1 0 0 0 -1 0 -1 -1 -1 -1 0]
[ 0 0 1 -1 0 0 -1 1 1 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + y-1*z + z-1 + y-1 + x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1105
Image of polytope 1105 PALP id: 1105
grdb id: 674536
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 -1 0 1 -1 1 0 1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? x + y + z + y-1*z + x-1*z + z-1 + y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1106
Image of polytope 1106 PALP id: 1106
grdb id: 674530
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 1 0 0 1 0 0]
[ 0 0 1 -1 0 1 -1 1 -1 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + x-1*y + y-1*z + x-1*z + z-1 + x-1*y*z-1 + y-1 + 2*x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1107
Image of polytope 1107 PALP id: 1107
grdb id: 674543
Integer points: [ 1 0 0 0 0 -1 0 -1 -1 -2 -1 0]
[ 0 1 0 0 -1 0 -1 0 -1 -1 -1 0]
[ 0 0 1 -1 0 0 -1 -1 0 -1 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + z-1 + y-1 + x-1 + y-1*z-1 + x-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1108
Image of polytope 1108 PALP id: 1108
grdb id: 12649
Integer points: [ 1 0 0 -1 1 0 0 -1 0 1 1 0]
[ 0 1 0 1 -1 0 -1 0 1 0 1 0]
[ 0 0 1 1 -1 -1 0 0 1 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
55 rank 2, number 19 x*y + y*z + x + y + z + x-1*y*z + x*z-1 + x*y-1*z-1 + z-1 + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 8 Lattice Minkowski decompositions of facet 3
Polytope 1109
Image of polytope 1109 PALP id: 1109
grdb id: 61964
Integer points: [ 1 0 0 -1 1 0 0 -1 -1 -1 0 0]
[ 0 1 0 1 -1 0 -1 0 1 0 1 0]
[ 0 0 1 1 -1 -1 0 0 0 1 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? y*z + x + y + z + x-1*y*z + x-1*y + x-1*z + x*y-1*z-1 + z-1 + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 6 Lattice Minkowski decompositions of facet 3
Polytope 1110
Image of polytope 1110 PALP id: 1110
grdb id: 61963
Integer points: [ 1 0 0 0 0 0 0 -1 -1 -1 -1 0]
[ 0 1 0 1 -1 -1 0 0 0 -1 -1 0]
[ 0 0 1 -1 1 0 -1 0 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + y*z-1 + y-1*z + z-1 + y-1 + x-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 6 Lattice Minkowski decompositions of facet 3
Polytope 1111
Image of polytope 1111 PALP id: 1111
grdb id: 61966
Integer points: [ 1 0 0 1 -1 0 0 -1 1 -1 0 0]
[ 0 1 0 -1 1 0 -1 0 -1 0 -1 0]
[ 0 0 1 0 0 -1 0 0 1 -1 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + x*y-1*z + z + x*y-1 + x-1*y + y-1*z + z-1 + y-1 + x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 6 Lattice Minkowski decompositions of facet 3
Polytope 1112
Image of polytope 1112 PALP id: 1112
grdb id: 61961
Integer points: [ 1 0 0 -1 1 -1 1 0 0 -1 0 0]
[ 0 1 0 1 0 0 -1 0 -1 0 1 0]
[ 0 0 1 1 -1 1 -1 -1 0 0 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? y*z + x + y + z + x-1*y*z + x*z-1 + x-1*z + x*y-1*z-1 + z-1 + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 5 Lattice Minkowski decompositions of facet 3
Polytope 1113
Image of polytope 1113 PALP id: 1113
grdb id: 61959
Integer points: [ 1 0 0 0 0 0 0 -1 -1 -1 -1 0]
[ 0 1 0 1 -1 0 -1 0 1 0 1 0]
[ 0 0 1 -1 1 -1 0 0 -1 1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + y*z-1 + x-1*y + y-1*z + x-1*z + z-1 + x-1*y*z-1 + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 5 Lattice Minkowski decompositions of facet 3
Polytope 1114
Image of polytope 1114 PALP id: 1114
grdb id: 547497
Integer points: [ 1 0 0 -10 -8 -6 -4 -2 -5 -3 -1 -2 0]
[ 0 1 0 -5 -4 -3 -2 -1 -2 -1 0 -1 0]
[ 0 0 1 -4 -3 -2 -1 0 -2 -1 0 -1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 73 1 none
Image of facet 43 1 irreducible and admissible
Image of facet 4 1 none
Polytope 1115
Image of polytope 1115 PALP id: 1115
grdb id: 546621
Integer points: [ 1 0 0 -3 -1 -1 0 -2 -1 -2 0 0 -1]
[ 0 1 1 -2 0 0 1 -1 0 -1 0 0 -1]
[ 0 0 2 -2 2 1 1 0 0 -1 1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 3 irreducible and admissible
Image of facet 74 1 none
Polytope 1116
Image of polytope 1116 PALP id: 1116
grdb id: 546627
Integer points: [ 1 0 0 -2 -4 -1 -2 -3 -1 -2 -3 0 -1]
[ 0 1 0 0 -4 -1 -2 -3 0 -1 -2 0 -1]
[ 0 0 1 -1 -3 0 -1 -2 0 -1 -2 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 8 1 none
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 1117
Image of polytope 1117 PALP id: 1117
grdb id: 546582
Integer points: [ 1 0 0 -4 -1 -2 -3 -1 -2 -1 0 -1 0]
[ 0 1 0 -2 -2 -2 -2 -1 -1 0 -1 -1 0]
[ 0 0 1 -1 2 1 0 1 0 0 1 0 0]
Degree: 52
Hilbert function: 1 + 29 t + 135 t2 + 371 t3 + 789 t4 + 1441 t5 + 2379 t6 + 3655 t7 + 5321 t8 + 7429 t9 + 10031 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 75 1 none
Image of facet 14 1 none
Polytope 1118
Image of polytope 1118 PALP id: 1118
grdb id: 546626
Integer points: [ 1 0 0 0 -4 -2 -1 0 -3 -2 -1 -1 0]
[ 0 1 0 -2 2 1 0 -1 1 0 -1 1 0]
[ 0 0 1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 4 1 none
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Polytope 1119
Image of polytope 1119 PALP id: 1119
grdb id: 546609
Integer points: [ 1 0 1 -4 0 -1 0 -2 -1 -3 -2 1 0]
[ 0 1 0 -1 -1 -1 0 -1 0 -1 0 0 0]
[ 0 0 2 -2 2 1 1 0 0 -1 -1 1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x*z2 + 2*x*z + x + y + 3*z + y-1*z2 + 4*x-1 + 4*x-1*y-1*z + 2*x-2*z-1 + 6*x-2*y-1 + 4*x-3*y-1*z-1 + x-4*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Image of facet 13 1 irreducible and admissible
Polytope 1120
Image of polytope 1120 PALP id: 1120
grdb id: 546615
Integer points: [ 1 1 0 -4 -2 -1 -3 -2 -1 0 -1 0 1]
[ 0 2 0 -2 -2 -1 -2 -1 0 1 -1 0 1]
[ 0 0 1 -1 1 1 0 0 0 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 4 1 none
Image of facet 77 1 none
Polytope 1121
Image of polytope 1121 PALP id: 1121
grdb id: 546651
Integer points: [ 1 1 0 -2 -2 -1 -1 -2 0 0 0 1 1]
[ 0 3 0 -2 -4 -2 -1 -3 -1 0 1 1 2]
[ 0 0 1 -1 -1 0 0 -1 0 0 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 4 2 none
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1122
Image of polytope 1122 PALP id: 1122
grdb id: 546636
Integer points: [ 1 0 0 -4 -6 -5 -4 -3 -2 -2 -1 -2 0]
[ 0 1 0 -1 -3 -2 -2 -1 0 -1 0 -1 0]
[ 0 0 1 -2 -2 -2 -1 -1 -1 0 0 -1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 4 1 none
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Image of facet 9 1 irreducible and admissible
Polytope 1123
Image of polytope 1123 PALP id: 1123
grdb id: 546628
Integer points: [ 1 0 0 -2 -6 -3 -5 -2 -4 -1 -3 -1 0]
[ 0 1 0 0 -4 -2 -3 -1 -2 0 -1 -1 0]
[ 0 0 1 -1 -1 0 -1 0 -1 0 -1 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 4 1 none
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Image of facet 13 1 irreducible and admissible
Polytope 1124
Image of polytope 1124 PALP id: 1124
grdb id: 546589
Integer points: [ 1 0 0 -1 -7 -3 -5 -2 -4 -1 -1 -3 0]
[ 0 1 0 -1 -4 -2 -3 -1 -2 0 -1 -2 0]
[ 0 0 1 1 -2 0 -1 0 -1 0 0 -1 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 14 1 none
Image of facet 79 1 none
Polytope 1125
Image of polytope 1125 PALP id: 1125
grdb id: 546629
Integer points: [ 1 0 0 -2 -8 -6 -4 -2 -5 -3 -1 -2 0]
[ 0 1 0 0 -4 -3 -2 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 -3 -2 -1 0 -2 -1 0 -1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 80 1 none
Image of facet 4 1 none
Image of facet 13 1 irreducible and admissible
Polytope 1126
Image of polytope 1126 PALP id: 1126
grdb id: 546434
Integer points: [ 1 0 0 -2 -2 -1 -1 -2 -1 -2 -2 0 0]
[ 0 1 0 0 -4 -2 -1 -3 0 -2 -1 -1 0]
[ 0 0 1 -1 -1 0 0 -1 0 -1 -1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 4 1 none
Image of facet 13 1 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 1127
Image of polytope 1127 PALP id: 1127
grdb id: 539635
Integer points: [ 1 0 0 0 -2 -2 -2 -1 -1 -1 0 -1 0]
[ 0 1 0 -2 0 2 1 -1 0 1 -1 1 0]
[ 0 0 1 -1 -1 1 0 -1 0 1 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 4 1 none
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Polytope 1128
Image of polytope 1128 PALP id: 1128
grdb id: 539628
Integer points: [ 1 0 0 -1 0 -3 -2 -1 -2 0 -1 -1 0]
[ 0 1 0 1 -2 1 1 0 0 -1 -1 1 0]
[ 0 0 1 1 -1 -1 0 0 -1 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 4 1 none
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Polytope 1129
Image of polytope 1129 PALP id: 1129
grdb id: 539636
Integer points: [ 1 0 0 2 1 -3 1 1 0 -1 0 -1 -2]
[ 0 1 0 -2 -2 2 -1 -1 0 1 -1 0 1]
[ 0 0 1 -1 -2 2 0 -1 0 1 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 13 1 irreducible and admissible
Image of facet 6 2 none
Polytope 1130
Image of polytope 1130 PALP id: 1130
grdb id: 539637
Integer points: [ 1 1 0 -2 0 -2 -1 -1 0 0 0 1 1]
[ 0 3 0 -4 1 -3 -1 -2 1 0 -1 2 1]
[ 0 0 1 -1 1 -1 0 0 0 0 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 4 2 none
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1131
Image of polytope 1131 PALP id: 1131
grdb id: 539548
Integer points: [ 1 0 0 -2 -1 -2 -2 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -2 -2 -1 -1 0 -1 0 -1 0]
[ 0 0 1 1 -2 -1 0 0 1 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 27 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1132
Image of polytope 1132 PALP id: 1132
grdb id: 539540
Integer points: [ 1 0 0 -2 -2 1 -1 0 -1 -2 -1 1 0]
[ 0 1 1 -1 -1 2 0 1 0 -1 0 1 0]
[ 0 0 2 -2 0 2 -1 1 0 -1 1 1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x*y2*z2 + 2*x*y*z + y*z2 + 3*y*z + x + y + 2*x-1*z + 4*x-1 + 2*x-1*z-1 + x-2*y-1 + 2*x-2*y-1*z-1 + x-2*y-1*z-2
32 ? x*y2*z2 + 2*x*y*z + y*z2 + 4*y*z + x + y + 2*x-1*z + 5*x-1 + 2*x-1*z-1 + x-2*y-1 + 2*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 5 irreducible and admissible
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Polytope 1133
Image of polytope 1133 PALP id: 1133
grdb id: 539453
Integer points: [ 1 0 0 -2 -1 -2 -1 -2 -1 -2 -1 0 0]
[ 0 1 0 -2 2 1 1 0 0 -1 -1 1 0]
[ 0 0 1 1 -2 -2 -1 -1 0 0 1 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + 2*y*z-1 + x-1*y2*z-2 + 3*x-1*y*z-1 + 4*x-1 + 2*x-1*y-1*z + x-2*y*z-2 + 3*x-2*z-1 + 3*x-2*y-1 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 9 1 irreducible and admissible
Polytope 1134
Image of polytope 1134 PALP id: 1134
grdb id: 539492
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 -2 2 1 0 0 -1 1 0 -1]
[ 0 0 1 1 0 -2 -1 0 -1 0 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Polytope 1135
Image of polytope 1135 PALP id: 1135
grdb id: 539569
Integer points: [ 1 0 0 0 -1 -2 -1 -1 0 -1 0 0 0]
[ 0 1 -1 1 0 -1 0 -1 0 0 1 0 0]
[ 0 0 0 2 -2 -2 0 -1 1 -1 1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 y*z2 + 2*y*z + x + y + 2*z + 2*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 3 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1136
Image of polytope 1136 PALP id: 1136
grdb id: 539570
Integer points: [ 1 1 -1 0 0 -2 -1 0 -1 -1 0 1 0]
[ 0 2 -2 0 2 0 0 1 1 -1 0 1 -1]
[ 0 0 0 1 -1 -1 0 0 -1 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 4 1 none
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1137
Image of polytope 1137 PALP id: 1137
grdb id: 539573
Integer points: [ 1 0 0 -2 -1 -3 -1 -1 -2 -2 0 0 -1]
[ 0 1 0 0 -2 -2 0 -1 -1 -2 0 -1 -1]
[ 0 0 1 -1 0 -2 0 0 -1 -1 0 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 83 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1138
Image of polytope 1138 PALP id: 1138
grdb id: 539505
Integer points: [ 1 0 0 -1 -3 -3 -2 -1 -3 -2 -1 0 -1]
[ 0 1 0 -1 -2 -2 -1 0 -2 -1 -1 0 -1]
[ 0 0 1 1 0 -2 0 0 -1 -1 0 0 -1]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 14 1 none
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 1139
Image of polytope 1139 PALP id: 1139
grdb id: 539510
Integer points: [ 1 0 0 -1 -3 -3 -3 -2 -2 -1 -1 -1 0]
[ 0 1 0 1 0 -2 -1 0 -1 0 0 -1 0]
[ 0 0 1 -1 -2 0 -1 -1 0 0 -1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 84 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1140
Image of polytope 1140 PALP id: 1140
grdb id: 539490
Integer points: [ 1 0 0 -1 -2 0 -1 0 -1 0 0 -1 0]
[ 0 1 0 1 1 -3 -1 -2 0 -1 -1 1 0]
[ 0 0 1 1 0 -2 -1 -1 0 0 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y*z + 2*x-1*y + 3*y-1 + 3*x-1 + x-2*y + 2*y-1*z-1 + 3*y-2*z-1 + 2*x-1*y-1*z-1 + y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1141
Image of polytope 1141 PALP id: 1141
grdb id: 539359
Integer points: [ 1 0 0 1 -3 -3 -3 -2 -2 -1 -1 -1 0]
[ 0 1 0 1 -2 0 -1 0 -1 0 0 -1 0]
[ 0 0 1 1 0 -2 -1 -1 0 0 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 85 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1142
Image of polytope 1142 PALP id: 1142
grdb id: 539476
Integer points: [ 1 0 0 1 -2 0 -1 0 -1 0 0 -1 0]
[ 0 1 0 -1 1 -3 -1 -2 0 -1 -1 1 0]
[ 0 0 1 -1 0 -2 -1 -1 0 0 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 14 1 none
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 1143
Image of polytope 1143 PALP id: 1143
grdb id: 539424
Integer points: [ 1 0 0 -3 -3 -1 -2 -2 -1 -1 -1 0 0]
[ 0 1 0 -1 -2 -2 -2 -1 -1 0 -1 -1 0]
[ 0 0 1 -1 0 2 1 0 1 0 0 1 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 86 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1144
Image of polytope 1144 PALP id: 1144
grdb id: 539508
Integer points: [ 1 0 0 -2 -3 -1 -2 -1 -2 -1 -1 0 0]
[ 0 1 0 -1 -2 -2 -1 0 -2 -1 -1 0 -1]
[ 0 0 1 -1 0 2 0 0 1 1 0 0 1]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
123 ? x + y + z + 2*y-1*z + 3*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*y-1 + 3*x-2*y-1 + 2*x-2*y-2*z + x-2*y-1*z-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1145
Image of polytope 1145 PALP id: 1145
grdb id: 539514
Integer points: [ 1 0 0 -2 -3 -1 -2 -2 -1 -1 -1 0 0]
[ 0 1 0 0 -2 -2 -2 -1 -1 0 -1 -1 0]
[ 0 0 1 -1 0 2 1 0 1 0 0 1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 87 1 none
Polytope 1146
Image of polytope 1146 PALP id: 1146
grdb id: 539478
Integer points: [ 1 0 0 0 -1 -3 -2 -2 -1 -1 -1 0 0]
[ 0 1 -1 0 2 0 1 0 1 0 0 1 0]
[ 0 0 0 1 -2 -2 -2 -1 -1 0 -1 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + 2*y*z-1 + x-1*y2*z-2 + 3*x-1*y*z-1 + y-1 + 3*x-1 + 2*x-1*z-1 + 2*x-2*y*z-2 + 3*x-2*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1147
Image of polytope 1147 PALP id: 1147
grdb id: 539565
Integer points: [ 1 0 0 1 -2 -3 0 -1 -2 -1 1 0 -1]
[ 0 1 -1 0 1 0 0 0 0 1 0 0 0]
[ 0 0 0 2 -2 -2 1 0 -1 -1 1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 5 1 none
Image of facet 13 1 irreducible and admissible
Polytope 1148
Image of polytope 1148 PALP id: 1148
grdb id: 539539
Integer points: [ 1 0 1 -3 -2 2 1 0 -1 -2 1 0 -1]
[ 0 1 0 0 -1 1 1 0 0 0 0 0 0]
[ 0 0 2 -2 0 2 1 1 0 -1 1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 88 1 none
Image of facet 1 5 irreducible and admissible
Polytope 1149
Image of polytope 1149 PALP id: 1149
grdb id: 539557
Integer points: [ 1 1 -3 0 -3 -1 -2 -2 -1 0 -1 0 1]
[ 0 2 -2 0 -1 1 0 -1 0 1 -1 0 1]
[ 0 0 0 1 -1 -1 -1 0 0 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 5 irreducible and admissible
Image of facet 89 1 none
Polytope 1150
Image of polytope 1150 PALP id: 1150
grdb id: 539547
Integer points: [ 1 1 0 -2 -3 -2 0 -1 -2 -1 1 0 -1]
[ 0 2 0 -1 -2 -2 1 0 -1 -1 1 0 -1]
[ 0 0 1 -1 0 1 0 0 0 1 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 13 1 irreducible and admissible
Image of facet 6 1 none
Polytope 1151
Image of polytope 1151 PALP id: 1151
grdb id: 539519
Integer points: [ 1 0 0 -2 -4 -2 -3 -1 -2 -3 -1 -1 0]
[ 0 1 0 0 -2 -2 -2 -1 -1 -1 0 -1 0]
[ 0 0 1 -1 -1 1 0 1 0 -1 0 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 4 1 none
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Polytope 1152
Image of polytope 1152 PALP id: 1152
grdb id: 539477
Integer points: [ 1 0 0 -1 -1 -4 -2 -3 -1 -2 -1 -2 0]
[ 0 1 0 -1 -1 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 1 -1 1 -2 0 -1 0 -1 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1153
Image of polytope 1153 PALP id: 1153
grdb id: 539571
Integer points: [ 1 0 0 0 -3 -4 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 -1 0 -1 0 0 -1 -1 -1 0 0]
[ 0 0 1 1 -2 -3 -1 0 -2 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 13 1 irreducible and admissible
Image of facet 6 1 none
Polytope 1154
Image of polytope 1154 PALP id: 1154
grdb id: 539493
Integer points: [ 1 0 0 0 -1 -4 -3 -2 -2 -1 -2 -1 0]
[ 0 1 -1 0 1 1 1 1 0 0 1 1 0]
[ 0 0 0 1 1 -2 -1 0 -1 0 -1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 14 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1155
Image of polytope 1155 PALP id: 1155
grdb id: 539411
Integer points: [ 1 1 -3 0 -1 1 0 0 -1 -2 1 0 -1]
[ 0 2 -2 0 1 3 2 1 0 -1 1 0 -1]
[ 0 0 0 1 -1 -1 -1 0 0 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 5 irreducible and admissible
Image of facet 91 1 none
Polytope 1156
Image of polytope 1156 PALP id: 1156
grdb id: 539528
Integer points: [ 1 0 1 0 -2 -4 -2 -1 -3 0 -1 0 1]
[ 0 1 -2 0 0 2 1 0 1 -1 1 0 -1]
[ 0 0 0 1 -1 -1 0 0 -1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 4 1 none
Image of facet 37 1 none
Polytope 1157
Image of polytope 1157 PALP id: 1157
grdb id: 539403
Integer points: [ 1 0 0 -3 -1 -5 -4 -2 -3 -1 -1 -2 0]
[ 0 1 0 -2 -1 -2 -2 -1 -1 0 -1 -1 0]
[ 0 0 1 0 1 -2 -1 0 -1 0 0 -1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 92 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1158
Image of polytope 1158 PALP id: 1158
grdb id: 539483
Integer points: [ 1 0 0 -2 -1 -5 -3 -2 -4 -1 -3 -1 0]
[ 0 1 0 0 -1 -3 -2 -1 -2 0 -1 -1 0]
[ 0 0 1 -1 1 -1 0 0 -1 0 -1 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 4 1 none
Polytope 1159
Image of polytope 1159 PALP id: 1159
grdb id: 539326
Integer points: [ 1 0 0 -1 -3 -5 -4 -2 -3 -1 -2 -1 0]
[ 0 1 0 1 -2 -3 -2 -1 -1 0 0 -1 0]
[ 0 0 1 -1 0 -1 -1 0 -1 0 -1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
76 ? x + y + z + x-1*y*z-1 + 3*x-1 + 2*x-1*y-1 + 4*x-2*z-1 + 3*x-2*y-1 + 6*x-3*y-1*z-1 + x-3*y-2 + 4*x-4*y-2*z-1 + x-5*y-3*z-1
164 ? x + y + z + x-1*y*z-1 + 4*x-1 + 2*x-1*y-1 + 4*x-2*z-1 + 4*x-2*y-1 + 6*x-3*y-1*z-1 + x-3*y-2 + 4*x-4*y-2*z-1 + x-5*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 93 1 Lattice Minkowski decompositions of facet 93
Polytope 1160
Image of polytope 1160 PALP id: 1160
grdb id: 539283
Integer points: [ 1 1 0 -4 -5 -1 -3 -2 -1 0 -1 0 1]
[ 0 2 0 -2 -3 -1 -2 -1 0 1 -1 0 1]
[ 0 0 1 -1 -1 1 0 0 0 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 4 1 none
Image of facet 94 1 none
Polytope 1161
Image of polytope 1161 PALP id: 1161
grdb id: 539479
Integer points: [ 1 0 0 0 -2 -6 -2 -4 -1 -3 -1 -3 0]
[ 0 1 -1 0 2 3 1 2 0 1 1 2 0]
[ 0 0 0 1 -1 -2 0 -1 0 -1 0 -1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Image of facet 95 1 none
Polytope 1162
Image of polytope 1162 PALP id: 1162
grdb id: 539033
Integer points: [ 1 0 0 -2 -2 0 -1 0 -1 -2 -1 0 0]
[ 0 1 0 0 -2 -2 0 -1 -1 -1 -2 0 -1]
[ 0 0 1 -1 -1 1 0 1 0 -1 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 4 1 none
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Polytope 1163
Image of polytope 1163 PALP id: 1163
grdb id: 539015
Integer points: [ 1 0 0 -2 0 -2 -1 -2 -1 -1 0 -1 0]
[ 0 1 0 0 -2 -2 -1 -1 0 -2 -1 -1 0]
[ 0 0 1 -1 1 1 1 0 0 1 1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
63 ? x + y + z + 2*y-1*z + 2*x-1 + y-2*z + 2*x-1*y-1*z + 2*x-1*y-1 + 2*x-1*y-2*z + x-2*z-1 + 2*x-2*y-1 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 1164
Image of polytope 1164 PALP id: 1164
grdb id: 539009
Integer points: [ 1 0 0 0 -2 -2 -1 -2 -1 -1 0 -1 0]
[ 0 1 0 -2 0 -2 -1 -1 0 -2 -1 -1 0]
[ 0 0 1 -1 -1 -1 0 -1 0 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
29 rank 2, number 23 x + y + z + 2*y-1 + 2*x-1 + 2*x-1*y-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-2*z-1 + 2*x-1*y-2*z-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 3 Lattice Minkowski decompositions of facet 16
Polytope 1165
Image of polytope 1165 PALP id: 1165
grdb id: 538641
Integer points: [ 1 0 0 -1 -2 -2 -1 -2 -1 -2 -1 0 0]
[ 0 1 0 -2 -1 2 1 1 0 0 -1 0 -1]
[ 0 0 1 0 -1 -1 0 -1 0 -1 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
114 ? x + y + z + 2*x-1*y + x-2*y2*z-1 + 2*y-1 + 3*x-1 + 3*x-2*y*z-1 + 3*x-1*y-1 + 3*x-2*z-1 + x-1*y-2 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 56 1 Lattice Minkowski decompositions of facet 56
Polytope 1166
Image of polytope 1166 PALP id: 1166
grdb id: 538687
Integer points: [ 1 0 0 0 -2 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 0 1 -1 2 1 0 1 0 1 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 2 none
Polytope 1167
Image of polytope 1167 PALP id: 1167
grdb id: 539003
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 -2 2 -2 -1 0 1 -1 -1 0 1]
[ 0 0 1 -1 2 -2 -1 0 1 0 -1 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
75 ? x-1*y2*z2 + 2*y*z + x + y + z + 4*x-1*y*z + 2*y-1 + 6*x-1 + 2*y-1*z-1 + y-2*z-1 + 4*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 5 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 13 1 irreducible and admissible
Polytope 1168
Image of polytope 1168 PALP id: 1168
grdb id: 538733
Integer points: [ 1 0 -1 0 -2 0 0 -1 0 -1 -1 0 0]
[ 0 1 1 0 -1 -3 -1 0 -2 -1 -2 0 -1]
[ 0 0 0 1 -1 1 1 0 1 0 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 4 1 none
Image of facet 56 1 Lattice Minkowski decompositions of facet 56
Polytope 1169
Image of polytope 1169 PALP id: 1169
grdb id: 538740
Integer points: [ 1 0 0 -2 0 -2 -1 -1 -2 -1 -2 0 0]
[ 0 1 0 0 -1 -3 0 -1 -1 -2 -2 0 -1]
[ 0 0 1 -1 1 -1 0 0 -1 0 -1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 4 1 none
Image of facet 9 1 irreducible and admissible
Polytope 1170
Image of polytope 1170 PALP id: 1170
grdb id: 538757
Integer points: [ 1 0 0 -1 -3 -3 -2 -1 -3 -2 -1 0 -1]
[ 0 1 0 0 -2 -2 -1 0 -2 -1 -1 0 -1]
[ 0 0 1 -1 0 -2 0 0 -1 -1 0 0 -1]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
126 ? x + y + z + 3*x-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*y-1 + 3*x-2*y-1*z-1 + x-3*y-2 + 2*x-3*y-2*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1171
Image of polytope 1171 PALP id: 1171
grdb id: 538746
Integer points: [ 1 0 0 -1 -1 -3 -2 -1 -2 -1 -1 0 0]
[ 0 1 0 1 -2 0 0 0 -1 -1 0 0 -1]
[ 0 0 1 -1 0 -2 -1 0 -1 0 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 14 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1172
Image of polytope 1172 PALP id: 1172
grdb id: 538681
Integer points: [ 1 0 0 0 -1 -3 -2 -1 -2 -1 -1 0 0]
[ 0 1 0 -1 -2 0 0 0 -1 -1 0 0 -1]
[ 0 0 1 1 0 -2 -1 0 -1 0 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
159 ? x + y + z + y-1*z + 2*y-1 + 3*x-1 + 2*x-1*z-1 + 3*x-1*y-1 + 3*x-2*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1173
Image of polytope 1173 PALP id: 1173
grdb id: 539021
Integer points: [ 1 -1 0 1 -2 -3 0 -2 -1 -1 0 1 -1]
[ 0 0 1 0 -1 -2 0 -1 -1 0 0 0 -1]
[ 0 0 0 2 -2 -2 1 -1 0 -1 0 1 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x*z2 + 2*x*z + x + y + 2*z + x-1 + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*y-1*z-1 + x-2*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 4 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1174
Image of polytope 1174 PALP id: 1174
grdb id: 539006
Integer points: [ 1 0 -1 1 -3 1 0 -1 -2 0 1 0 -1]
[ 0 1 -1 0 0 -1 0 0 0 -1 0 0 0]
[ 0 0 0 2 -2 2 1 0 -1 1 1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
136 ? x*z2 + 2*x*z + x*y-1*z2 + x + y + 4*z + 2*y-1*z + 6*x-1 + 2*x-1*z-1 + x-1*y-1 + 4*x-2*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 5 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 13 1 irreducible and admissible
Polytope 1175
Image of polytope 1175 PALP id: 1175
grdb id: 539007
Integer points: [ 1 0 0 -2 1 -3 0 -1 -2 -1 1 0 -1]
[ 0 1 0 -2 2 -2 1 0 -1 -1 1 0 -1]
[ 0 0 1 -1 2 -2 1 0 -1 0 1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
135 ? x*y2*z2 + 2*x*y*z + 4*y*z + x + y + z + 6*x-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 4*x-2*y-1*z-1 + x-2*y-2*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 5 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 13 1 irreducible and admissible
Polytope 1176
Image of polytope 1176 PALP id: 1176
grdb id: 539052
Integer points: [ 1 0 0 -1 -3 2 1 0 -1 -2 1 0 -1]
[ 0 1 0 -1 0 -1 -1 -1 0 0 0 0 0]
[ 0 0 1 -1 -2 2 1 0 0 -1 1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
24 ? x2*y-1*z2 + 2*x*z + x + y + 3*x*y-1*z + z + 3*y-1 + 3*x-1 + 2*x-1*z-1 + x-1*y-1*z-1 + 3*x-2*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 9 2 irreducible and admissible
Polytope 1177
Image of polytope 1177 PALP id: 1177
grdb id: 538676
Integer points: [ 1 0 0 0 -1 -4 -3 -2 -2 -1 -2 -1 0]
[ 0 1 -1 0 0 -3 -2 -1 -2 -1 -1 0 0]
[ 0 0 0 1 1 -2 -1 0 -1 0 -1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 14 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1178
Image of polytope 1178 PALP id: 1178
grdb id: 537416
Integer points: [ 1 0 0 0 -2 -2 -1 -1 -2 -1 -2 -2 0]
[ 0 1 -1 0 2 -2 -1 0 -1 1 0 1 0]
[ 0 0 0 1 -1 -1 0 0 -1 0 -1 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
32 ? x + y + z + 2*x-1*y + x-2*y2*z-1 + y-1 + 4*x-1 + 4*x-2*y*z-1 + 2*x-1*y-1 + 6*x-2*z-1 + 4*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 1179
Image of polytope 1179 PALP id: 1179
grdb id: 507688
Integer points: [ 1 1 -1 0 -1 -2 0 -1 -1 0 0 0 1]
[ 0 2 -2 0 0 -1 1 0 -1 1 0 -1 1]
[ 0 0 0 1 -1 -1 1 0 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 2 none
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1180
Image of polytope 1180 PALP id: 1180
grdb id: 507690
Integer points: [ 1 1 -1 0 0 -1 -1 -1 0 -1 0 1 0]
[ 0 2 -2 0 2 1 -1 0 1 -1 0 1 -1]
[ 0 0 0 1 -1 -1 1 0 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 4 1 none
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1181
Image of polytope 1181 PALP id: 1181
grdb id: 507672
Integer points: [ 1 0 1 0 -2 -3 -1 -2 -1 0 -1 0 1]
[ 0 1 -2 0 0 1 1 1 0 -1 1 0 -1]
[ 0 0 0 1 -1 -1 1 0 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 4 1 none
Image of facet 45 1 none
Polytope 1182
Image of polytope 1182 PALP id: 1182
grdb id: 507691
Integer points: [ 1 0 0 1 1 1 -3 1 0 -1 0 -1 -2]
[ 0 1 0 0 -1 -2 2 -1 0 1 -1 0 1]
[ 0 0 1 -1 0 -2 2 -1 0 1 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 49 2 Lattice Minkowski decompositions of facet 49
Image of facet 6 2 none
Polytope 1183
Image of polytope 1183 PALP id: 1183
grdb id: 507651
Integer points: [ 1 0 0 -2 0 -2 -1 -1 0 -1 0 -1 0]
[ 0 1 0 0 -2 -1 -2 -1 -1 0 -1 0 0]
[ 0 0 1 -1 -1 -2 -2 -1 0 0 -1 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + 2*y-1 + 2*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + y-2*z-1 + 3*x-1*y-1*z-1 + x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1184
Image of polytope 1184 PALP id: 1184
grdb id: 507308
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -2 -1 1 0 1 0 -1 0 -1]
[ 0 0 1 -1 0 1 1 1 0 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 37 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1185
Image of polytope 1185 PALP id: 1185
grdb id: 507329
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -1 -2 -2 0 -1 0 -1 0 -1]
[ 0 0 1 -1 1 0 -1 0 0 -1 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + 3*x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 9 1 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1186
Image of polytope 1186 PALP id: 1186
grdb id: 507588
Integer points: [ 1 0 0 0 -2 -1 -2 -1 -2 -1 -1 0 -1]
[ 0 1 -1 0 -1 -1 -1 0 -1 0 -1 0 -1]
[ 0 0 0 1 0 1 -2 0 -1 -1 0 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + y-1 + 2*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + 2*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1187
Image of polytope 1187 PALP id: 1187
grdb id: 507587
Integer points: [ 1 0 0 0 -1 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 -1 0 1 1 -1 0 0 -1 1 0 0]
[ 0 0 0 1 1 0 -2 -1 0 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + x-1*y*z + 2*x-1*y + y-1 + 3*x-1 + x-2*y + 2*x-1*z-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1188
Image of polytope 1188 PALP id: 1188
grdb id: 507627
Integer points: [ 1 0 0 0 -1 0 -2 -1 0 -1 0 -1 0]
[ 0 1 0 0 1 -2 0 -1 -1 0 -1 0 0]
[ 0 0 1 -1 -1 -1 -1 -1 0 0 -1 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
25 ? x + y + z + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1189
Image of polytope 1189 PALP id: 1189
grdb id: 507636
Integer points: [ 1 0 0 0 0 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 0 -1 0 1 -1 0 0 -1 1 0 0]
[ 0 0 1 0 -1 0 -2 -1 0 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + 2*x-1*y + z-1 + y-1 + 2*x-1 + x-2*y + 2*x-1*z-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Polytope 1190
Image of polytope 1190 PALP id: 1190
grdb id: 507649
Integer points: [ 1 0 1 -2 0 -2 0 -1 0 -1 1 0 -1]
[ 0 1 -2 1 0 0 -2 -1 -1 0 -1 0 1]
[ 0 0 0 0 1 -1 -1 -1 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
3 ? x + y + z + 2*x*y-1 + 2*x-1*y + x*y-2 + y-1 + x-1 + x-2*y + y-2*z-1 + 2*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 48 1 Lattice Minkowski decompositions of facet 48
Polytope 1191
Image of polytope 1191 PALP id: 1191
grdb id: 507243
Integer points: [ 1 0 1 0 -2 -1 -2 -1 -2 -1 0 -1 0]
[ 0 1 -1 0 -2 1 0 0 -1 -1 -1 0 0]
[ 0 0 0 1 -1 1 1 1 0 0 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 37 1 none
Image of facet 8 1 none
Polytope 1192
Image of polytope 1192 PALP id: 1192
grdb id: 507655
Integer points: [ 1 0 -1 0 1 1 -2 0 -1 0 -1 0 1]
[ 0 1 0 0 -2 -2 1 -1 0 -1 1 0 -1]
[ 0 0 0 1 1 2 -2 1 -1 0 -1 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + 2*x*y-1*z + z + x*y-2*z2 + x*y-2*z + 2*y-1*z + 2*x-1*y*z-1 + 3*y-1 + x-1 + 3*x-1*z-1 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 9 1 irreducible and admissible
Polytope 1193
Image of polytope 1193 PALP id: 1193
grdb id: 507586
Integer points: [ 1 0 0 -1 0 -2 2 -1 1 0 0 -1 1]
[ 0 1 0 1 -1 1 -1 1 0 0 0 0 -1]
[ 0 0 1 1 0 0 -2 0 -1 0 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + x-1*y*z + 2*x*z-1 + 2*x-1*y + x2*y-1*z-2 + 2*x*y-1*z-1 + 2*z-1 + y-1 + 2*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 1194
Image of polytope 1194 PALP id: 1194
grdb id: 507661
Integer points: [ 1 0 0 -1 0 0 -1 -1 0 0 0 0 0]
[ 0 1 1 0 -1 -1 -2 -1 0 -1 0 1 0]
[ 0 0 2 0 -2 0 -2 -1 1 -1 0 1 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 5 1 none
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1195
Image of polytope 1195 PALP id: 1195
grdb id: 507639
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 -1 0 2 -2 2 -1 0 1 -1 0 1]
[ 0 0 0 1 1 -2 2 -1 0 1 -1 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 5 1 none
Image of facet 49 2 Lattice Minkowski decompositions of facet 49
Polytope 1196
Image of polytope 1196 PALP id: 1196
grdb id: 507659
Integer points: [ 1 0 0 0 1 -2 -2 -1 0 -1 1 0 -1]
[ 0 1 0 0 -2 1 2 1 -1 0 -1 0 1]
[ 0 0 1 -1 0 0 -1 -1 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 5 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1197
Image of polytope 1197 PALP id: 1197
grdb id: 507638
Integer points: [ 1 0 0 1 -2 2 -2 1 -1 0 0 -1 -1]
[ 0 1 0 -1 1 -2 0 -1 0 -1 0 0 1]
[ 0 0 1 -1 0 -1 1 0 1 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 8 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1198
Image of polytope 1198 PALP id: 1198
grdb id: 507660
Integer points: [ 1 0 0 1 1 -1 -2 0 1 0 -1 0 -1]
[ 0 1 0 0 -2 2 1 1 -1 0 1 -1 0]
[ 0 0 1 -1 0 -1 0 -1 0 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 6 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1199
Image of polytope 1199 PALP id: 1199
grdb id: 507646
Integer points: [ 1 1 0 0 -1 -2 0 0 1 0 -1 0 -1]
[ 0 2 0 -1 -1 -1 -1 -1 1 0 -1 1 0]
[ 0 0 1 -1 1 0 1 0 0 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 8 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1200
Image of polytope 1200 PALP id: 1200
grdb id: 507311
Integer points: [ 1 0 -1 0 -2 -3 -3 -2 -1 -2 -1 -1 0]
[ 0 1 1 0 0 -2 -3 -1 0 -2 -1 -1 0]
[ 0 0 0 1 -1 -2 -2 -1 0 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 66 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 9 1 irreducible and admissible
Polytope 1201
Image of polytope 1201 PALP id: 1201
grdb id: 507202
Integer points: [ 1 0 0 -3 -1 -1 -3 -2 -3 -2 -1 -1 0]
[ 0 1 0 -2 0 -1 -2 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 1 1 1 1 0 0 0 0 0]
Degree: 50
Hilbert function: 1 + 28 t + 130 t2 + 357 t3 + 759 t4 + 1386 t5 + 2288 t6 + 3515 t7 + 5117 t8 + 7144 t9 + 9646 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 37 1 none
Polytope 1202
Image of polytope 1202 PALP id: 1202
grdb id: 507563
Integer points: [ 1 0 0 -1 -3 -2 -3 -2 -2 -1 -1 -1 0]
[ 0 1 0 1 -1 -2 -2 -1 0 -1 0 -1 0]
[ 0 0 1 -1 -1 1 0 0 -1 1 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
164 ? x + y + z + x-1*y*z-1 + 4*x-1 + 2*x-1*y-1*z + 2*x-1*y-1 + 2*x-2*z-1 + 4*x-2*y-1 + x-2*y-2*z + x-3*y-1*z-1 + x-3*y-2
76 ? x + y + z + x-1*y*z-1 + 3*x-1 + 2*x-1*y-1*z + 2*x-1*y-1 + 2*x-2*z-1 + 3*x-2*y-1 + x-2*y-2*z + x-3*y-1*z-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 96 1 Lattice Minkowski decompositions of facet 96
Polytope 1203
Image of polytope 1203 PALP id: 1203
grdb id: 507599
Integer points: [ 1 0 0 0 -2 -2 -3 -2 -1 -1 -1 -1 0]
[ 0 1 0 1 -2 -1 -2 -1 0 -1 0 -1 0]
[ 0 0 1 1 -1 -2 -2 -1 0 0 -1 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 6 1 none
Polytope 1204
Image of polytope 1204 PALP id: 1204
grdb id: 507601
Integer points: [ 1 0 0 0 -1 -3 -3 -2 -1 -2 -1 -1 0]
[ 0 1 0 -1 1 0 -1 0 0 -1 -1 0 0]
[ 0 0 1 1 -1 -2 -2 -1 0 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 6 1 none
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 1205
Image of polytope 1205 PALP id: 1205
grdb id: 507323
Integer points: [ 1 0 0 0 0 -1 -3 -1 -1 -2 -2 0 -1]
[ 0 1 -1 0 -1 -2 0 -1 0 -1 0 0 0]
[ 0 0 0 1 -1 -1 1 0 1 0 1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1206
Image of polytope 1206 PALP id: 1206
grdb id: 507326
Integer points: [ 1 0 0 0 0 -1 -3 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 1 0 -2 -1 0 -1 0 -1 0]
[ 0 0 0 1 -1 1 -1 0 0 -1 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 8 1 none
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1207
Image of polytope 1207 PALP id: 1207
grdb id: 507626
Integer points: [ 1 0 0 0 1 -2 -3 -1 -2 -1 0 -1 0]
[ 0 1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 0 0 1 -1 0 -1 0 -1 -1 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 6 1 none
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 13 1 irreducible and admissible
Polytope 1208
Image of polytope 1208 PALP id: 1208
grdb id: 507488
Integer points: [ 1 0 1 -2 0 -1 1 0 0 -1 1 0 -1]
[ 0 1 -2 1 0 -1 -3 -1 -2 0 -1 0 1]
[ 0 0 0 0 1 -1 -1 0 -1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
134 ? x + y + z + 2*x*y-1 + 2*x-1*y + x*y-2 + y-1 + 2*x-1 + x-2*y + x*y-3*z-1 + 2*y-2*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 47 1 Lattice Minkowski decompositions of facet 47
Polytope 1209
Image of polytope 1209 PALP id: 1209
grdb id: 507569
Integer points: [ 1 0 -1 0 -2 -3 -3 -1 -2 -1 -2 -1 0]
[ 0 1 -1 0 2 1 2 1 1 0 0 1 0]
[ 0 0 0 1 -1 -2 -2 0 -1 0 -1 -1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
152 rank 3, number 22 x + y + z + 2*x-1*y + 2*x-1*y*z-1 + x-2*y2*z-1 + x-1 + 2*x-2*y*z-1 + x-1*y-1 + x-3*y2*z-2 + 2*x-2*z-1 + x-3*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 71 1 Lattice Minkowski decompositions of facet 71
Polytope 1210
Image of polytope 1210 PALP id: 1210
grdb id: 507250
Integer points: [ 1 0 -1 0 -2 0 -3 -1 0 -1 -2 0 -1]
[ 0 1 -1 0 0 2 -2 1 1 0 -1 0 -1]
[ 0 0 0 1 -1 1 -2 0 1 0 -1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
80 ? y2*z + 2*y*z + x + y + z + 2*x-1*y + 3*x-1 + x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + 3*x-2*y-1*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Polytope 1211
Image of polytope 1211 PALP id: 1211
grdb id: 507584
Integer points: [ 1 0 0 2 -2 0 -3 -1 -1 -2 0 -1 1]
[ 0 1 0 -1 0 -1 1 0 1 1 0 0 -1]
[ 0 0 1 -1 1 1 0 1 0 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 8 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1212
Image of polytope 1212 PALP id: 1212
grdb id: 507424
Integer points: [ 1 0 1 -3 -2 -1 1 0 -1 -2 1 0 -1]
[ 0 1 0 0 -1 -1 1 0 0 0 0 0 0]
[ 0 0 2 -2 0 1 1 1 0 -1 1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 97 1 none
Polytope 1213
Image of polytope 1213 PALP id: 1213
grdb id: 507208
Integer points: [ 1 0 1 0 -3 0 -1 -2 -1 0 -1 0 1]
[ 0 1 -2 0 2 -1 0 1 0 -1 1 0 -1]
[ 0 0 0 1 -1 1 1 0 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 26 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 8 1 none
Polytope 1214
Image of polytope 1214 PALP id: 1214
grdb id: 507610
Integer points: [ 1 0 1 0 -1 -2 -3 0 -1 -2 1 0 -1]
[ 0 1 -2 0 0 1 2 -1 0 1 -1 0 1]
[ 0 0 0 1 -1 0 -1 0 0 -1 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 6 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1215
Image of polytope 1215 PALP id: 1215
grdb id: 506999
Integer points: [ 1 1 -3 0 -1 0 1 0 -1 -2 1 0 -1]
[ 0 2 -2 0 1 2 1 1 0 -1 1 0 -1]
[ 0 0 0 1 -1 -1 1 0 0 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 98 1 none
Polytope 1216
Image of polytope 1216 PALP id: 1216
grdb id: 507648
Integer points: [ 1 1 -1 -1 0 -2 -2 -1 -2 0 0 0 1]
[ 0 2 -2 0 0 -3 -1 -1 -2 -1 0 1 1]
[ 0 0 0 0 1 -1 -1 0 -1 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
24 ? x*y2 + 2*x*y + x + 2*y + z + 2*y-1 + x-1 + 2*x-1*y-1 + x-1*y-2 + x-2*y-1*z-1 + 2*x-2*y-2*z-1 + x-2*y-3*z-1
75 ? x*y2 + 2*x*y + x + 2*y + z + 2*y-1 + x-1 + 3*x-1*y-1 + x-1*y-2 + x-2*y-1*z-1 + 2*x-2*y-2*z-1 + x-2*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 5 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1217
Image of polytope 1217 PALP id: 1217
grdb id: 507658
Integer points: [ 1 1 -1 -1 0 0 -2 -1 0 -1 0 0 1]
[ 0 2 -2 0 0 -1 -3 -1 -1 -2 0 1 1]
[ 0 0 0 0 1 -1 -1 0 0 -1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 6 1 none
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1218
Image of polytope 1218 PALP id: 1218
grdb id: 507510
Integer points: [ 1 1 0 -2 -3 -3 1 0 -1 -2 1 0 -1]
[ 0 2 0 0 -2 -1 1 1 0 -1 1 0 -1]
[ 0 0 1 -1 0 -1 1 0 0 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 99 1 none
Polytope 1219
Image of polytope 1219 PALP id: 1219
grdb id: 507548
Integer points: [ 1 1 0 -2 -3 -1 -3 -2 -1 0 -1 0 1]
[ 0 2 0 -1 -2 -1 -2 -1 0 1 -1 0 1]
[ 0 0 1 -1 0 1 -1 0 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 6 1 none
Image of facet 49 2 Lattice Minkowski decompositions of facet 49
Polytope 1220
Image of polytope 1220 PALP id: 1220
grdb id: 507248
Integer points: [ 1 0 0 -3 0 -4 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 -1 -1 -2 -2 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 1 -1 1 1 0 0 0 0 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 8 1 none
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Polytope 1221
Image of polytope 1221 PALP id: 1221
grdb id: 507608
Integer points: [ 1 0 0 -2 -2 -3 -4 -3 -1 -1 -2 0 -1]
[ 0 1 0 -1 -2 -2 -3 -2 -1 0 -1 0 -1]
[ 0 0 1 0 -1 -2 -2 -1 0 0 -1 0 -1]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
37 rank 3, number 17 x + y + z + 2*x-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1 + 2*x-3*y-2*z-1 + x-3*y-2*z-2 + x-4*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1222
Image of polytope 1222 PALP id: 1222
grdb id: 507347
Integer points: [ 1 0 0 -2 -1 -2 -4 -3 -2 -1 -1 0 -3]
[ 0 1 0 -1 0 -1 -3 -2 -1 0 -1 0 -2]
[ 0 0 1 -1 1 1 -1 0 0 0 0 0 -1]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 8 1 none
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Polytope 1223
Image of polytope 1223 PALP id: 1223
grdb id: 507542
Integer points: [ 1 0 0 -2 0 -1 -4 -3 -1 -2 -1 -2 0]
[ 0 1 -1 -1 0 -2 -3 -2 -1 -2 0 -1 0]
[ 0 0 0 0 1 -1 -2 -1 0 -1 0 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 46 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1224
Image of polytope 1224 PALP id: 1224
grdb id: 507307
Integer points: [ 1 0 0 -1 -1 -3 -4 -2 -3 -1 -2 -1 0]
[ 0 1 0 -1 1 -2 -2 -1 -1 0 0 -1 0]
[ 0 0 1 1 -1 0 -1 0 -1 0 -1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
164 ? x + y + z + x-1*y*z-1 + 4*x-1 + x-1*y-1*z + 2*x-1*y-1 + 3*x-2*z-1 + 4*x-2*y-1 + 3*x-3*y-1*z-1 + x-3*y-2 + x-4*y-2*z-1
76 ? x + y + z + x-1*y*z-1 + 3*x-1 + x-1*y-1*z + 2*x-1*y-1 + 3*x-2*z-1 + 3*x-2*y-1 + 3*x-3*y-1*z-1 + x-3*y-2 + x-4*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Image of facet 9 1 irreducible and admissible
Polytope 1225
Image of polytope 1225 PALP id: 1225
grdb id: 507642
Integer points: [ 1 0 0 0 -1 -2 -4 -3 -1 -2 -1 -2 0]
[ 0 1 -1 0 1 1 1 1 0 0 1 1 0]
[ 0 0 0 1 -1 0 -2 -1 0 -1 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
76 ? x + y + z + 2*x-1*y + x-1*y*z-1 + y-1 + 2*x-1 + x-2*y + 2*x-2*y*z-1 + 2*x-2*z-1 + 2*x-3*y*z-1 + x-4*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Polytope 1226
Image of polytope 1226 PALP id: 1226
grdb id: 507201
Integer points: [ 1 0 -1 0 -1 -3 -3 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 2 2 3 2 1 1 0 1 0]
[ 0 0 0 1 -1 -2 -2 -1 0 -1 0 -1 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 42 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Polytope 1227
Image of polytope 1227 PALP id: 1227
grdb id: 506691
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 1 -1 1 -1 0 1 0 -1 0 0]
[ 0 0 1 1 -1 -1 1 1 0 0 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + x-1*y*z-1 + 4*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Polytope 1228
Image of polytope 1228 PALP id: 1228
grdb id: 505533
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 2 0 1 -1 0 1 0]
[ 0 0 1 -1 0 2 -1 1 0 1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
29 rank 2, number 23 x + y + z + x-1*y2*z-1 + 3*x-1*y + 3*x-1*z + x-1*y-1*z2 + 2*x-1*y*z-1 + 4*x-1 + 2*x-1*y-1*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Polytope 1229
Image of polytope 1229 PALP id: 1229
grdb id: 505549
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 1 1 -1 -1 0 0 0 -1 -1 0]
[ 0 0 1 0 -1 -1 2 1 0 -1 1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
55 rank 2, number 19 x + y + z + x-1*y + 2*x-1*z + x-1*y-1*z2 + x-1*y*z-1 + 4*x-1 + 3*x-1*y-1*z + 2*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 9 1 irreducible and admissible
Polytope 1230
Image of polytope 1230 PALP id: 1230
grdb id: 505191
Integer points: [ 1 0 -1 0 -1 -2 -2 -1 -2 -1 -2 0 0]
[ 0 1 1 0 -2 1 -2 -1 -1 0 0 -1 0]
[ 0 0 0 1 0 -1 -1 0 -1 0 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
64 ? x + y + z + x-1*y + 2*y-1 + 4*x-1 + x-2*y*z-1 + 3*x-1*y-1 + 3*x-2*z-1 + x-1*y-2 + 3*x-2*y-1*z-1 + x-2*y-2*z-1
122 ? x + y + z + x-1*y + 2*y-1 + 2*x-1 + x-2*y*z-1 + 2*x-1*y-1 + 3*x-2*z-1 + x-1*y-2 + 3*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Image of facet 9 1 irreducible and admissible
Polytope 1231
Image of polytope 1231 PALP id: 1231
grdb id: 506816
Integer points: [ 1 0 0 -2 1 -1 1 0 -1 0 1 0 -1]
[ 0 1 0 1 -2 0 -2 -1 0 -1 -1 0 1]
[ 0 0 1 0 0 -1 -1 0 0 -1 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
127 ? x + y + z + 2*x*y-1 + 2*x-1*y + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 9 1 irreducible and admissible
Polytope 1232
Image of polytope 1232 PALP id: 1232
grdb id: 506525
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 1 -2 0 0 -1 -1 0 0 -1]
[ 0 0 1 0 1 0 -2 -1 0 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 y*z + x + y + z + 2*z-1 + 2*y-1 + x-1 + 2*x-1*z-1 + 2*x-1*y-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 1233
Image of polytope 1233 PALP id: 1233
grdb id: 506818
Integer points: [ 1 0 0 -1 1 -2 1 -1 0 1 0 -1 0]
[ 0 1 0 -1 -1 0 0 0 0 0 -1 0 0]
[ 0 0 1 1 -1 1 -2 1 0 -1 0 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
75 ? x + y + z + 2*x*z-1 + 2*x-1*z + x*z-2 + x*y-1*z-1 + 3*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 9 1 irreducible and admissible
Polytope 1234
Image of polytope 1234 PALP id: 1234
grdb id: 506708
Integer points: [ 1 0 0 0 -1 -2 -2 -1 -2 -1 -1 0 -1]
[ 0 1 -1 0 0 1 1 1 1 0 1 0 0]
[ 0 0 0 1 1 0 -2 0 -1 0 -1 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + 2*x-1*y + x-1*z + 2*x-1*y*z-1 + y-1 + 2*x-1 + x-2*y + 2*x-1*z-1 + 2*x-2*y*z-1 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1235
Image of polytope 1235 PALP id: 1235
grdb id: 506661
Integer points: [ 1 0 0 0 -1 0 -2 -1 0 -1 0 -1 0]
[ 0 1 0 0 1 -2 0 -1 -1 0 -1 0 0]
[ 0 0 1 -1 0 -1 1 0 0 1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*y + 2*x-1*z + z-1 + 2*y-1 + 2*x-1 + x-2*z + 2*y-1*z-1 + 2*x-1*y-1 + y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1236
Image of polytope 1236 PALP id: 1236
grdb id: 506616
Integer points: [ 1 0 0 0 -1 0 -2 -1 -1 -1 0 0 0]
[ 0 1 0 0 1 -2 0 0 0 -1 0 -1 -1]
[ 0 0 1 -1 1 -1 1 1 0 0 0 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*y*z + 2*x-1*z + z-1 + 2*y-1 + 2*x-1 + x-2*z + 2*y-1*z-1 + 2*x-1*y-1 + y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 1237
Image of polytope 1237 PALP id: 1237
grdb id: 506627
Integer points: [ 1 0 0 0 0 -2 -2 -1 -2 -1 -1 0 -1]
[ 0 1 -1 0 1 -1 1 1 0 0 0 0 -1]
[ 0 0 0 1 -1 0 -2 -1 -1 0 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
80 ? x + y + z + y*z-1 + 2*x-1*y*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + x-2*y*z-2 + 2*x-2*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1238
Image of polytope 1238 PALP id: 1238
grdb id: 506628
Integer points: [ 1 0 0 0 0 -2 -2 -1 -2 -1 -1 0 -1]
[ 0 1 -1 0 1 1 1 1 1 0 1 0 0]
[ 0 0 0 1 -1 0 -2 0 -1 0 -1 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
77 ? x + y + z + y*z-1 + 2*x-1*y + 2*x-1*y*z-1 + y-1 + 2*x-1 + x-2*y + 2*x-1*z-1 + 2*x-2*y*z-1 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1239
Image of polytope 1239 PALP id: 1239
grdb id: 506821
Integer points: [ 1 0 0 1 1 -2 -2 -1 0 -1 0 -1 0]
[ 0 1 0 -1 0 -1 0 -1 -1 0 0 0 0]
[ 0 0 1 0 -1 0 -1 0 0 0 0 -1 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 5 1 none
Polytope 1240
Image of polytope 1240 PALP id: 1240
grdb id: 505372
Integer points: [ 1 0 1 -1 0 1 -2 -1 0 -1 0 -1 0]
[ 0 1 -1 1 0 -2 -2 -1 -1 -2 -2 0 0]
[ 0 0 0 0 1 -1 -1 0 0 -1 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 4 1 none
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1241
Image of polytope 1241 PALP id: 1241
grdb id: 505520
Integer points: [ 1 0 -1 0 -2 -1 -2 -2 -2 -1 -1 -1 0]
[ 0 1 -1 0 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 0 1 -1 2 2 0 1 1 0 1 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 14 1 none
Polytope 1242
Image of polytope 1242 PALP id: 1242
grdb id: 506663
Integer points: [ 1 0 -1 0 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 -1 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 0 0 1 -1 0 2 1 0 1 0 1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
69 ? x + y + z + 2*y-1*z + 2*y-1 + x-1 + 2*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*y-1 + 2*x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1243
Image of polytope 1243 PALP id: 1243
grdb id: 505553
Integer points: [ 1 0 0 -1 -2 -1 -2 -2 -2 -1 -1 -1 0]
[ 0 1 0 -1 -1 -1 -1 -1 -1 0 0 -1 0]
[ 0 0 1 -1 -1 1 2 1 0 1 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 14 1 none
Polytope 1244
Image of polytope 1244 PALP id: 1244
grdb id: 506786
Integer points: [ 1 0 0 -1 -2 -1 -2 -2 -1 -1 -1 -1 0]
[ 0 1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 0 2 2 1 0 1 0 1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
160 ? x + y + z + 2*x-1*z + x-1*y-1*z2 + 2*x-1 + 3*x-1*y-1*z + x-2*y-1*z2 + 3*x-1*y-1 + 2*x-2*y-1*z + x-1*y-1*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1245
Image of polytope 1245 PALP id: 1245
grdb id: 506554
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 -1 -2 2 1 0 -1 1 0 -1]
[ 0 0 1 -1 0 2 -2 -1 0 1 -1 0 1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
135 ? x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 4*x-1*y*z-1 + 6*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 49 2 Lattice Minkowski decompositions of facet 49
Polytope 1246
Image of polytope 1246 PALP id: 1246
grdb id: 506617
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -1 -2 2 -1 0 0 1 -1 0]
[ 0 0 1 0 -1 0 -1 0 0 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*y2*z-1 + x-1*y + 3*x-1*y*z-1 + 2*y-1 + 3*x-1 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 9 2 irreducible and admissible
Polytope 1247
Image of polytope 1247 PALP id: 1247
grdb id: 505173
Integer points: [ 1 0 0 0 -1 -2 -2 -1 -1 -2 -1 0 0]
[ 0 1 0 -1 -2 0 2 1 0 1 -1 0 -1]
[ 0 0 1 1 0 -1 -1 0 0 -1 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
114 ? x + y + z + 2*x-1*y + y-1*z + x-2*y2*z-1 + 2*y-1 + 3*x-1 + 2*x-2*y*z-1 + 3*x-1*y-1 + x-2*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Polytope 1248
Image of polytope 1248 PALP id: 1248
grdb id: 506601
Integer points: [ 1 0 0 0 0 -2 -2 -1 -1 -2 0 -1 -1]
[ 0 1 -1 0 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 0 1 -1 0 2 1 0 1 0 1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + 2*x-1*z + y-1 + 2*x-1 + 2*x-1*y-1*z + x-2*y-1*z2 + y-1*z-1 + 2*x-1*y-1 + 2*x-2*y-1*z + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1249
Image of polytope 1249 PALP id: 1249
grdb id: 506750
Integer points: [ 1 0 0 0 0 -2 -2 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 2 0 -1 1 0 0 -1 1 0]
[ 0 0 0 1 1 -1 -2 0 -1 0 -1 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
60 rank 2, number 18 y2*z + 2*y*z + x + y + z + 2*x-1*y + y-1 + 2*x-1 + 2*x-1*z-1 + 2*x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1250
Image of polytope 1250 PALP id: 1250
grdb id: 506814
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 0 -2 -1 2 0 1 -1 0 1 -1]
[ 0 0 1 -1 1 1 -2 0 -1 1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
24 ? x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + z-1 + 3*x-1*y*z-1 + 2*y-1 + 3*x-1 + y-2*z + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 5 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1251
Image of polytope 1251 PALP id: 1251
grdb id: 506553
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 -1 -2 2 -1 0 1 -1 0 1]
[ 0 0 1 -1 0 -2 2 -1 0 1 -1 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
75 ? x-1*y2*z2 + 2*y*z + x + y + z + 4*x-1*y*z + z-1 + y-1 + 6*x-1 + 2*y-1*z-1 + 4*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 49 2 Lattice Minkowski decompositions of facet 49
Polytope 1252
Image of polytope 1252 PALP id: 1252
grdb id: 506828
Integer points: [ 1 0 0 0 0 -1 -1 0 0 0 0 -1 0]
[ 0 1 1 -1 -1 -1 1 0 -1 0 1 0 0]
[ 0 0 2 -2 0 -1 1 -1 -1 0 1 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
75 ? y*z2 + 2*y*z + x + y + 2*z + x-1*y*z + 2*z-1 + y-1 + 2*x-1 + 2*y-1*z-1 + y-1*z-2 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 6 irreducible and admissible
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1253
Image of polytope 1253 PALP id: 1253
grdb id: 506765
Integer points: [ 1 0 1 0 0 0 -2 -1 0 -1 0 -1 0]
[ 0 1 -1 0 0 -2 2 0 -1 1 -1 1 0]
[ 0 0 0 1 -1 -1 1 0 0 1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + 2*x-1*y*z + x-2*y2*z + x*y-1 + 2*x-1*y + z-1 + 2*y-1 + 2*x-1 + 2*y-1*z-1 + y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 1254
Image of polytope 1254 PALP id: 1254
grdb id: 506827
Integer points: [ 1 1 -1 -1 0 1 1 1 1 0 0 0 -1]
[ 0 2 -2 0 0 0 2 1 1 -1 0 1 -1]
[ 0 0 0 0 1 -1 -1 0 -1 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
101 ? x*y2 + x*y2*z-1 + 2*x*y + 2*x*y*z-1 + x + 2*y + z + x*z-1 + 2*y-1 + x-1 + 2*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 6 irreducible and admissible
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1255
Image of polytope 1255 PALP id: 1255
grdb id: 505194
Integer points: [ 1 0 -1 0 -2 -1 -2 -1 -2 -1 -2 0 0]
[ 0 1 1 0 0 -2 -3 -1 -2 0 -1 -1 0]
[ 0 0 0 1 -1 0 -1 0 -1 0 -1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
132 ? x + y + z + x-1*y + 2*y-1 + 3*x-1 + 4*x-1*y-1 + x-2*z-1 + x-1*y-2 + 3*x-2*y-1*z-1 + 3*x-2*y-2*z-1 + x-2*y-3*z-1
145 ? x + y + z + x-1*y + 2*y-1 + 2*x-1 + 2*x-1*y-1 + x-2*z-1 + x-1*y-2 + 3*x-2*y-1*z-1 + 3*x-2*y-2*z-1 + x-2*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Image of facet 9 1 irreducible and admissible
Polytope 1256
Image of polytope 1256 PALP id: 1256
grdb id: 505709
Integer points: [ 1 0 -1 0 -2 0 -2 -1 -1 -2 -1 0 0]
[ 0 1 1 0 -1 -1 -3 -2 -1 -2 0 -1 0]
[ 0 0 0 1 -1 1 -1 0 0 -1 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 4 1 none
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Polytope 1257
Image of polytope 1257 PALP id: 1257
grdb id: 506685
Integer points: [ 1 0 0 -1 -1 -2 -3 -2 -2 -1 -1 -1 0]
[ 0 1 0 -1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 1 1 1 0 1 0 0 1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 8 1 none
Polytope 1258
Image of polytope 1258 PALP id: 1258
grdb id: 506758
Integer points: [ 1 0 0 0 -2 -1 -2 -1 -1 -2 0 -1 -1]
[ 0 1 -1 0 -1 0 -3 -2 -1 -2 0 -1 0]
[ 0 0 0 1 0 1 -2 -1 0 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + x-1*z + y-1 + 2*x-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + 2*x-1*y-2*z-1 + 2*x-2*y-2*z-1 + x-2*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1259
Image of polytope 1259 PALP id: 1259
grdb id: 505542
Integer points: [ 1 0 1 -2 0 0 -3 0 -1 -1 -2 0 -1]
[ 0 1 -1 1 0 -2 1 -1 -1 0 0 0 1]
[ 0 0 0 0 1 -1 -1 0 -1 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
100 ? x + y + z + x*y-1 + 2*x-1*y + 2*y-1 + 3*x-1 + x-2*y + y-2*z-1 + 3*x-1*y-1*z-1 + 3*x-2*z-1 + x-3*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1260
Image of polytope 1260 PALP id: 1260
grdb id: 506749
Integer points: [ 1 0 1 0 0 -2 -3 -1 0 -2 -1 -1 0]
[ 0 1 -1 0 -1 -1 0 -1 -1 0 0 0 0]
[ 0 0 0 1 -1 0 1 0 0 1 1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 6 1 none
Polytope 1261
Image of polytope 1261 PALP id: 1261
grdb id: 506549
Integer points: [ 1 0 -1 0 1 -3 1 0 -1 -2 1 0 -1]
[ 0 1 -1 0 2 -2 2 1 0 -1 1 0 -1]
[ 0 0 0 1 1 -2 2 1 0 -1 1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
136 ? x*y2*z2 + x*y2*z + 2*x*y*z + 4*y*z + x + y + z + 6*x-1 + x-1*y-1 + 2*x-1*y-1*z-1 + 4*x-2*y-1*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 49 2 Lattice Minkowski decompositions of facet 49
Polytope 1262
Image of polytope 1262 PALP id: 1262
grdb id: 505556
Integer points: [ 1 0 0 0 -2 -1 -4 -2 -3 -1 -2 -1 0]
[ 0 1 0 -1 -1 -1 -1 -1 -1 0 0 -1 0]
[ 0 0 1 1 -1 1 -2 0 -1 0 -1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
47 ? x + y + z + y-1*z + 3*x-1 + x-1*y-1*z + 2*x-1*y-1 + 2*x-2*z-1 + 3*x-2*y-1 + x-2*y-1*z-1 + 3*x-3*y-1*z-1 + x-4*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1263
Image of polytope 1263 PALP id: 1263
grdb id: 506666
Integer points: [ 1 0 0 0 -1 -2 -4 -3 -1 -2 -1 -2 0]
[ 0 1 -1 0 0 1 1 1 0 0 1 1 0]
[ 0 0 0 1 -1 0 -2 -1 0 -1 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
65 ? x + y + z + 2*x-1*y + y-1 + 2*x-1 + x-2*y + x-1*z-1 + 2*x-2*y*z-1 + 2*x-2*z-1 + 2*x-3*y*z-1 + x-4*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1264
Image of polytope 1264 PALP id: 1264
grdb id: 503704
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 1 -2 -2 -1 0 -1 0 -1 0]
[ 0 0 1 0 -1 0 -1 0 0 -1 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
143 ? x + y + z + x-1*y + x-1*y*z-1 + 2*y-1 + 3*x-1 + 3*x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 9 2 irreducible and admissible
Polytope 1265
Image of polytope 1265 PALP id: 1265
grdb id: 503547
Integer points: [ 1 0 0 0 -1 0 -2 -1 -1 0 -1 0 0]
[ 0 1 0 0 1 -2 0 0 -1 -1 0 0 -1]
[ 0 0 1 -1 0 -1 -1 0 -1 0 -1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + x-1*y + z-1 + 2*y-1 + 2*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 1266
Image of polytope 1266 PALP id: 1266
grdb id: 503525
Integer points: [ 1 0 0 0 0 -2 -2 -1 -1 -2 0 -1 -1]
[ 0 1 0 -1 0 -1 -1 0 -1 -1 0 0 -1]
[ 0 0 1 0 -1 0 -2 0 0 -1 0 -1 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? x + y + z + z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + 2*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 1267
Image of polytope 1267 PALP id: 1267
grdb id: 503423
Integer points: [ 1 0 0 0 -2 -2 0 -1 -2 -1 0 -1 0]
[ 0 1 -1 0 0 -2 2 -1 -1 0 1 1 0]
[ 0 0 0 1 -1 -1 1 0 -1 0 1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
32 ? y2*z + 2*y*z + x + y + z + 2*x-1*y + y-1 + 4*x-1 + 2*x-1*y-1 + x-2*z-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Polytope 1268
Image of polytope 1268 PALP id: 1268
grdb id: 502589
Integer points: [ 1 0 0 0 0 -2 -2 -1 -1 -2 -1 -2 0]
[ 0 1 -1 0 -1 -1 2 1 0 1 -1 0 0]
[ 0 0 0 1 1 -1 -1 0 0 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
32 ? x + y + z + 2*x-1*y + y-1*z + x-2*y2*z-1 + y-1 + 4*x-1 + 3*x-2*y*z-1 + 2*x-1*y-1 + 3*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 9 1 irreducible and admissible
Polytope 1269
Image of polytope 1269 PALP id: 1269
grdb id: 413290
Integer points: [ 1 0 0 -1 0 -1 -2 -2 -2 -1 -1 -1 0]
[ 0 1 0 0 -1 1 0 -2 -1 0 -1 -1 0]
[ 0 0 1 -1 -1 0 -1 -1 -1 0 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1270
Image of polytope 1270 PALP id: 1270
grdb id: 413296
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 -1 -1 -2 0 0 -1 0 -1]
[ 0 0 1 -1 1 -1 1 0 0 1 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
25 ? x + y + z + x-1*y*z + 2*x-1*z + z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + 2*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 1271
Image of polytope 1271 PALP id: 1271
grdb id: 413299
Integer points: [ 1 0 0 0 1 -2 -1 -2 -1 0 -1 -1 0]
[ 0 1 0 0 -1 1 -1 0 0 -1 0 1 0]
[ 0 0 1 -1 -1 0 1 1 0 0 1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + 2*x-1*y + 2*x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + x-2*y + x-1*y-1*z + x-2*z
17 rank 1, V22 x + y + z + 2*x-1*y + 2*x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 3*x-1 + x-2*y + x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1272
Image of polytope 1272 PALP id: 1272
grdb id: 413311
Integer points: [ 1 0 0 0 1 -1 -1 -2 0 -1 1 0 -1]
[ 0 1 0 0 -2 1 1 1 -1 0 -1 0 1]
[ 0 0 1 -1 0 -1 1 0 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 5 1 none
Polytope 1273
Image of polytope 1273 PALP id: 1273
grdb id: 413307
Integer points: [ 1 0 0 0 1 -1 0 -1 0 -1 -1 0 0]
[ 0 1 0 0 -1 1 -2 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 0 1 -1 -2 0 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
35 rank 2, number 15 x + y + z + x-1*y*z + x*y-1 + z-1 + 2*y-1 + 3*x-1 + y-1*z-1 + y-2*z-1 + 3*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1274
Image of polytope 1274 PALP id: 1274
grdb id: 413312
Integer points: [ 1 0 0 1 0 1 -1 -2 1 0 -1 0 -1]
[ 0 1 0 0 1 -2 1 1 -1 0 1 -1 0]
[ 0 0 1 -1 -1 0 1 0 0 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 6 1 none
Polytope 1275
Image of polytope 1275 PALP id: 1275
grdb id: 413301
Integer points: [ 1 0 1 -2 0 0 -1 -1 -1 0 -1 0 1]
[ 0 1 -2 1 0 -2 1 -1 0 -1 1 0 -1]
[ 0 0 0 0 1 -1 1 -1 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
3 ? x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + x*y-2 + y-1 + x-1 + x-2*y + y-2*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 50 1 Lattice Minkowski decompositions of facet 50
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Polytope 1276
Image of polytope 1276 PALP id: 1276
grdb id: 413298
Integer points: [ 1 0 1 0 -1 -2 -1 -2 -1 0 -1 0 1]
[ 0 1 -2 0 0 1 1 1 0 -1 1 0 -1]
[ 0 0 0 1 -1 0 1 -1 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 6 1 none
Polytope 1277
Image of polytope 1277 PALP id: 1277
grdb id: 413297
Integer points: [ 1 0 -1 0 0 -2 -1 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 1 0 2 2 1 1 0 1 0]
[ 0 0 0 1 -1 -1 -1 -1 0 -1 0 -1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1278
Image of polytope 1278 PALP id: 1278
grdb id: 413293
Integer points: [ 1 0 0 -1 -1 -1 -1 1 -1 -1 0 0 1]
[ 0 1 0 0 -1 2 1 -2 0 1 -1 0 -1]
[ 0 0 1 -1 0 -1 0 2 0 -1 1 0 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1279
Image of polytope 1279 PALP id: 1279
grdb id: 413294
Integer points: [ 1 0 0 0 -1 -1 -2 -2 -2 -1 -1 -1 0]
[ 0 1 -1 0 1 -1 2 0 1 0 0 1 0]
[ 0 0 0 1 -1 1 -1 1 0 0 1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
164 ? x + y + z + 2*x-1*y + 2*x-1*z + x-1*y*z-1 + x-2*y2*z-1 + y-1 + 3*x-1 + 2*x-2*y + x-1*y-1*z + x-2*z
76 ? x + y + z + 2*x-1*y + 2*x-1*z + x-1*y*z-1 + x-2*y2*z-1 + y-1 + 2*x-1 + 2*x-2*y + x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1280
Image of polytope 1280 PALP id: 1280
grdb id: 413310
Integer points: [ 1 0 0 0 0 -1 2 -1 1 0 1 0 -1]
[ 0 1 0 0 -1 0 2 -2 1 -1 1 0 -1]
[ 0 0 1 -1 0 0 -1 2 -1 1 0 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x2*y2*z-1 + 2*x*y + 2*x*y*z-1 + x + y + z + 2*y-1*z + z-1 + y-1 + x-1 + 2*x-1*y-1*z + x-1*y-2*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1281
Image of polytope 1281 PALP id: 1281
grdb id: 413304
Integer points: [ 1 1 -1 -1 0 -1 -1 -1 0 -1 0 1 0]
[ 0 2 -2 0 0 -2 -1 -1 -1 -1 0 1 1]
[ 0 0 0 0 1 -1 -1 1 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x*y2 + 2*x*y + x + 2*y + z + 2*y-1 + x-1 + x-1*y-1*z + x-1*y-1 + x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 1282
Image of polytope 1282 PALP id: 1282
grdb id: 413309
Integer points: [ 1 1 -1 -1 0 0 -1 -1 0 -1 0 1 0]
[ 0 2 -2 0 0 -1 -1 -2 -1 -1 0 1 1]
[ 0 0 0 0 1 -1 1 -1 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 6 1 none
Polytope 1283
Image of polytope 1283 PALP id: 1283
grdb id: 413313
Integer points: [ 1 1 0 0 -1 -1 -1 -1 0 -1 0 1 0]
[ 0 2 0 0 -2 0 -1 -1 1 -1 0 1 -1]
[ 0 0 1 -1 0 0 -1 1 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 5 1 none
Polytope 1284
Image of polytope 1284 PALP id: 1284
grdb id: 413295
Integer points: [ 1 0 0 0 -1 -2 -2 -3 -2 -1 -1 -1 0]
[ 0 1 0 -1 -1 0 -1 -1 -1 0 0 -1 0]
[ 0 0 1 -1 0 -1 -2 -2 -1 0 -1 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1285
Image of polytope 1285 PALP id: 1285
grdb id: 413275
Integer points: [ 1 0 1 -2 0 1 -1 0 0 -1 1 0 -1]
[ 0 1 -2 1 0 -3 1 -2 -1 0 -1 0 1]
[ 0 0 0 0 1 -1 1 -1 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
134 ? x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + x*y-2 + y-1 + 2*x-1 + x-2*y + x*y-3*z-1 + y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 51 1 Lattice Minkowski decompositions of facet 51
Polytope 1286
Image of polytope 1286 PALP id: 1286
grdb id: 413305
Integer points: [ 1 1 -1 -1 0 -2 0 -2 -1 0 0 0 1]
[ 0 2 -2 0 0 -3 1 -2 -1 1 0 -1 1]
[ 0 0 0 0 1 -1 1 -1 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
75 ? x*y2 + 2*x*y + y*z + x + 2*y + z + 2*y-1 + x-1 + 3*x-1*y-1 + x-1*y-2 + x-2*y-2*z-1 + x-2*y-3*z-1
24 ? x*y2 + 2*x*y + y*z + x + 2*y + z + 2*y-1 + x-1 + 2*x-1*y-1 + x-1*y-2 + x-2*y-2*z-1 + x-2*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 1 4 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1287
Image of polytope 1287 PALP id: 1287
grdb id: 413067
Integer points: [ 1 0 0 -1 1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 -1 0 -1 -1 -1 0 -1 -1 0]
[ 0 0 1 0 -1 1 1 -1 0 0 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1288
Image of polytope 1288 PALP id: 1288
grdb id: 413046
Integer points: [ 1 0 -1 0 -1 -2 -1 -2 -2 -1 -1 0 0]
[ 0 1 1 0 -1 0 -2 -2 -1 -1 0 -1 0]
[ 0 0 0 1 -1 -1 0 -1 -1 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + x-1*y + 2*y-1 + x-1 + x-1*y-1 + x-1*y-1*z-1 + x-2*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 48 1 Lattice Minkowski decompositions of facet 48
Polytope 1289
Image of polytope 1289 PALP id: 1289
grdb id: 412762
Integer points: [ 1 0 -1 0 -1 -1 -2 -2 -2 -1 -1 0 0]
[ 0 1 1 0 0 -2 1 -1 0 0 -1 0 -1]
[ 0 0 0 1 -1 0 -1 -1 -1 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
77 ? x + y + z + x-1*y + 2*y-1 + x-1 + x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + 2*x-2*z-1 + x-1*y-2 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 47 1 Lattice Minkowski decompositions of facet 47
Polytope 1290
Image of polytope 1290 PALP id: 1290
grdb id: 413106
Integer points: [ 1 0 -1 0 0 -1 -2 -2 -1 -1 -1 0 0]
[ 0 1 1 0 -2 -1 -1 -2 -1 0 -2 -1 0]
[ 0 0 0 1 -1 -1 -1 -1 0 0 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1291
Image of polytope 1291 PALP id: 1291
grdb id: 413178
Integer points: [ 1 0 0 -1 -2 -1 0 -2 -1 -2 -1 0 0]
[ 0 1 0 -1 0 -2 -1 -2 0 -1 -1 0 -1]
[ 0 0 1 -1 -1 0 1 -1 0 -1 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
147 ? x + y + z + y-1*z + 2*y-1 + 2*x-1 + 3*x-1*y-1 + x-1*y-1*z-1 + x-2*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1292
Image of polytope 1292 PALP id: 1292
grdb id: 413261
Integer points: [ 1 0 0 -1 -1 1 -1 1 0 -1 0 1 0]
[ 0 1 0 1 0 -1 -1 0 0 0 0 0 -1]
[ 0 0 1 1 0 -1 1 -2 -1 1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
24 ? x + y + z + x-1*y*z + 2*x*z-1 + 2*x-1*z + x*z-2 + x*y-1*z-1 + 2*z-1 + 2*y-1 + x-1 + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 1 4 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1293
Image of polytope 1293 PALP id: 1293
grdb id: 413177
Integer points: [ 1 0 0 0 -2 1 -1 0 0 -1 1 0 -1]
[ 0 1 0 -1 1 -2 0 -1 -1 0 -1 0 1]
[ 0 0 1 -1 0 0 1 1 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 28 1 none
Polytope 1294
Image of polytope 1294 PALP id: 1294
grdb id: 413055
Integer points: [ 1 0 0 0 -1 -2 -1 -2 -1 -1 -1 0 0]
[ 0 1 -1 0 1 0 -2 -1 0 -1 0 0 -1]
[ 0 0 0 1 0 -1 -2 -2 0 -1 -1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
80 ? x + y + z + x-1*y + y-1 + 2*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1*z-1 + x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
107 rank 3, number 11 x + y + z + x-1*y + y-1 + 2*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1*z-1 + x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1295
Image of polytope 1295 PALP id: 1295
grdb id: 413098
Integer points: [ 1 0 0 0 -1 -1 -2 -2 -2 -1 -1 -1 0]
[ 0 1 0 -1 -1 1 -1 1 0 0 -1 0 0]
[ 0 0 1 -1 0 0 -1 -1 -1 0 -1 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
66 rank 2, number 24 x + y + z + x-1*y + 2*x-1 + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1*z-1
16 ? x + y + z + x-1*y + 3*x-1 + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1296
Image of polytope 1296 PALP id: 1296
grdb id: 413172
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 0 0 -2 -2 -1 -1 0 -1 0]
[ 0 0 0 1 -1 1 -1 -2 0 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + x-1*z + y-1 + 2*x-1 + 2*y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 1297
Image of polytope 1297 PALP id: 1297
grdb id: 413170
Integer points: [ 1 0 0 0 -1 0 -2 -2 -1 -1 0 -1 0]
[ 0 1 0 -1 1 -1 1 1 0 0 -1 1 0]
[ 0 0 1 -1 1 1 0 1 1 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y*z + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + 2*y-1 + 2*x-1 + x-2*y + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1298
Image of polytope 1298 PALP id: 1298
grdb id: 413244
Integer points: [ 1 0 0 0 -1 1 -2 -2 -1 0 -1 0 -1]
[ 0 1 -1 0 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 0 0 1 1 -1 0 -1 0 -1 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 6 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1299
Image of polytope 1299 PALP id: 1299
grdb id: 413257
Integer points: [ 1 0 0 0 -1 1 -2 1 0 -1 1 0 -1]
[ 0 1 0 0 1 -1 1 -2 -1 0 -1 0 1]
[ 0 0 1 -1 1 -1 0 0 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
75 ? x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + x*y-1*z-1 + z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Polytope 1300
Image of polytope 1300 PALP id: 1300
grdb id: 413028
Integer points: [ 1 0 0 0 0 -1 -2 -2 -1 0 -1 -1 0]
[ 0 1 0 -1 -1 0 1 1 0 -1 0 1 0]
[ 0 0 1 -1 1 1 0 -1 0 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + 2*x-1*y + y-1*z + x-1*z + 2*y-1 + 3*x-1 + x-2*y + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 1301
Image of polytope 1301 PALP id: 1301
grdb id: 413229
Integer points: [ 1 0 0 0 1 -1 -2 -2 -1 -1 0 -1 0]
[ 0 1 -1 0 -1 -1 0 -1 0 -1 -1 0 0]
[ 0 0 0 1 -1 -1 1 0 0 0 -1 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 6 1 none
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1302
Image of polytope 1302 PALP id: 1302
grdb id: 413050
Integer points: [ 1 0 0 0 1 -1 -2 -2 -1 -1 0 -1 0]
[ 0 1 0 -1 0 0 -1 -2 0 -1 0 -1 0]
[ 0 0 1 0 -1 -1 0 1 0 0 -1 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x*z-1 + 2*z-1 + y-1 + 2*x-1 + 2*x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-2*y-1 + x-2*y-2*z
38 ? x + y + z + x*z-1 + 2*z-1 + y-1 + 2*x-1 + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-2*y-1 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1303
Image of polytope 1303 PALP id: 1303
grdb id: 413245
Integer points: [ 1 0 0 0 1 -1 -2 -2 -1 -1 0 -1 0]
[ 0 1 0 0 -1 1 0 -1 0 -1 -1 0 0]
[ 0 0 1 -1 0 1 1 0 1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y*z + x*y-1 + 2*x-1*z + z-1 + 3*y-1 + x-1 + x-2*z + 3*x-1*y-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1304
Image of polytope 1304 PALP id: 1304
grdb id: 413259
Integer points: [ 1 0 0 1 -1 0 1 -2 -1 0 -1 0 1]
[ 0 1 0 -2 1 -1 -2 1 0 -1 1 0 -1]
[ 0 0 1 -1 1 -1 0 0 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
127 ? x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Polytope 1305
Image of polytope 1305 PALP id: 1305
grdb id: 413184
Integer points: [ 1 0 0 1 0 -1 -2 -2 0 -1 -1 0 -1]
[ 0 1 0 0 -1 -2 -1 -2 -1 -1 -1 0 0]
[ 0 0 1 -1 1 1 0 1 0 0 1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 8 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1306
Image of polytope 1306 PALP id: 1306
grdb id: 413232
Integer points: [ 1 0 0 1 0 1 -2 1 1 0 -1 0 -1]
[ 0 1 0 0 1 -2 1 1 -1 0 1 -1 0]
[ 0 0 1 -1 -1 0 0 -1 0 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x*y*z-1 + x + y + z + x*z-1 + y*z-1 + 2*x*y-1 + 2*x-1*y + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1307
Image of polytope 1307 PALP id: 1307
grdb id: 413173
Integer points: [ 1 0 1 -2 0 -1 0 -2 0 -1 -1 0 -1]
[ 0 1 -1 1 0 1 -2 0 -1 0 -1 0 1]
[ 0 0 0 0 1 1 -1 -1 0 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
100 ? x + y + z + x-1*y*z + x*y-1 + 2*x-1*y + 2*y-1 + 3*x-1 + x-2*y + y-2*z-1 + 2*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1308
Image of polytope 1308 PALP id: 1308
grdb id: 413018
Integer points: [ 1 0 1 -2 0 1 -1 0 0 -1 1 0 -1]
[ 0 1 -2 1 0 -2 0 -1 -1 0 -1 0 1]
[ 0 0 0 0 1 -1 1 1 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 29 1 none
Polytope 1309
Image of polytope 1309 PALP id: 1309
grdb id: 413078
Integer points: [ 1 0 1 -1 0 -1 -1 -1 -1 0 -1 -1 0]
[ 0 1 -1 1 0 0 0 -2 -1 -1 0 -1 0]
[ 0 0 0 0 1 -1 1 -1 0 0 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1310
Image of polytope 1310 PALP id: 1310
grdb id: 413233
Integer points: [ 1 0 1 -1 0 1 -1 -2 -1 0 -1 0 0]
[ 0 1 -1 1 0 1 -1 1 1 1 0 0 -1]
[ 0 0 0 0 1 -1 0 -1 -1 -1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 6 1 none
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1311
Image of polytope 1311 PALP id: 1311
grdb id: 413074
Integer points: [ 1 0 1 -1 0 1 -1 -1 -1 0 0 -1 0]
[ 0 1 -1 1 0 -2 0 -2 -1 -1 -2 0 0]
[ 0 0 0 0 1 -1 1 -1 0 0 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 4 1 none
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 1312
Image of polytope 1312 PALP id: 1312
grdb id: 413150
Integer points: [ 1 0 1 0 -1 -2 1 -1 0 -1 0 0 -1]
[ 0 1 -1 0 0 1 -2 0 -1 0 -1 0 1]
[ 0 0 0 1 -1 0 -1 1 0 0 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*y-1 + 2*x-1*y + x-1*z + 2*y-1 + 2*x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 1313
Image of polytope 1313 PALP id: 1313
grdb id: 413104
Integer points: [ 1 0 1 0 -1 -1 -2 -2 -1 0 -1 -1 0]
[ 0 1 -1 0 -1 1 -1 0 -1 -1 0 0 0]
[ 0 0 0 1 -1 1 0 1 0 0 1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? x + y + z + x-1*y*z + x*y-1 + 2*x-1*z + 3*y-1 + x-1 + x-2*z + 3*x-1*y-1 + x-1*y-1*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1314
Image of polytope 1314 PALP id: 1314
grdb id: 413253
Integer points: [ 1 0 -1 0 -1 -2 1 1 0 -1 0 1 0]
[ 0 1 1 0 0 1 -2 -2 -1 0 -1 -1 0]
[ 0 0 0 1 -1 -1 1 2 1 0 0 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + 2*x*y-1*z + z + x*y-2*z2 + x-1*y + x*y-2*z + 3*y-1*z + 2*y-1 + 3*x-1 + x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1315
Image of polytope 1315 PALP id: 1315
grdb id: 413048
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 0 -2 -1 -2 0 -1 -1 0 -1]
[ 0 0 1 -1 1 1 2 2 0 1 0 0 1]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? x + y + z + 2*y-1*z + x-1*z + x-1*y-1*z2 + 2*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1316
Image of polytope 1316 PALP id: 1316
grdb id: 412653
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -2 -1 2 0 1 0 -1 0 -1]
[ 0 0 1 -1 0 1 -1 1 0 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 45 1 none
Polytope 1317
Image of polytope 1317 PALP id: 1317
grdb id: 413138
Integer points: [ 1 0 0 -1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 1 1 -2 1 0 -1 1 0 -1]
[ 0 0 1 -1 1 2 -2 0 0 -1 1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? y*z2 + 2*y*z + x + y + z + x-1*y*z + x-1*y + 3*x-1 + 2*y-1*z-1 + x-1*z-1 + 3*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Polytope 1318
Image of polytope 1318 PALP id: 1318
grdb id: 413137
Integer points: [ 1 0 0 0 -2 0 -1 -2 -2 -1 -1 -1 0]
[ 0 1 -1 0 0 1 2 2 1 1 1 0 0]
[ 0 0 0 1 -1 1 1 1 0 0 1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1319
Image of polytope 1319 PALP id: 1319
grdb id: 413255
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 0 0 -1 -1]
[ 0 1 -1 0 -1 0 2 2 1 0 1 0 1]
[ 0 0 0 1 1 1 -1 -2 0 0 -1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + 2*y*z-1 + x-1*y2*z-1 + 2*x-1*y + x-1*z + x-1*y2*z-2 + 3*x-1*y*z-1 + y-1 + 3*x-1 + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1320
Image of polytope 1320 PALP id: 1320
grdb id: 413110
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 1 0 -2 2 1 -1 0 -1 0]
[ 0 0 1 -1 0 -1 0 -1 -1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + y*z-1 + x-1*y2*z-1 + x-1*y + 2*x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*z-1 + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1321
Image of polytope 1321 PALP id: 1321
grdb id: 413237
Integer points: [ 1 0 0 0 0 -1 -2 2 -1 0 -1 1 1]
[ 0 1 0 0 -1 1 0 -1 0 0 0 -1 0]
[ 0 0 1 -1 0 0 1 -2 1 0 0 -1 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + 2*x*z-1 + x-1*y + 2*x-1*z + x2*y-1*z-2 + 2*x*y-1*z-1 + z-1 + y-1 + 2*x-1 + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1322
Image of polytope 1322 PALP id: 1322
grdb id: 413239
Integer points: [ 1 0 0 1 -1 0 -2 -1 -1 0 1 -1 0]
[ 0 1 0 -2 2 -1 1 0 1 0 -1 0 -1]
[ 0 0 1 0 -1 1 0 1 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + x-1*y2*z-1 + 2*x*y-1 + x-1*y + y-1*z + x-1*z + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1323
Image of polytope 1323 PALP id: 1323
grdb id: 413262
Integer points: [ 1 0 0 1 -1 0 0 -1 0 -1 0 1 0]
[ 0 1 0 -2 2 0 -1 0 1 1 0 -1 -1]
[ 0 0 1 2 -2 -1 0 0 -1 -1 0 1 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
75 ? x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + z-1 + 2*x-1*y*z-1 + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Polytope 1324
Image of polytope 1324 PALP id: 1324
grdb id: 413095
Integer points: [ 1 0 1 -2 0 -2 0 -1 -1 0 1 -1 0]
[ 0 1 -2 1 0 2 -1 0 1 0 -1 0 -1]
[ 0 0 0 0 1 -1 1 1 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
94 ? x + y + z + 2*x*y-1 + x-1*y + y-1*z + x-1*z + x-2*y2*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1325
Image of polytope 1325 PALP id: 1325
grdb id: 413263
Integer points: [ 1 0 1 -1 0 -1 1 0 0 -1 0 1 0]
[ 0 1 0 0 -1 0 1 -1 0 0 0 0 0]
[ 0 0 2 -2 0 0 1 -1 -1 -1 0 1 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
109 ? x*y*z + x*z2 + 2*x*z + x + y + 2*z + 2*z-1 + y-1 + x-1 + y-1*z-1 + 2*x-1*z-1 + x-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Polytope 1326
Image of polytope 1326 PALP id: 1326
grdb id: 413260
Integer points: [ 1 1 -1 -1 0 1 0 1 1 0 0 0 -1]
[ 0 2 -2 0 0 0 1 1 1 -1 0 1 -1]
[ 0 0 0 0 1 -1 1 -1 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
101 ? x*y2 + 2*x*y + y*z + x*y*z-1 + x + 2*y + z + x*z-1 + 2*y-1 + x-1 + 2*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Polytope 1327
Image of polytope 1327 PALP id: 1327
grdb id: 412991
Integer points: [ 1 0 -1 -1 0 -1 -2 -2 -2 -1 -1 0 0]
[ 0 1 1 -2 0 -2 -1 -3 -2 -1 0 -1 0]
[ 0 0 0 0 1 -1 -1 -1 -1 0 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
95 ? x + y + z + x-1*y + 2*y-1 + 2*x-1 + x-1*y-1 + x-1*y-2 + x-1*y-2*z-1 + x-2*y-1*z-1 + 2*x-2*y-2*z-1 + x-2*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 47 1 Lattice Minkowski decompositions of facet 47
Polytope 1328
Image of polytope 1328 PALP id: 1328
grdb id: 412569
Integer points: [ 1 0 -1 0 -1 0 -2 -2 -1 -1 -1 0 0]
[ 0 1 1 0 -2 -1 -2 -3 -2 -1 0 -1 0]
[ 0 0 0 1 -1 1 -1 -1 0 0 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 45 1 none
Polytope 1329
Image of polytope 1329 PALP id: 1329
grdb id: 412994
Integer points: [ 1 0 0 -2 -1 -3 -1 -3 -2 -1 -2 0 -1]
[ 0 1 0 -1 0 -2 -1 -2 -1 0 -1 0 -1]
[ 0 0 1 -1 1 0 1 1 1 0 0 0 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
93 ? x + y + z + x-1*z + 2*x-1 + x-1*y-1*z + 2*x-1*y-1 + 2*x-2*y-1*z + x-2*y-1 + x-2*y-1*z-1 + x-3*y-2*z + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 47 1 Lattice Minkowski decompositions of facet 47
Polytope 1330
Image of polytope 1330 PALP id: 1330
grdb id: 412989
Integer points: [ 1 0 0 -2 0 -3 -3 -2 -1 -2 -1 -1 0]
[ 0 1 0 0 -1 -1 -2 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 1 -1 0 1 1 0 0 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
92 ? x + y + z + y-1*z + 3*x-1 + 2*x-1*y-1*z + 2*x-1*y-1 + x-2*z-1 + 4*x-2*y-1 + x-2*y-2*z + x-3*y-1*z-1 + x-3*y-2
102 ? x + y + z + y-1*z + 2*x-1 + 2*x-1*y-1*z + 2*x-1*y-1 + x-2*z-1 + 2*x-2*y-1 + x-2*y-2*z + x-3*y-1*z-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Polytope 1331
Image of polytope 1331 PALP id: 1331
grdb id: 412937
Integer points: [ 1 0 0 -1 -1 -2 -3 -3 -2 -1 -2 -1 0]
[ 0 1 0 -1 1 1 0 -1 0 0 -1 0 0]
[ 0 0 1 0 0 -1 -2 -2 -1 0 -1 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
87 ? x + y + z + x-1*y + 3*x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + 4*x-2*z-1 + 2*x-2*y-1*z-1 + x-3*z-2 + x-3*y-1*z-2
160 ? x + y + z + x-1*y + 2*x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + 2*x-2*z-1 + 2*x-2*y-1*z-1 + x-3*z-2 + x-3*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Polytope 1332
Image of polytope 1332 PALP id: 1332
grdb id: 413114
Integer points: [ 1 0 0 -1 -1 -1 -3 -3 -2 -1 -2 -1 0]
[ 0 1 0 -1 0 -1 -2 -2 -1 0 -1 -1 0]
[ 0 0 1 -1 1 1 0 1 0 0 1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
98 rank 3, number 21 x + y + z + x-1*z + 3*x-1 + x-1*y-1*z + x-1*y-1 + 2*x-2*y-1*z + x-1*y-1*z-1 + 3*x-2*y-1 + x-3*y-2*z + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1333
Image of polytope 1333 PALP id: 1333
grdb id: 413217
Integer points: [ 1 0 0 -1 -1 -1 -3 -3 -2 -1 -2 0 -1]
[ 0 1 0 -1 1 1 0 1 1 0 0 0 0]
[ 0 0 1 0 0 -1 -2 -2 -1 0 -1 0 -1]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
61 rank 2, number 27 x + y + z + x-1*y + x-1*y*z-1 + x-1 + 2*x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1 + x-2*z-1 + x-3*y*z-2 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 48 1 Lattice Minkowski decompositions of facet 48
Polytope 1334
Image of polytope 1334 PALP id: 1334
grdb id: 412821
Integer points: [ 1 0 0 -1 -1 -1 -3 -3 -2 -2 -1 -1 0]
[ 0 1 0 0 -1 1 -1 -2 0 -1 0 -1 0]
[ 0 0 1 -1 0 0 -2 -2 -1 -1 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 46 1 none
Polytope 1335
Image of polytope 1335 PALP id: 1335
grdb id: 413140
Integer points: [ 1 0 0 -1 0 -2 -3 -2 -1 -2 -1 -1 0]
[ 0 1 0 0 -1 -1 -2 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 1 -1 0 1 1 0 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
47 ? x + y + z + y-1*z + 3*x-1 + 2*x-1*y-1*z + x-1*z-1 + x-1*y-1 + 3*x-2*y-1 + x-2*y-2*z + x-2*y-1*z-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1336
Image of polytope 1336 PALP id: 1336
grdb id: 412993
Integer points: [ 1 0 0 -1 0 -2 -2 -3 -1 -2 -1 -1 0]
[ 0 1 -1 1 0 0 -2 -2 -1 -1 0 -1 0]
[ 0 0 0 0 1 -1 -1 -2 0 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 46 1 none
Polytope 1337
Image of polytope 1337 PALP id: 1337
grdb id: 412983
Integer points: [ 1 0 0 -1 0 -2 -2 -3 -1 -2 -1 -1 0]
[ 0 1 0 -1 1 -1 1 0 1 0 0 0 0]
[ 0 0 1 0 1 -1 -1 -2 0 -1 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
95 ? y*z + x + y + z + 2*x-1*y + 4*x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + 3*x-2*z-1 + x-2*y-1*z-1 + x-3*z-2
119 ? y*z + x + y + z + 2*x-1*y + 2*x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + 2*x-2*z-1 + x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Polytope 1338
Image of polytope 1338 PALP id: 1338
grdb id: 413231
Integer points: [ 1 0 0 -1 0 -2 -1 -2 -1 -1 0 -1 0]
[ 0 1 -1 0 0 -2 -2 -3 -1 -2 0 -1 -1]
[ 0 0 0 0 1 -1 -2 -2 0 -1 0 -1 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
28 rank 2, number 25 x + y + z + y-1 + x-1 + 2*y-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + 2*x-1*y-2*z-1 + x-1*y-2*z-2 + x-2*y-2*z-1 + x-2*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1339
Image of polytope 1339 PALP id: 1339
grdb id: 412752
Integer points: [ 1 0 0 -1 1 0 -2 -3 -1 -1 -2 0 -1]
[ 0 1 0 0 1 1 -1 -2 0 0 -1 0 -1]
[ 0 0 1 -1 1 1 1 0 1 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
148 ? x*y*z + y*z + x + y + z + 2*x-1*z + x-1 + x-1*z-1 + 2*x-1*y-1 + x-2*y-1*z + 2*x-2*y-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 47 1 Lattice Minkowski decompositions of facet 47
Polytope 1340
Image of polytope 1340 PALP id: 1340
grdb id: 413143
Integer points: [ 1 0 0 0 -1 -2 -2 -3 -2 -1 -1 -1 0]
[ 0 1 -1 0 1 1 -1 0 0 0 -1 0 0]
[ 0 0 0 1 0 -1 -2 -2 -1 0 -1 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
29 rank 2, number 23 x + y + z + x-1*y + y-1 + 3*x-1 + x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1*z-1 + 3*x-2*z-1 + x-2*y-1*z-2 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1341
Image of polytope 1341 PALP id: 1341
grdb id: 413182
Integer points: [ 1 0 0 0 -1 -2 -2 -3 -2 -1 -1 -1 0]
[ 0 1 0 -1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 -1 1 1 1 0 0 0 1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 8 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1342
Image of polytope 1342 PALP id: 1342
grdb id: 412982
Integer points: [ 1 0 0 0 -1 -2 -2 -3 -1 -2 -1 0 -1]
[ 0 1 0 -1 1 1 -1 0 0 0 -1 0 0]
[ 0 0 1 1 0 -1 -1 -2 0 -1 0 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
66 rank 2, number 24 x + y + z + x-1*y + y-1*z + 2*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + 2*x-2*z-1 + x-2*y-1*z-1 + x-3*z-2
122 ? x + y + z + x-1*y + y-1*z + 4*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + 3*x-2*z-1 + x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Polytope 1343
Image of polytope 1343 PALP id: 1343
grdb id: 413131
Integer points: [ 1 0 0 0 -1 -2 -1 -3 -2 -2 -1 -1 0]
[ 0 1 -1 0 -2 -1 0 -2 -1 -2 -1 0 0]
[ 0 0 0 1 -1 -1 1 -1 0 -1 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 8 1 none
Polytope 1344
Image of polytope 1344 PALP id: 1344
grdb id: 413249
Integer points: [ 1 0 0 1 0 0 -2 -3 -1 -1 -2 0 -1]
[ 0 1 -1 1 0 1 1 0 1 0 0 0 0]
[ 0 0 0 0 1 -1 -2 -2 -1 0 -1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
55 rank 2, number 19 x*y + x + y + z + y*z-1 + 2*x-1*y*z-1 + y-1 + 3*x-1 + x-1*z-1 + x-2*y*z-2 + 3*x-2*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1345
Image of polytope 1345 PALP id: 1345
grdb id: 413077
Integer points: [ 1 0 0 0 -1 0 -1 -3 -2 -1 -2 -1 0]
[ 0 1 -1 0 0 -1 0 2 1 0 1 1 0]
[ 0 0 0 1 -1 1 1 -1 0 0 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 1346
Image of polytope 1346 PALP id: 1346
grdb id: 412649
Integer points: [ 1 0 0 -2 -3 -1 -4 -2 -3 -2 -1 -1 0]
[ 0 1 0 -2 -2 0 -3 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 -1 1 -1 1 0 0 0 0 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 45 1 none
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1347
Image of polytope 1347 PALP id: 1347
grdb id: 413085
Integer points: [ 1 -1 0 0 -2 2 0 3 -1 1 0 2 1]
[ 0 0 1 0 0 -1 -1 -2 0 -1 0 -1 0]
[ 0 0 0 1 1 -1 -1 -3 1 -1 0 -2 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + x2*y-1*z-1 + 3*x*z-1 + 2*x-1*z + 3*x2*y-1*z-2 + 2*x*y-1*z-1 + x-1 + x-2*z + x3*y-2*z-3 + y-1*z-1
52 rank 2, number 52 x + y + z + x2*y-1*z-1 + 3*x*z-1 + 2*x-1*z + 3*x2*y-1*z-2 + 3*x*y-1*z-1 + x-1 + x-2*z + x3*y-2*z-3 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1348
Image of polytope 1348 PALP id: 1348
grdb id: 411764
Integer points: [ 1 0 0 -1 -1 -1 0 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 0 2 2 1 1 0 1 0]
[ 0 0 1 -1 0 1 1 1 0 1 0 1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
63 ? y2*z + 2*y*z + x-1*y2*z + x + y + z + 2*x-1*y*z + 2*x-1*y + x-1*z + 2*x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1349
Image of polytope 1349 PALP id: 1349
grdb id: 409714
Integer points: [ 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 -1 2 1 0 1 0 0]
[ 0 0 1 -1 0 1 1 1 1 1 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
69 ? y*z + x-1*y2*z + x + y + z + 3*x-1*y*z + 2*x-1*y + 3*x-1*z + 3*x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1350
Image of polytope 1350 PALP id: 1350
grdb id: 411409
Integer points: [ 1 0 -1 0 -2 -1 0 -2 -1 -2 -1 0 0]
[ 0 1 1 0 0 -2 -1 -2 -1 -1 0 -1 0]
[ 0 0 0 1 -1 0 1 -1 0 -1 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
145 ? x + y + z + x-1*y + y-1*z + 2*y-1 + 2*x-1 + 2*x-1*y-1 + x-2*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
132 ? x + y + z + x-1*y + y-1*z + 2*y-1 + 3*x-1 + 4*x-1*y-1 + x-2*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Polytope 1351
Image of polytope 1351 PALP id: 1351
grdb id: 412146
Integer points: [ 1 0 -1 0 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 1 0 0 -1 -2 -2 -1 0 -1 -1 0]
[ 0 0 0 1 -1 1 0 -1 0 0 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 6 1 none
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1352
Image of polytope 1352 PALP id: 1352
grdb id: 411509
Integer points: [ 1 0 -1 0 0 -2 -1 -2 -1 -2 -1 0 0]
[ 0 1 1 0 -1 1 -2 -1 0 0 -1 0 -1]
[ 0 0 0 1 1 -1 0 -1 0 -1 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
64 ? x + y + z + x-1*y + y-1*z + 2*y-1 + 4*x-1 + x-2*y*z-1 + 3*x-1*y-1 + 2*x-2*z-1 + x-1*y-2 + x-2*y-1*z-1
122 ? x + y + z + x-1*y + y-1*z + 2*y-1 + 2*x-1 + x-2*y*z-1 + 2*x-1*y-1 + 2*x-2*z-1 + x-1*y-2 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Polytope 1353
Image of polytope 1353 PALP id: 1353
grdb id: 412315
Integer points: [ 1 0 -1 0 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 1 0 -1 0 -2 -2 -1 0 -1 -1 0]
[ 0 0 0 1 -1 -1 0 -1 0 0 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
114 ? x + y + z + x-1*y + 2*y-1 + 3*x-1 + y-1*z-1 + x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1354
Image of polytope 1354 PALP id: 1354
grdb id: 411717
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 0 0 -1]
[ 0 1 0 0 0 -2 -1 -2 -1 0 -1 0 -1]
[ 0 0 1 -1 1 0 1 -1 0 0 0 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? x + y + z + x-1*z + 2*y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 1355
Image of polytope 1355 PALP id: 1355
grdb id: 409734
Integer points: [ 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 1 -1 1 -2 0 -1 0 -1 0]
[ 0 0 1 -1 0 1 1 1 1 1 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + x-1*y*z + x-1*y + y-1*z + 3*x-1*z + 3*x-1 + 3*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1356
Image of polytope 1356 PALP id: 1356
grdb id: 412319
Integer points: [ 1 0 0 -1 -1 0 -1 0 -1 0 0 0 0]
[ 0 1 0 1 0 -1 0 -1 0 -1 -1 0 0]
[ 0 0 1 0 1 1 -1 -2 0 0 -1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + x-1*y + y-1*z + x-1*z + 2*z-1 + 3*y-1 + 2*x-1 + 3*y-1*z-1 + x-1*z-1 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1357
Image of polytope 1357 PALP id: 1357
grdb id: 412094
Integer points: [ 1 0 0 -1 0 -2 -1 -2 -1 -2 -1 -1 0]
[ 0 1 0 0 -1 0 -2 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 1 -1 1 1 1 0 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? x + y + z + y-1*z + 2*x-1 + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z + x-2*z-1 + 2*x-2*y-1 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1358
Image of polytope 1358 PALP id: 1358
grdb id: 412182
Integer points: [ 1 0 0 -1 0 -1 -2 -2 -1 -2 -1 -1 0]
[ 0 1 0 0 -1 0 -1 -1 -1 -1 0 -1 0]
[ 0 0 1 -1 1 1 -1 1 1 0 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? x + y + z + y-1*z + x-1*z + 2*x-1 + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-2*y-1*z + 2*x-2*y-1 + x-2*y-1*z-1
65 ? x + y + z + y-1*z + x-1*z + 3*x-1 + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-2*y-1*z + 2*x-2*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1359
Image of polytope 1359 PALP id: 1359
grdb id: 411745
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 0 -2 -2 0 -1 -1 0 -1]
[ 0 0 1 -1 1 1 0 1 0 1 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
147 ? x + y + z + y-1*z + x-1*z + 2*y-1 + 2*x-1 + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 1360
Image of polytope 1360 PALP id: 1360
grdb id: 412197
Integer points: [ 1 0 0 -1 0 -1 0 -1 -1 0 -1 -1 0]
[ 0 1 0 0 -1 0 -2 -2 -1 -1 -1 0 0]
[ 0 0 1 -1 -1 1 -1 -1 0 0 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + x-1*z + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1361
Image of polytope 1361 PALP id: 1361
grdb id: 411768
Integer points: [ 1 0 0 0 -2 0 -1 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 -1 -1 0 -1 -1 -1 0 -1 0]
[ 0 0 0 1 -1 1 1 1 1 0 0 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 1362
Image of polytope 1362 PALP id: 1362
grdb id: 412324
Integer points: [ 1 0 0 0 -2 0 -1 1 -1 0 -1 0 1]
[ 0 1 0 0 1 -1 0 -2 0 -1 1 0 -1]
[ 0 0 1 -1 0 1 1 0 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
91 ? x + y + z + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Polytope 1363
Image of polytope 1363 PALP id: 1363
grdb id: 409707
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 1 0 1 -2 -1 -1 0 0 0]
[ 0 0 0 1 0 1 -1 -1 0 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y + x-1*z + x-1*y*z-1 + y-1 + 3*x-1 + 3*x-1*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1364
Image of polytope 1364 PALP id: 1364
grdb id: 412320
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 1 -1 -2 0 -1 0 -1 0]
[ 0 0 1 -1 0 -1 -1 0 -1 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
88 ? x + y + z + x-1*y + z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + 2*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1365
Image of polytope 1365 PALP id: 1365
grdb id: 412375
Integer points: [ 1 0 0 0 0 -1 0 -1 0 0 0 -1 -1]
[ 0 1 0 1 -1 1 -1 -2 0 -1 0 -1 0]
[ 0 0 1 -1 1 0 -1 0 -1 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 5 1 none
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1366
Image of polytope 1366 PALP id: 1366
grdb id: 412323
Integer points: [ 1 0 0 0 1 1 -2 1 0 -1 1 0 -1]
[ 0 1 0 0 0 -1 1 -2 -1 0 -1 0 1]
[ 0 0 1 -1 -1 -1 0 0 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
109 ? x + y + z + x*z-1 + 2*x*y-1 + 2*x-1*y + x*y-1*z-1 + z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Polytope 1367
Image of polytope 1367 PALP id: 1367
grdb id: 412314
Integer points: [ 1 0 0 1 -2 -1 1 0 0 -1 1 0 -1]
[ 0 1 0 -1 1 0 -2 -1 -1 0 -1 0 1]
[ 0 0 1 -1 0 1 0 1 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
127 ? x + y + z + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + x*y-1*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Polytope 1368
Image of polytope 1368 PALP id: 1368
grdb id: 412180
Integer points: [ 1 0 0 1 -1 -2 0 1 0 -1 -1 0 0]
[ 0 1 0 -1 0 0 -2 -2 -1 -1 0 -1 0]
[ 0 0 1 0 -1 -1 -1 -1 0 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
55 rank 2, number 19 x + y + z + x*y-1 + 2*y-1 + 2*x-1 + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1369
Image of polytope 1369 PALP id: 1369
grdb id: 412347
Integer points: [ 1 0 1 -1 0 1 -1 -2 0 -1 0 -1 0]
[ 0 1 -1 1 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 0 0 0 1 -1 0 -1 0 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 6 1 none
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1370
Image of polytope 1370 PALP id: 1370
grdb id: 412350
Integer points: [ 1 0 1 0 0 -2 1 -2 -1 0 -1 0 -1]
[ 0 1 -1 -1 0 1 -2 1 0 -1 0 0 1]
[ 0 0 0 0 1 0 -1 -1 0 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
128 ? x + y + z + x*y-1 + 2*x-1*y + y-1 + 2*x-1 + x-2*y + x*y-2*z-1 + 3*y-1*z-1 + 3*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1371
Image of polytope 1371 PALP id: 1371
grdb id: 412178
Integer points: [ 1 0 0 0 -1 -1 -2 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 -1 1 0 2 0 1 0 1 0]
[ 0 0 0 1 -1 -1 -1 -1 0 -1 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + 2*x-1*y + x-1*y*z-1 + x-2*y2*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1372
Image of polytope 1372 PALP id: 1372
grdb id: 411847
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 1 2 -2 0 -1 0 1 0]
[ 0 0 0 1 0 0 -1 -1 0 -1 -1 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
60 rank 2, number 18 x + y + z + x-1*y2*z-1 + x-1*y + 4*x-1*y*z-1 + y-1 + 2*x-1 + 6*x-1*z-1 + x-1*y-1 + 4*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 13 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Polytope 1373
Image of polytope 1373 PALP id: 1373
grdb id: 411823
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 1 0 2 -2 -1 0 1 -1 0]
[ 0 0 1 1 0 -1 -1 0 0 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*y2*z-1 + x-1*y + y-1*z + 2*x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*z-1 + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1374
Image of polytope 1374 PALP id: 1374
grdb id: 412119
Integer points: [ 1 0 -1 0 0 -1 0 -1 -1 0 -1 -1 0]
[ 0 1 1 0 -1 -1 -2 -3 -2 -1 0 -1 0]
[ 0 0 0 1 -1 0 -1 -2 -1 0 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + x-1*y + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*y-1 + y-2*z-1 + 2*x-1*y-1*z-1 + 2*x-1*y-2*z-1 + x-1*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1375
Image of polytope 1375 PALP id: 1375
grdb id: 412044
Integer points: [ 1 0 0 -1 0 -1 -3 -3 -1 -2 -2 0 -1]
[ 0 1 -1 0 0 -2 -2 -3 -1 -2 -1 0 -1]
[ 0 0 0 0 1 -1 -2 -2 0 -1 -1 0 -1]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? x + y + z + y-1 + x-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1 + 2*x-2*y-1*z-1 + 3*x-2*y-2*z-1 + x-3*y-2*z-2 + x-3*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1376
Image of polytope 1376 PALP id: 1376
grdb id: 409711
Integer points: [ 1 0 0 -1 0 -1 -1 -3 -1 -2 -1 -2 0]
[ 0 1 -1 1 0 -1 -2 -3 -1 -2 0 -1 0]
[ 0 0 0 0 1 -1 -1 -2 0 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 14 1 none
Polytope 1377
Image of polytope 1377 PALP id: 1377
grdb id: 412355
Integer points: [ 1 0 0 0 -1 -2 -2 -3 -1 -2 0 -1 -1]
[ 0 1 -1 0 1 0 1 1 0 1 0 0 1]
[ 0 0 0 1 0 -1 -2 -2 0 -1 0 -1 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + x-1*y + 2*x-1*y*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + 2*x-2*y*z-1 + x-2*y*z-2 + x-2*z-1 + x-3*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1378
Image of polytope 1378 PALP id: 1378
grdb id: 412310
Integer points: [ 1 0 0 0 -1 -1 -3 -3 -1 -2 -2 0 -1]
[ 0 1 -1 0 1 1 0 1 0 0 1 0 0]
[ 0 0 0 1 0 -1 -2 -2 0 -1 -1 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
147 ? x + y + z + x-1*y + x-1*y*z-1 + y-1 + 3*x-1 + 2*x-1*z-1 + 2*x-2*y*z-1 + 3*x-2*z-1 + x-3*y*z-2 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 9 1 irreducible and admissible
Polytope 1379
Image of polytope 1379 PALP id: 1379
grdb id: 411814
Integer points: [ 1 0 0 0 -1 0 -1 -3 -2 -1 -1 0 -2]
[ 0 1 -1 0 -1 -1 -1 -1 -1 0 -1 0 -1]
[ 0 0 0 1 -1 1 1 -1 0 0 0 0 -1]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 8 1 none
Polytope 1380
Image of polytope 1380 PALP id: 1380
grdb id: 412326
Integer points: [ 1 0 0 0 0 -1 -2 -3 -1 -2 -1 -1 0]
[ 0 1 -1 0 -1 0 2 2 1 1 0 1 0]
[ 0 0 0 1 1 -1 -1 -2 0 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + 2*x-1*y + y-1*z + 2*x-1*y*z-1 + x-2*y2*z-1 + y-1 + 3*x-1 + x-1*z-1 + 3*x-2*y*z-1 + x-3*y2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1381
Image of polytope 1381 PALP id: 1381
grdb id: 417933
Integer points: [ 1 0 0 0 -1 -2 -1 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 0 0 -2 -2 -1 -1 0 -1 0]
[ 0 0 0 1 -1 -1 -1 -1 0 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + y-1 + 2*x-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + x-1*y-2*z-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1382
Image of polytope 1382 PALP id: 1382
grdb id: 418768
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 1 1 -1 -2 -1 0 0 -1 0]
[ 0 0 1 1 0 -1 -1 0 0 0 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
143 ? x + y + z + x-1*y + y-1*z + x-1*y*z-1 + 2*y-1 + 3*x-1 + 2*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1383
Image of polytope 1383 PALP id: 1383
grdb id: 246294
Integer points: [ 1 0 1 -1 0 1 -1 -1 -1 -1 0 0 0]
[ 0 1 -1 1 0 1 0 1 -1 0 1 0 -1]
[ 0 0 0 0 1 -1 1 -1 0 0 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 6 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1384
Image of polytope 1384 PALP id: 1384
grdb id: 246275
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 0 -1 0 1 -2 0 -1 0 -1]
[ 0 0 1 1 -1 0 1 0 -2 0 -1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
68 ? x + y + z + x-1*y*z + x-1*y + x-1*z + x-1 + 2*y-1*z-1 + x-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 51 1 Lattice Minkowski decompositions of facet 51
Polytope 1385
Image of polytope 1385 PALP id: 1385
grdb id: 246296
Integer points: [ 1 0 0 -1 1 0 0 -1 -2 0 -1 0 -1]
[ 0 1 0 1 -1 0 1 -1 0 -1 0 0 0]
[ 0 0 1 1 -1 -1 1 1 1 0 1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
35 rank 2, number 15 y*z + x + y + z + x-1*y*z + x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1386
Image of polytope 1386 PALP id: 1386
grdb id: 246280
Integer points: [ 1 0 0 0 -1 -1 -1 -2 -2 -2 -1 -1 0]
[ 0 1 -1 0 0 0 -1 -1 -1 -1 0 -1 0]
[ 0 0 0 1 -1 1 1 -1 1 0 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1387
Image of polytope 1387 PALP id: 1387
grdb id: 246285
Integer points: [ 1 0 0 0 0 -1 -2 -1 -2 -1 -1 -1 0]
[ 0 1 -1 0 -1 0 -1 -1 -1 0 -1 -1 0]
[ 0 0 0 1 -1 -1 0 1 -1 0 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + x-2*y-1*z-1
77 ? x + y + z + y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1388
Image of polytope 1388 PALP id: 1388
grdb id: 246297
Integer points: [ 1 0 0 0 0 -1 -1 -2 -2 -1 -1 -1 0]
[ 0 1 0 0 -1 1 -1 0 1 0 0 1 0]
[ 0 0 1 -1 0 -1 1 1 0 0 1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + 2*x-1*y + 2*x-1*z + z-1 + x-1*y*z-1 + y-1 + 2*x-1 + x-2*y + x-1*y-1*z + x-2*z
32 ? x + y + z + 2*x-1*y + 2*x-1*z + z-1 + x-1*y*z-1 + y-1 + 3*x-1 + x-2*y + x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1389
Image of polytope 1389 PALP id: 1389
grdb id: 246279
Integer points: [ 1 0 0 0 -1 -1 -2 -2 -3 -2 -1 -1 0]
[ 0 1 0 -1 0 1 0 1 1 1 1 0 0]
[ 0 0 1 -1 -1 1 -1 1 0 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
148 ? x + y + z + x-1*y*z + 3*x-1*y + x-2*y*z + x-1 + 3*x-2*y + y-1*z-1 + x-1*z-1 + x-3*y + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Polytope 1390
Image of polytope 1390 PALP id: 1390
grdb id: 246185
Integer points: [ 1 0 0 -1 0 0 -1 -1 -1 -1 0 -1 0]
[ 0 1 0 1 -1 -1 0 -1 -1 -1 -1 0 0]
[ 0 0 1 0 -1 1 1 -1 1 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1391
Image of polytope 1391 PALP id: 1391
grdb id: 246197
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 1 -1 1 1 0 0 0]
[ 0 0 1 -1 0 1 1 1 -1 0 1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
55 rank 2, number 19 y*z + x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + z-1 + x-1*y*z-1 + y-1 + 2*x-1 + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1392
Image of polytope 1392 PALP id: 1392
grdb id: 246264
Integer points: [ 1 0 0 1 -1 1 0 -1 0 0 0 0 -1]
[ 0 1 0 0 0 1 -1 0 -1 -1 0 0 0]
[ 0 0 1 -1 1 0 1 -1 -1 0 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x*y + x + y + z + x*z-1 + y-1*z + x-1*z + 2*z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1393
Image of polytope 1393 PALP id: 1393
grdb id: 246267
Integer points: [ 1 0 0 1 1 -1 -1 -1 -1 0 -1 0 0]
[ 0 1 0 0 -1 0 1 -1 0 0 0 0 -1]
[ 0 0 1 -1 0 1 0 0 -1 -1 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 5 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1394
Image of polytope 1394 PALP id: 1394
grdb id: 246053
Integer points: [ 1 0 1 -1 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 1 0 1 -1 0 -1 0 0 -1 0]
[ 0 0 0 0 1 -1 0 1 -1 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
85 rank 3, number 8 x + y + z + x*y-1 + x-1*y + x-1*z + x-1*y*z-1 + 2*y-1 + 3*x-1 + 2*x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
36 rank 3, number 7 x + y + z + x*y-1 + x-1*y + x-1*z + x-1*y*z-1 + 2*y-1 + 2*x-1 + 2*x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1395
Image of polytope 1395 PALP id: 1395
grdb id: 246126
Integer points: [ 1 0 1 -1 0 -1 0 -1 -1 -1 -1 0 0]
[ 0 1 -1 1 0 -1 -1 0 -1 -1 0 -1 0]
[ 0 0 0 0 1 -1 1 1 1 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 8 2 none
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Polytope 1396
Image of polytope 1396 PALP id: 1396
grdb id: 246220
Integer points: [ 1 0 1 -1 0 1 -1 -1 -1 -1 0 0 0]
[ 0 1 -1 1 0 -1 0 -1 -1 0 -1 -1 0]
[ 0 0 0 0 1 -1 1 0 -1 0 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 6 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1397
Image of polytope 1397 PALP id: 1397
grdb id: 246249
Integer points: [ 1 0 1 -1 0 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 1 0 -1 2 -1 0 0 1 -1 0]
[ 0 0 0 0 1 1 -1 0 -1 0 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
128 ? x + y + z + x-1*y2*z-1 + x*y-1 + x-1*y + y-1*z + 2*x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1398
Image of polytope 1398 PALP id: 1398
grdb id: 245921
Integer points: [ 1 0 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 1 0 -1 -2 -2 0 -1 -1 0 -1 0]
[ 0 0 0 1 -1 0 -1 1 1 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
147 ? x + y + z + x-1*y + x-1*z + 2*y-1 + 2*x-1 + x-1*y-1*z + x-1*y-1 + x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 51 1 Lattice Minkowski decompositions of facet 51
Polytope 1399
Image of polytope 1399 PALP id: 1399
grdb id: 246050
Integer points: [ 1 0 -1 0 -1 1 -2 0 -2 -1 -1 0 0]
[ 0 1 1 0 -1 -1 0 -1 -1 -1 0 -1 0]
[ 0 0 0 1 -1 1 -1 1 -1 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + x*y-1*z + z + x-1*y + y-1*z + 2*y-1 + 2*x-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-1
32 ? x + y + x*y-1*z + z + x-1*y + y-1*z + 2*y-1 + 3*x-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1400
Image of polytope 1400 PALP id: 1400
grdb id: 246081
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 0 -1 0 -2 -1 -1 0 -1 0]
[ 0 0 1 0 -1 -1 1 0 1 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + x-1*y + x-1*z + 2*y-1 + x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 50 1 Lattice Minkowski decompositions of facet 50
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1401
Image of polytope 1401 PALP id: 1401
grdb id: 245979
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 0 1 0 -1 -2 0 -1 0 -1]
[ 0 0 1 0 -1 -1 1 1 0 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + x-1*y + x-1*z + x-1*y*z-1 + 2*y-1 + x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 51 1 Lattice Minkowski decompositions of facet 51
Polytope 1402
Image of polytope 1402 PALP id: 1402
grdb id: 246164
Integer points: [ 1 0 0 0 -1 -1 -2 -1 -2 -2 -1 -1 0]
[ 0 1 -1 0 -1 0 -1 -1 -1 -1 0 -1 0]
[ 0 0 0 1 -1 1 -1 1 1 0 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1403
Image of polytope 1403 PALP id: 1403
grdb id: 246125
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 1 -1 0 -2 -2 0 -1 0 -1]
[ 0 0 0 1 0 0 -1 -1 -2 0 -1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
80 ? x + y + z + x-1*y + y-1 + 2*x-1 + 2*y-1*z-1 + x-1*z-1 + x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2*z-1 + x-1*y-2*z-2
107 rank 3, number 11 x + y + z + x-1*y + y-1 + 2*x-1 + 2*y-1*z-1 + x-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1404
Image of polytope 1404 PALP id: 1404
grdb id: 246108
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 1 0 -1 -2 -2 0 -1 0 -1]
[ 0 0 1 1 -1 -1 1 0 1 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + y-1*z + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z + x-1*y-2
8 ? x + y + z + y-1*z + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1405
Image of polytope 1405 PALP id: 1405
grdb id: 246251
Integer points: [ 1 0 0 0 -1 -1 -1 0 -1 -1 0 0 0]
[ 0 1 0 0 1 0 1 -2 -1 0 -1 -1 0]
[ 0 0 1 -1 0 1 -1 1 1 0 0 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y + 2*y-1*z + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + y-2*z + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1406
Image of polytope 1406 PALP id: 1406
grdb id: 246234
Integer points: [ 1 0 0 0 -1 0 -2 -1 -2 -1 -1 -1 0]
[ 0 1 -1 0 0 -1 -1 -2 -2 0 -1 -1 0]
[ 0 0 0 1 -1 1 0 1 1 0 0 1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
47 ? x + y + z + y-1*z + y-1 + 2*x-1 + 2*x-1*y-1*z + x-1*z-1 + x-1*y-1 + x-1*y-2*z + x-2*y-1 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1407
Image of polytope 1407 PALP id: 1407
grdb id: 246131
Integer points: [ 1 0 0 0 -1 0 -2 -1 -2 -1 -1 -1 0]
[ 0 1 -1 0 0 -1 1 1 1 0 0 1 0]
[ 0 0 0 1 -1 1 0 1 1 1 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
147 ? x + y + z + x-1*y*z + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + y-1 + 3*x-1 + x-2*y + x-1*z-1
112 rank 3, number 15 x + y + z + x-1*y*z + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + y-1 + 2*x-1 + x-2*y + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1408
Image of polytope 1408 PALP id: 1408
grdb id: 246247
Integer points: [ 1 0 0 0 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 0 1 -1 -1 0 0 -1 0 0]
[ 0 0 1 0 0 -1 1 -1 -2 -1 0 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + y*z-1 + 2*z-1 + y-1 + x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + x-1*z-2 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1409
Image of polytope 1409 PALP id: 1409
grdb id: 246094
Integer points: [ 1 0 0 0 0 -1 -1 -2 -2 -1 -1 -1 0]
[ 0 1 -1 0 -1 1 -2 -1 -2 -1 0 -1 0]
[ 0 0 0 1 -1 0 -1 -1 -1 0 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 1410
Image of polytope 1410 PALP id: 1410
grdb id: 246236
Integer points: [ 1 0 0 0 0 -1 -1 -2 -2 -1 -1 -1 0]
[ 0 1 -1 0 1 0 0 1 1 0 1 1 0]
[ 0 0 0 1 -1 -1 1 0 -1 0 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
66 rank 2, number 24 x + y + z + y*z-1 + 2*x-1*y + x-1*z + 2*x-1*y*z-1 + y-1 + x-1 + x-2*y + x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1411
Image of polytope 1411 PALP id: 1411
grdb id: 246158
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 1 0 0 -2 -1 -1 0 0]
[ 0 0 0 1 -1 0 -1 1 -1 0 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
80 ? x + y + z + x-1*y + x-1*z + y-1 + 2*x-1 + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1412
Image of polytope 1412 PALP id: 1412
grdb id: 246228
Integer points: [ 1 0 0 0 0 0 -2 -1 -2 -1 0 -1 -1]
[ 0 1 0 0 -1 -1 -1 -2 -2 -1 0 -1 0]
[ 0 0 1 -1 0 1 0 1 1 0 0 1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
29 rank 2, number 23 x + y + z + y-1*z + z-1 + y-1 + 2*x-1 + 2*x-1*y-1*z + x-1*y-1 + x-1*y-2*z + x-2*y-1 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1413
Image of polytope 1413 PALP id: 1413
grdb id: 246229
Integer points: [ 1 0 0 0 0 0 -1 -2 -2 -1 -1 0 -1]
[ 0 1 0 0 -1 1 1 0 -1 0 0 0 -1]
[ 0 0 1 -1 0 1 0 -1 -2 0 -1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
55 rank 2, number 19 y*z + x + y + z + x-1*y + z-1 + y-1 + 2*x-1 + x-1*z-1 + 2*x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1414
Image of polytope 1414 PALP id: 1414
grdb id: 246260
Integer points: [ 1 0 0 0 0 0 1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 1 -1 -1 0 0 0 0 0 0]
[ 0 0 1 1 -1 0 1 1 -2 0 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + x*y-1*z + z + y*z-1 + y-1*z + x-1*z + 2*z-1 + y-1 + 3*x-1 + 3*x-1*z-1 + x-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1415
Image of polytope 1415 PALP id: 1415
grdb id: 246266
Integer points: [ 1 0 0 0 0 1 1 1 -2 1 0 -1 -1]
[ 0 1 0 0 -1 0 -1 -1 1 -1 0 0 1]
[ 0 0 1 -1 0 1 -1 1 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x*z + x + y + x*y-1*z + z + 2*x*y-1 + 2*x-1*y + x*y-1*z-1 + z-1 + y-1 + 2*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Polytope 1416
Image of polytope 1416 PALP id: 1416
grdb id: 246242
Integer points: [ 1 0 0 0 1 0 -1 -1 -2 -1 0 -1 0]
[ 0 1 0 0 -1 -1 1 -1 0 0 -1 0 0]
[ 0 0 1 -1 0 -1 1 0 1 0 0 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*y*z + x*y-1 + 2*x-1*z + z-1 + 2*y-1 + 2*x-1 + x-2*z + y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1417
Image of polytope 1417 PALP id: 1417
grdb id: 246243
Integer points: [ 1 0 0 0 1 0 -1 -1 -2 -1 0 -1 0]
[ 0 1 0 0 -1 1 0 0 -1 -1 -1 0 0]
[ 0 0 1 -1 0 -1 1 -1 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + y*z-1 + x*y-1 + x-1*z + z-1 + 3*y-1 + x-1 + x-1*z-1 + 3*x-1*y-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Polytope 1418
Image of polytope 1418 PALP id: 1418
grdb id: 246269
Integer points: [ 1 0 0 0 1 1 -1 -2 -1 -1 1 0 -1]
[ 0 1 -1 0 -1 1 -1 0 1 0 0 0 0]
[ 0 0 0 1 -1 -1 0 1 0 0 -1 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x*y*z-1 + x + y + z + 2*x*z-1 + x-1*y + 2*x-1*z + x*y-1*z-1 + y-1 + 2*x-1 + x-2*z + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1419
Image of polytope 1419 PALP id: 1419
grdb id: 246212
Integer points: [ 1 0 0 1 0 -1 0 -1 -2 -1 0 0 -1]
[ 0 1 0 -1 0 1 1 -1 0 0 -1 0 0]
[ 0 0 1 0 -1 0 -1 0 1 0 0 0 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + y*z-1 + x*y-1 + x-1*y + 2*x-1*z + z-1 + 2*y-1 + x-1 + x-2*z + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1420
Image of polytope 1420 PALP id: 1420
grdb id: 246196
Integer points: [ 1 0 1 -1 0 1 -1 -2 0 -1 -1 0 0]
[ 0 1 -1 1 0 -1 -1 -1 -1 -1 0 -1 0]
[ 0 0 0 0 1 1 -1 -1 1 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1421
Image of polytope 1421 PALP id: 1421
grdb id: 246161
Integer points: [ 1 0 1 0 -1 -1 -1 -2 -2 -1 0 -1 0]
[ 0 1 -1 0 0 -1 0 -1 -1 -1 -1 0 0]
[ 0 0 0 1 -1 -1 1 0 -1 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + x*y-1 + x-1*z + 3*y-1 + x-1 + x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + x-2*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Polytope 1422
Image of polytope 1422 PALP id: 1422
grdb id: 246217
Integer points: [ 1 0 1 0 -1 -1 -1 -2 -2 -1 -1 0 0]
[ 0 1 -1 0 1 -1 -1 0 -1 0 0 -1 0]
[ 0 0 0 1 -1 0 -1 -1 -1 0 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x*y-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + 2*x-1*z-1 + x-1*y-1 + x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 5 Lattice Minkowski decompositions of facet 11
Polytope 1423
Image of polytope 1423 PALP id: 1423
grdb id: 246155
Integer points: [ 1 0 1 0 0 -2 1 0 -1 0 -1 0 -1]
[ 0 1 -1 0 -1 1 -2 -2 -1 -1 0 0 1]
[ 0 0 0 1 -1 0 -1 -1 -1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1424
Image of polytope 1424 PALP id: 1424
grdb id: 246062
Integer points: [ 1 0 1 0 0 -1 -2 0 -1 0 -1 0 -1]
[ 0 1 -1 0 -1 0 1 -1 0 -1 0 0 1]
[ 0 0 0 1 -1 -1 0 1 1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
85 rank 3, number 8 x + y + z + x*y-1 + 2*x-1*y + y-1*z + x-1*z + 2*y-1 + 2*x-1 + x-2*y + y-1*z-1 + x-1*z-1
134 ? x + y + z + x*y-1 + 2*x-1*y + y-1*z + x-1*z + 2*y-1 + 3*x-1 + x-2*y + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1425
Image of polytope 1425 PALP id: 1425
grdb id: 246208
Integer points: [ 1 0 1 0 0 -1 0 -1 -2 0 -1 -1 0]
[ 0 1 -1 0 0 1 -1 -1 0 -1 0 0 0]
[ 0 0 0 1 -1 0 -1 0 1 0 0 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x*y-1 + x-1*y + 2*x-1*z + z-1 + 2*y-1 + x-1 + x-2*z + y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1426
Image of polytope 1426 PALP id: 1426
grdb id: 246198
Integer points: [ 1 0 1 0 1 -1 0 -2 0 0 -1 0 -1]
[ 0 1 -1 0 -1 0 -1 1 -1 -1 0 0 1]
[ 0 0 0 1 -1 1 -1 0 1 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 1427
Image of polytope 1427 PALP id: 1427
grdb id: 246241
Integer points: [ 1 0 0 -1 0 0 -1 -1 -1 0 0 0 -1]
[ 0 1 -1 0 0 -2 2 1 2 -1 0 1 1]
[ 0 0 0 0 1 1 -1 0 -2 1 0 -1 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + 2*y*z-1 + x-1*y2*z-1 + x-1*y + 2*y-1*z + x-1*y2*z-2 + 2*x-1*y*z-1 + y-1 + x-1 + y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Polytope 1428
Image of polytope 1428 PALP id: 1428
grdb id: 246222
Integer points: [ 1 0 0 0 -2 1 0 2 1 1 -1 0 -1]
[ 0 1 -1 0 1 -1 -1 -2 -2 -1 0 0 1]
[ 0 0 0 1 0 -1 -1 -1 -1 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + 2*x*y-1 + 2*x-1*y + x2*y-2*z-1 + x*y-1*z-1 + y-1 + 2*x-1 + x-2*y + x*y-2*z-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 1429
Image of polytope 1429 PALP id: 1429
grdb id: 246223
Integer points: [ 1 0 0 0 -1 2 1 -2 0 1 -1 0 -1]
[ 0 1 -1 0 0 -1 -1 1 -1 -1 0 0 1]
[ 0 0 0 1 1 -1 -1 0 1 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x2*y-1*z-1 + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + x*y-1*z-1 + y-1 + 2*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 5 Lattice Minkowski decompositions of facet 11
Polytope 1430
Image of polytope 1430 PALP id: 1430
grdb id: 245971
Integer points: [ 1 0 0 -1 -2 -1 -3 -3 -2 -2 -1 -1 0]
[ 0 1 0 -1 -1 0 -2 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 -1 1 0 -1 1 0 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
63 ? x + y + z + x-1*z + 2*x-1 + 2*x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + x-2*y-1 + x-2*y-1*z-1 + x-3*y-2 + x-3*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 51 1 Lattice Minkowski decompositions of facet 51
Polytope 1431
Image of polytope 1431 PALP id: 1431
grdb id: 246112
Integer points: [ 1 0 0 0 -1 -1 -2 -2 -3 -1 -2 0 -1]
[ 0 1 -1 0 -1 1 -1 1 0 0 0 0 0]
[ 0 0 0 1 0 0 -1 -1 -2 0 -1 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
28 rank 2, number 25 x + y + z + x-1*y + y-1 + x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + x-2*z-1 + x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 50 1 Lattice Minkowski decompositions of facet 50
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1432
Image of polytope 1432 PALP id: 1432
grdb id: 246200
Integer points: [ 1 0 0 0 -1 -1 -2 -2 -3 -2 -1 -1 0]
[ 0 1 0 -1 0 -1 -2 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 1 -1 -1 1 0 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
103 ? x + y + z + x-1*z + 3*x-1 + y-1*z-1 + 3*x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + 3*x-2*y-1 + x-2*y-2*z-1 + x-3*y-2
112 rank 3, number 15 x + y + z + x-1*z + 3*x-1 + y-1*z-1 + 2*x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + 3*x-2*y-1 + x-2*y-2*z-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Polytope 1433
Image of polytope 1433 PALP id: 1433
grdb id: 250966
Integer points: [ 1 0 0 -1 -1 -1 -1 0 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 1 1 1 1 0 0 0]
[ 0 0 1 -1 0 1 -1 1 1 0 1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
47 ? y*z + x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + x-1*y*z-1 + 3*x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 1434
Image of polytope 1434 PALP id: 1434
grdb id: 251070
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 1 1 0 -1 -1 -1 0 0 0]
[ 0 0 0 1 0 -1 1 -1 1 0 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + x-1*y + x-1*z + x-1*y*z-1 + y-1 + 3*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 1435
Image of polytope 1435 PALP id: 1435
grdb id: 251552
Integer points: [ 1 0 0 0 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 0 -1 0 -1 -1 -1 0 -1 0]
[ 0 0 1 -1 -1 1 1 -1 1 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + y-1*z + x-1*z + 2*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1436
Image of polytope 1436 PALP id: 1436
grdb id: 251596
Integer points: [ 1 0 0 0 0 -1 1 -1 0 0 -1 0 0]
[ 0 1 0 1 -1 0 -1 0 -1 -1 0 0 0]
[ 0 0 1 -1 1 1 0 -1 -1 0 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + y*z-1 + x*y-1 + y-1*z + x-1*z + 2*z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1437
Image of polytope 1437 PALP id: 1437
grdb id: 251061
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 -1 1 -1 0 -1 0 0]
[ 0 0 1 -1 0 1 -1 1 1 0 0 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? y*z + x + y + z + x-1*y*z + 2*x-1*z + z-1 + y-1 + 2*x-1 + x-1*y-1*z + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1438
Image of polytope 1438 PALP id: 1438
grdb id: 251091
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 -1 1 0 -1 1 1 0 1 0 0]
[ 0 0 1 -1 1 -1 0 0 2 1 1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 y*z + x-1*y*z2 + x + y + z + 2*x-1*y*z + x-1*y + 2*x-1*z + 3*x-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1439
Image of polytope 1439 PALP id: 1439
grdb id: 251444
Integer points: [ 1 0 0 0 -1 -1 0 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 -1 -1 0 -1 -1 -1 0 0]
[ 0 0 0 1 -1 -1 1 1 2 0 1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + y-1*z + x-1*z + x-1*y-1*z2 + y-1 + 2*x-1 + 3*x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1440
Image of polytope 1440 PALP id: 1440
grdb id: 251434
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 -1 1 2 -1 0 0 1 0]
[ 0 0 0 1 1 0 0 -1 -1 0 -1 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
60 rank 2, number 18 x + y + z + x-1*y2*z-1 + x-1*y + y-1*z + 3*x-1*y*z-1 + y-1 + 2*x-1 + 3*x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1441
Image of polytope 1441 PALP id: 1441
grdb id: 251574
Integer points: [ 1 0 -1 0 -1 0 -1 0 -1 0 -1 -1 0]
[ 0 1 1 0 0 -1 -1 -2 -2 -1 0 -1 0]
[ 0 0 0 1 -1 -1 0 -1 -1 0 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + x-1*y + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1 + x-1*y-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1442
Image of polytope 1442 PALP id: 1442
grdb id: 250852
Integer points: [ 1 0 0 -1 -1 -1 -1 -2 -2 -2 -1 -1 0]
[ 0 1 0 0 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 0 1 -1 -1 1 1 -1 1 0 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
65 ? x + y + z + x-1*z + 3*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + 2*x-2*y-1 + x-2*y-1*z-1
119 ? x + y + z + x-1*z + 2*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + 2*x-2*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1443
Image of polytope 1443 PALP id: 1443
grdb id: 250962
Integer points: [ 1 0 0 -1 0 -1 -2 -1 -2 -1 -2 -1 0]
[ 0 1 -1 1 0 -1 0 -2 -2 -1 -1 0 0]
[ 0 0 0 0 1 -1 -1 -1 -1 0 -1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + x-1*y + y-1 + 2*x-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-2*z-1 + x-1*y-2*z-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 1444
Image of polytope 1444 PALP id: 1444
grdb id: 250763
Integer points: [ 1 0 0 0 -1 -2 0 -1 -2 -1 -1 -1 0]
[ 0 1 -1 0 -1 -1 -1 0 -1 -1 -1 0 0]
[ 0 0 0 1 -1 0 1 1 1 1 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
69 ? x + y + z + y-1*z + x-1*z + y-1 + 2*x-1 + 2*x-1*y-1*z + 2*x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + x-2*y-1
87 ? x + y + z + y-1*z + x-1*z + y-1 + 2*x-1 + 2*x-1*y-1*z + 3*x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1445
Image of polytope 1445 PALP id: 1445
grdb id: 251086
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 1 0 1 0 -2 -1 0 -1 0]
[ 0 0 0 1 0 -1 1 1 -1 0 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + x-1*y*z + x-1*y + x-1*z + y-1 + 3*x-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1446
Image of polytope 1446 PALP id: 1446
grdb id: 251085
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 -1 1 0 1 0 -2 -1 0 -1 0]
[ 0 0 1 1 -1 -1 0 1 1 1 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + x-1*y + y-1*z + x-1*z + x-1*y*z-1 + 3*x-1 + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1447
Image of polytope 1447 PALP id: 1447
grdb id: 251470
Integer points: [ 1 0 0 0 -1 -1 -1 -1 0 -1 0 0 0]
[ 0 1 0 0 1 1 0 -1 -2 0 -1 0 -1]
[ 0 0 1 -1 0 -1 -1 0 1 0 0 0 1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*y + 2*y-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + y-2*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1448
Image of polytope 1448 PALP id: 1448
grdb id: 251029
Integer points: [ 1 0 0 0 -1 -1 0 -2 -2 -1 -2 -1 0]
[ 0 1 -1 0 1 0 -1 1 -1 -1 0 0 0]
[ 0 0 0 1 0 -1 1 -1 -1 0 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? x + y + z + x-1*y + y-1*z + y-1 + 3*x-1 + x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + 2*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 1449
Image of polytope 1449 PALP id: 1449
grdb id: 251082
Integer points: [ 1 0 0 0 -1 -1 0 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 1 -1 0 -2 -1 -1 0 0]
[ 0 0 0 1 -1 0 1 1 1 0 1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
103 ? x + y + z + x-1*y + y-1*z + x-1*z + y-1 + 2*x-1 + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1450
Image of polytope 1450 PALP id: 1450
grdb id: 251528
Integer points: [ 1 0 0 0 -1 0 -1 -2 -2 -1 -1 -1 0]
[ 0 1 -1 0 0 1 0 1 1 0 1 1 0]
[ 0 0 0 1 -1 1 1 0 1 0 0 1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? y*z + x + y + z + 2*x-1*y*z + 2*x-1*y + x-1*z + x-2*y*z + y-1 + x-1 + x-2*y + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1451
Image of polytope 1451 PALP id: 1451
grdb id: 251489
Integer points: [ 1 0 0 0 -1 0 -1 -1 -1 -1 0 0 -1]
[ 0 1 0 0 0 -1 0 -2 -2 -1 -1 0 -1]
[ 0 0 1 -1 0 0 1 -1 -2 0 -1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + x-1*z + z-1 + y-1 + x-1 + 2*y-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1452
Image of polytope 1452 PALP id: 1452
grdb id: 251469
Integer points: [ 1 0 0 0 -1 0 -1 -1 -1 0 -1 -1 0]
[ 0 1 0 0 0 1 1 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 0 -1 -1 -1 0 0 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + y*z-1 + z-1 + x-1*y*z-1 + 2*y-1 + x-1 + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1453
Image of polytope 1453 PALP id: 1453
grdb id: 251391
Integer points: [ 1 0 0 0 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 -1 0 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 0 -1 1 1 0 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
88 ? x + y + z + x-1*y + x-1*z + z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1454
Image of polytope 1454 PALP id: 1454
grdb id: 251060
Integer points: [ 1 0 0 0 -1 0 -1 0 -2 -1 0 0 -1]
[ 0 1 0 0 1 -1 1 -1 1 0 -1 0 0]
[ 0 0 1 -1 0 1 -1 -1 -1 -1 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y + y-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1455
Image of polytope 1455 PALP id: 1455
grdb id: 251399
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 1 0 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 -1 0 1 1 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
85 rank 3, number 8 x + y + z + y*z-1 + x-1*y + x-1*z + z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1456
Image of polytope 1456 PALP id: 1456
grdb id: 251473
Integer points: [ 1 0 0 0 0 0 -1 -2 -2 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 -1 0 -1 -1 0 0 0]
[ 0 0 1 -1 0 -1 1 1 1 0 0 1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + 2*x-1*z + z-1 + y-1 + 2*x-1 + x-1*y-1*z + x-2*z + y-1*z-1 + 2*x-1*y-1 + x-2*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1457
Image of polytope 1457 PALP id: 1457
grdb id: 251490
Integer points: [ 1 0 0 0 0 0 -1 -2 -2 -1 -1 -1 0]
[ 0 1 0 0 -1 1 0 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 0 -1 1 1 1 0 0 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + y*z-1 + x-1*z + z-1 + y-1 + 2*x-1 + 2*x-1*y-1*z + 2*x-1*y-1 + x-2*y-1*z + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1458
Image of polytope 1458 PALP id: 1458
grdb id: 251556
Integer points: [ 1 0 0 0 0 0 -1 -2 -2 -1 -1 0 -1]
[ 0 1 0 0 -1 1 1 0 1 1 0 0 0]
[ 0 0 1 -1 0 1 1 -1 0 0 0 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 y*z + x + y + z + x-1*y*z + 2*x-1*y + z-1 + y-1 + x-1 + x-2*y + 2*x-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1459
Image of polytope 1459 PALP id: 1459
grdb id: 251332
Integer points: [ 1 0 0 0 0 0 -1 -1 -2 0 -1 0 -1]
[ 0 1 0 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 0 1 -1 1 -1 -1 1 0 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
32 ? x + y + z + y-1*z + z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-2*y-1
159 ? x + y + z + y-1*z + z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1460
Image of polytope 1460 PALP id: 1460
grdb id: 250869
Integer points: [ 1 0 0 0 0 0 -1 -1 -2 0 -1 0 -1]
[ 0 1 0 0 -1 -1 0 0 1 -1 0 0 1]
[ 0 0 1 -1 1 -1 -1 1 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + 2*x-1*y + y-1*z + x-1*z + z-1 + 2*y-1 + 2*x-1 + x-2*y + y-1*z-1 + x-1*z-1
3 ? x + y + z + 2*x-1*y + y-1*z + x-1*z + z-1 + 2*y-1 + 3*x-1 + x-2*y + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1461
Image of polytope 1461 PALP id: 1461
grdb id: 251485
Integer points: [ 1 0 0 0 1 -1 1 -1 0 0 -1 0 0]
[ 0 1 0 -1 -1 0 -1 0 -1 -1 0 0 0]
[ 0 0 1 0 0 1 -1 -1 -2 -1 0 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x*y-1 + x-1*z + x*y-1*z-1 + 2*z-1 + y-1 + 2*x-1 + 2*y-1*z-1 + x-1*z-1 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1462
Image of polytope 1462 PALP id: 1462
grdb id: 251066
Integer points: [ 1 0 1 -1 0 -1 0 -2 0 0 -1 -1 0]
[ 0 1 -1 1 0 0 -1 0 -2 -1 0 -1 0]
[ 0 0 0 0 1 -1 -1 -1 -1 0 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + x*y-1 + x-1*y + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1463
Image of polytope 1463 PALP id: 1463
grdb id: 251055
Integer points: [ 1 0 1 -1 0 1 -2 0 0 0 -1 -1 0]
[ 0 1 -1 1 0 -1 1 -1 -1 -1 0 0 0]
[ 0 0 0 0 1 1 -1 -1 1 0 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + x*y-1*z + z + x*y-1 + x-1*y + y-1*z + 2*y-1 + 2*x-1 + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1464
Image of polytope 1464 PALP id: 1464
grdb id: 251542
Integer points: [ 1 0 0 0 0 -1 -1 -2 -2 -1 -1 -1 0]
[ 0 1 -1 0 -1 0 2 1 2 0 1 1 0]
[ 0 0 0 1 1 -1 -1 -1 -1 0 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + x-1*y2*z-1 + 2*x-1*y + y-1*z + 2*x-1*y*z-1 + x-2*y2*z-1 + y-1 + 2*x-1 + x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1465
Image of polytope 1465 PALP id: 1465
grdb id: 251577
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 -2 0 2 -1 1 0 1 -1 0]
[ 0 0 0 1 1 -1 -1 0 0 0 -1 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
60 rank 2, number 18 x + y + z + x-1*y2*z-1 + x-1*y + 2*y-1*z + 2*x-1*y*z-1 + y-1 + 2*x-1 + y-2*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1466
Image of polytope 1466 PALP id: 1466
grdb id: 250714
Integer points: [ 1 0 0 0 -2 -2 0 -3 -1 -2 -1 -1 0]
[ 0 1 -1 0 0 1 1 1 1 1 1 0 0]
[ 0 0 0 1 -1 -1 1 -1 1 0 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
43 ? y*z + x + y + z + x-1*y*z + 2*x-1*y + y-1 + 3*x-1 + 2*x-2*y + x-2*y*z-1 + x-2*z-1 + x-3*y*z-1
87 ? y*z + x + y + z + x-1*y*z + 3*x-1*y + y-1 + 2*x-1 + 2*x-2*y + x-2*y*z-1 + x-2*z-1 + x-3*y*z-1
69 ? y*z + x + y + z + x-1*y*z + 2*x-1*y + y-1 + 2*x-1 + 2*x-2*y + x-2*y*z-1 + x-2*z-1 + x-3*y*z-1
131 ? y*z + x + y + z + x-1*y*z + 3*x-1*y + y-1 + 3*x-1 + 2*x-2*y + x-2*y*z-1 + x-2*z-1 + x-3*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 23 2 Lattice Minkowski decompositions of facet 23
Polytope 1467
Image of polytope 1467 PALP id: 1467
grdb id: 251114
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -3 -2 -1 -2 0]
[ 0 1 -1 0 0 -1 1 1 1 1 0 0 0]
[ 0 0 0 1 -1 0 0 -1 -2 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + x-1*y + x-1*y*z-1 + y-1 + 2*x-1 + x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1 + 2*x-2*z-1 + x-3*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 1468
Image of polytope 1468 PALP id: 1468
grdb id: 251408
Integer points: [ 1 0 1 -1 0 0 -1 -2 -3 -1 -2 0 -1]
[ 0 1 -1 1 -1 0 -1 1 0 0 0 0 0]
[ 0 0 0 0 0 1 -1 -1 -2 0 -1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + x*y-1 + x-1*y + y-1 + 3*x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1*z-1 + 3*x-2*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Polytope 1469
Image of polytope 1469 PALP id: 1469
grdb id: 251478
Integer points: [ 1 0 1 -1 0 0 -1 -2 -3 -1 -2 0 -1]
[ 0 1 -1 1 -1 0 1 0 1 0 1 0 0]
[ 0 0 0 0 0 1 -1 -1 -2 0 -1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x*y-1 + x-1*y + x-1*y*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + 2*x-2*y*z-1 + x-2*z-1 + x-3*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1470
Image of polytope 1470 PALP id: 1470
grdb id: 249647
Integer points: [ 1 0 0 0 0 0 -1 -2 -2 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 0 -1 -1 -1 -1 0 0]
[ 0 0 1 -1 0 1 1 0 1 0 1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? x + y + z + y-1*z + x-1*z + z-1 + y-1 + 2*x-1 + 2*x-1*y-1*z + 2*x-1*y-1 + x-2*y-1*z + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1471
Image of polytope 1471 PALP id: 1471
grdb id: 249313
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 0 0 -2 0 -1 -1 0]
[ 0 0 1 -1 0 1 1 -1 1 0 0 1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + y-1*z + x-1*z + z-1 + y-1 + 2*x-1 + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1472
Image of polytope 1472 PALP id: 1472
grdb id: 672935
Integer points: [ 1 0 0 -1 1 0 -1 1 0 -1 0 0 -1]
[ 0 1 0 1 -1 0 0 -1 -1 -1 -1 0 0]
[ 0 0 1 1 -1 -1 0 0 1 1 0 0 1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y*z + x*y-1 + y-1*z + 2*x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + x-1 + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 1473
Image of polytope 1473 PALP id: 1473
grdb id: 672934
Integer points: [ 1 0 0 -1 0 0 -1 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 0 -1 0 -1 -2 -2 -1 -1 0]
[ 0 0 0 0 1 -1 -1 -1 -1 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
28 rank 2, number 25 x + y + z + y-1 + x-1 + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2*z-1 + x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1474
Image of polytope 1474 PALP id: 1474
grdb id: 672933
Integer points: [ 1 0 0 0 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 0 -1 -1 -1 -2 -2 -1 -1 0]
[ 0 0 1 -1 0 1 1 -1 0 1 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
29 rank 2, number 23 x + y + z + y-1*z + z-1 + 2*y-1 + x-1 + x-1*y-1*z + x-1*y-1 + x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1475
Image of polytope 1475 PALP id: 1475
grdb id: 672931
Integer points: [ 1 0 0 0 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 0 1 0 -1 -1 -2 -1 0 -1]
[ 0 0 1 -1 0 1 1 -1 1 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
55 rank 2, number 19 y*z + x + y + z + x-1*z + z-1 + 2*y-1 + x-1 + x-1*y-1*z + x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1476
Image of polytope 1476 PALP id: 1476
grdb id: 672929
Integer points: [ 1 0 0 0 0 -1 -1 -1 -2 -2 -1 -1 0]
[ 0 1 -1 0 1 -1 0 0 -1 -1 0 -1 0]
[ 0 0 0 1 -1 1 -1 1 1 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + y*z-1 + x-1*z + y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-2*y-1*z + x-2*y-1
144 rank 3, number 12 x + y + z + y*z-1 + x-1*z + y-1 + 3*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-2*y-1*z + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Polytope 1477
Image of polytope 1477 PALP id: 1477
grdb id: 672930
Integer points: [ 1 0 0 0 0 1 -1 0 -1 -2 -1 0 -1]
[ 0 1 0 0 -1 -1 1 -1 -1 0 0 0 0]
[ 0 0 1 -1 0 -1 0 -1 0 1 0 0 1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
60 rank 2, number 18 x + y + z + x-1*y + 2*x-1*z + x*y-1*z-1 + z-1 + y-1 + x-1 + x-2*z + y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1478
Image of polytope 1478 PALP id: 1478
grdb id: 674217
Integer points: [ 1 0 0 0 -1 0 -1 0 -1 -1 0 -1 0]
[ 0 1 0 0 0 -1 1 -1 -1 -1 -1 0 0]
[ 0 0 1 -1 0 1 -1 -1 0 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + y-1*z + z-1 + x-1*y*z-1 + 2*y-1 + x-1 + y-1*z-1 + 2*x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 1479
Image of polytope 1479 PALP id: 1479
grdb id: 674196
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 1 0 0 -1 -1 -1 0 0]
[ 0 0 0 1 -1 0 -1 1 -1 1 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + x-1*y + x-1*z + y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
144 rank 3, number 12 x + y + z + x-1*y + x-1*z + y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1480
Image of polytope 1480 PALP id: 1480
grdb id: 674170
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 0 0 -1 -1 -1 0 0]
[ 0 0 1 -1 0 0 -1 1 1 -1 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + x-1*y + x-1*z + z-1 + y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
159 ? x + y + z + x-1*y + x-1*z + z-1 + y-1 + 3*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1481
Image of polytope 1481 PALP id: 1481
grdb id: 674247
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 -1 0 1 1 0 -1 -1 0 0]
[ 0 0 1 -1 1 0 1 0 1 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y*z + y*z-1 + x-1*y + y-1*z + x-1*z + 2*z-1 + 2*y-1 + x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1482
Image of polytope 1482 PALP id: 1482
grdb id: 674214
Integer points: [ 1 0 0 0 1 -1 0 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 1 -1 0 -1 -1 0 -1 0]
[ 0 0 1 -1 0 -1 1 -1 0 1 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x*y-1 + y-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Polytope 1483
Image of polytope 1483 PALP id: 1483
grdb id: 674241
Integer points: [ 1 0 0 1 -1 0 0 -1 -1 -1 -1 0 0]
[ 0 1 0 0 0 -1 -1 1 1 0 0 0 0]
[ 0 0 1 -1 1 0 1 1 0 -1 0 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y*z + x*z-1 + x-1*y + y-1*z + x-1*z + 2*z-1 + y-1 + 2*x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 1484
Image of polytope 1484 PALP id: 1484
grdb id: 674244
Integer points: [ 1 0 0 1 -1 0 0 1 1 -1 0 0 -1]
[ 0 1 0 -1 1 0 -1 -1 0 -1 -1 0 0]
[ 0 0 1 -1 1 -1 0 0 -1 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + x-1*y*z + x*z-1 + x*y-1 + x*y-1*z-1 + z-1 + y-1 + 2*x-1 + 2*y-1*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Polytope 1485
Image of polytope 1485 PALP id: 1485
grdb id: 674229
Integer points: [ 1 0 1 -1 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 1 0 0 -1 1 0 -1 0 -1 0]
[ 0 0 0 0 1 -1 0 1 1 -1 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + x-1*y*z + x*y-1 + x-1*y + x-1*z + 2*y-1 + 2*x-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
88 ? x + y + z + x-1*y*z + x*y-1 + x-1*y + x-1*z + 2*y-1 + 3*x-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Polytope 1486
Image of polytope 1486 PALP id: 1486
grdb id: 674222
Integer points: [ 1 0 1 -1 0 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 1 0 -1 1 -1 0 -1 0 -1 0]
[ 0 0 0 0 1 -1 1 0 1 -1 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y*z + x*y-1 + x-1*y + x-1*z + 2*y-1 + x-1 + y-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1487
Image of polytope 1487 PALP id: 1487
grdb id: 674234
Integer points: [ 1 0 1 0 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 0 1 1 0 0 -1 0 0 -1]
[ 0 0 0 1 -1 0 1 1 -1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y*z + x*y-1 + x-1*y + x-1*z + z-1 + 2*y-1 + x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1488
Image of polytope 1488 PALP id: 1488
grdb id: 674246
Integer points: [ 1 0 0 0 0 -1 0 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 0 -1 0 -1 -1 -1 -1 0]
[ 0 0 1 -1 0 0 1 1 -1 2 0 1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + y-1*z + x-1*z + x-1*y-1*z2 + z-1 + y-1 + x-1 + 3*x-1*y-1*z + 3*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Polytope 1489
Image of polytope 1489 PALP id: 1489
grdb id: 674218
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 -1 0 1 2 0 1 0]
[ 0 0 1 -1 0 1 -1 -1 1 1 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
55 rank 2, number 19 y*z + x-1*y2*z + x + y + z + x-1*y*z + 2*x-1*y + z-1 + y-1 + 2*x-1 + x-1*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1490
Image of polytope 1490 PALP id: 1490
grdb id: 674237
Integer points: [ 1 0 -1 0 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 0 -1 -1 -2 -1 -2 -1 -1 0]
[ 0 0 0 1 -1 1 -1 0 1 1 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + y-1*z + 2*y-1 + x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
103 ? x + y + z + y-1*z + 2*y-1 + x-1 + x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Polytope 1491
Image of polytope 1491 PALP id: 1491
grdb id: 674235
Integer points: [ 1 0 0 0 0 -1 -1 -1 -2 -2 -1 -1 0]
[ 0 1 -1 0 1 -1 1 0 0 1 0 1 0]
[ 0 0 0 1 -1 0 0 -1 -1 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
66 rank 2, number 24 x + y + z + y*z-1 + x-1*y + 2*x-1*y*z-1 + y-1 + x-1 + x-1*z-1 + x-2*y*z-1 + x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1492
Image of polytope 1492 PALP id: 1492
grdb id: 674206
Integer points: [ 1 0 0 0 0 -1 -1 -1 -2 -2 -1 -1 0]
[ 0 1 0 0 -1 0 0 -1 -1 -1 0 -1 0]
[ 0 0 1 -1 0 -1 1 1 0 1 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + x-1*z + z-1 + y-1 + x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-2*y-1*z + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1493
Image of polytope 1493 PALP id: 1493
grdb id: 674238
Integer points: [ 1 0 1 -1 0 -1 -1 -1 -2 -2 -1 0 0]
[ 0 1 -1 1 0 0 -1 -1 0 -1 0 -1 0]
[ 0 0 0 0 1 -1 0 -1 -1 -1 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + x*y-1 + x-1*y + 2*y-1 + x-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1494
Image of polytope 1494 PALP id: 1494
grdb id: 674224
Integer points: [ 1 0 1 -1 0 -1 -1 -1 -2 -2 -1 0 0]
[ 0 1 -1 1 0 1 0 -1 1 0 0 0 -1]
[ 0 0 0 0 1 -1 -1 0 -1 -1 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x*y-1 + x-1*y + x-1*y*z-1 + 2*y-1 + x-1 + x-1*z-1 + x-2*y*z-1 + x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1495
Image of polytope 1495 PALP id: 1495
grdb id: 674209
Integer points: [ 1 0 1 -1 0 -1 1 0 -1 -2 0 -1 0]
[ 0 1 -1 1 0 1 -2 -1 0 1 -1 0 0]
[ 0 0 0 0 1 1 -1 -1 1 1 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y*z + x*y-1 + x-1*y + x-1*z + x-2*y*z + 2*y-1 + 2*x-1 + x*y-2*z-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1496
Image of polytope 1496 PALP id: 1496
grdb id: 674248
Integer points: [ 1 0 1 -1 0 -1 0 -2 2 0 1 0 -1]
[ 0 1 -1 1 -1 0 0 2 -1 -1 -1 0 1]
[ 0 0 0 0 0 0 1 1 -1 -1 -1 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + 2*x-1*y*z + x-2*y2*z + x2*y-1*z-1 + x*y-1 + x-1*y + 2*x*y-1*z-1 + y-1 + x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Polytope 1497
Image of polytope 1497 PALP id: 1497
grdb id: 673893
Integer points: [ 1 0 0 0 -1 -1 0 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 1 -1 -1 0 -1 -1 0 0]
[ 0 0 0 1 -1 0 1 -1 1 1 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + x-1*y + y-1*z + x-1*z + y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
122 ? x + y + z + x-1*y + y-1*z + x-1*z + y-1 + 3*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1498
Image of polytope 1498 PALP id: 1498
grdb id: 674053
Integer points: [ 1 0 0 0 -1 0 -1 -1 0 -1 -1 0 0]
[ 0 1 0 0 1 -1 1 0 -1 0 0 -1 0]
[ 0 0 1 -1 0 1 -1 1 -1 -1 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y + y-1*z + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1499
Image of polytope 1499 PALP id: 1499
grdb id: 674080
Integer points: [ 1 0 0 0 -1 0 0 -1 -1 -1 0 -1 0]
[ 0 1 0 0 1 -1 -1 0 -1 -1 -1 0 0]
[ 0 0 1 -1 0 1 -1 1 0 1 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + x-1*y + y-1*z + x-1*z + z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 1500
Image of polytope 1500 PALP id: 1500
grdb id: 674146
Integer points: [ 1 0 0 0 -1 1 0 0 1 -1 0 0 -1]
[ 0 1 0 1 1 -1 0 -1 -1 -1 -1 0 0]
[ 0 0 1 -1 0 0 -1 1 1 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + x*y-1*z + z + y*z-1 + x*y-1 + x-1*y + y-1*z + z-1 + 2*y-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 1501
Image of polytope 1501 PALP id: 1501
grdb id: 674057
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 1 1 -1 -1 0 0 0]
[ 0 0 1 -1 0 1 0 -1 0 -1 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y + y-1*z + z-1 + x-1*y*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1502
Image of polytope 1502 PALP id: 1502
grdb id: 674139
Integer points: [ 1 0 0 1 -1 0 -1 0 -1 0 0 -1 0]
[ 0 1 0 -1 1 0 0 -1 0 -1 -1 0 0]
[ 0 0 1 0 0 -1 -1 1 1 -1 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
3 ? x + y + z + x*y-1 + x-1*y + y-1*z + x-1*z + z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1503
Image of polytope 1503 PALP id: 1503
grdb id: 674142
Integer points: [ 1 0 0 1 -1 0 0 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 1 0 -1 0 -1 -1 0 -1 0]
[ 0 0 1 0 0 -1 -1 -1 0 -1 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
88 ? x + y + z + x*y-1 + x-1*y + z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1504
Image of polytope 1504 PALP id: 1504
grdb id: 674149
Integer points: [ 1 0 0 1 -1 0 1 -1 0 -1 -1 0 0]
[ 0 1 0 -1 1 0 -1 0 -1 -1 0 -1 0]
[ 0 0 1 0 0 -1 1 -1 1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
85 rank 3, number 8 x + y + x*y-1*z + z + x*y-1 + x-1*y + y-1*z + z-1 + 2*y-1 + 2*x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 1505
Image of polytope 1505 PALP id: 1505
grdb id: 674141
Integer points: [ 1 0 0 1 -1 0 1 1 -1 0 0 -1 0]
[ 0 1 0 -1 1 0 0 -1 -1 -1 -1 0 0]
[ 0 0 1 0 0 -1 -1 -1 0 -1 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
85 rank 3, number 8 x + y + z + x*z-1 + x*y-1 + x-1*y + x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1506
Image of polytope 1506 PALP id: 1506
grdb id: 673876
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -2 -2 -2 -1 0]
[ 0 1 -1 0 0 -1 1 1 -1 1 0 0 0]
[ 0 0 0 1 -1 0 0 -1 -1 -1 -1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + x-1*y + x-1*y*z-1 + y-1 + 2*x-1 + x-1*z-1 + x-2*y*z-1 + x-1*y-1 + 2*x-2*z-1 + x-2*y-1*z-1
147 ? x + y + z + x-1*y + x-1*y*z-1 + y-1 + 3*x-1 + x-1*z-1 + x-2*y*z-1 + x-1*y-1 + 2*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1507
Image of polytope 1507 PALP id: 1507
grdb id: 674094
Integer points: [ 1 0 0 0 -1 -1 0 -1 -2 -2 -1 -1 0]
[ 0 1 -1 0 1 0 -1 0 1 1 0 1 0]
[ 0 0 0 1 -1 -1 1 1 -1 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? x + y + z + 2*x-1*y + y-1*z + x-1*z + x-1*y*z-1 + y-1 + 3*x-1 + x-2*y + x-1*z-1 + x-2*y*z-1
16 ? x + y + z + 2*x-1*y + y-1*z + x-1*z + x-1*y*z-1 + y-1 + 2*x-1 + x-2*y + x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1508
Image of polytope 1508 PALP id: 1508
grdb id: 674052
Integer points: [ 1 0 0 0 -1 0 -1 -2 -2 -1 -1 -1 0]
[ 0 1 -1 0 0 -1 -1 -1 -1 -1 0 -1 0]
[ 0 0 0 1 -1 1 -1 0 -1 1 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
103 ? x + y + z + y-1*z + y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + x-2*y-1 + x-2*y-1*z-1
112 rank 3, number 15 x + y + z + y-1*z + y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-2*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1509
Image of polytope 1509 PALP id: 1509
grdb id: 674087
Integer points: [ 1 0 0 0 0 -1 0 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 0 -1 -1 0 -1 -1 0 0]
[ 0 0 1 -1 0 1 -1 0 -1 -2 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + x-1*z + z-1 + y-1 + 2*x-1 + y-1*z-1 + x-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1510
Image of polytope 1510 PALP id: 1510
grdb id: 674145
Integer points: [ 1 0 0 0 0 0 0 -1 -1 -2 -1 -1 0]
[ 0 1 0 1 -1 0 -1 0 -1 -1 -1 0 0]
[ 0 0 1 -1 1 -1 0 0 -1 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + y*z-1 + y-1*z + z-1 + y-1 + x-1 + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Polytope 1511
Image of polytope 1511 PALP id: 1511
grdb id: 674147
Integer points: [ 1 0 0 1 -1 0 0 -1 -2 -2 -1 -1 0]
[ 0 1 0 0 0 0 -1 -1 -1 -1 0 -1 0]
[ 0 0 1 -1 1 -1 0 1 1 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + x*z-1 + x-1*z + z-1 + y-1 + 2*x-1 + x-1*y-1*z + 2*x-1*y-1 + x-2*y-1*z + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 1512
Image of polytope 1512 PALP id: 1512
grdb id: 674047
Integer points: [ 1 0 1 -1 0 0 -1 -1 -2 -2 -1 -1 0]
[ 0 1 -1 1 -1 0 1 -1 1 0 0 0 0]
[ 0 0 0 0 0 1 -1 -1 -1 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x*y-1 + x-1*y + x-1*y*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Polytope 1513
Image of polytope 1513 PALP id: 1513
grdb id: 673689
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 0 0 -1 -1 -1 0 0]
[ 0 0 1 -1 0 1 -1 1 -1 1 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + y-1*z + x-1*z + z-1 + y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1514
Image of polytope 1514 PALP id: 1514
grdb id: 673746
Integer points: [ 1 0 0 0 0 0 0 -1 -1 -2 -1 -1 0]
[ 0 1 0 1 -1 0 -1 0 1 1 0 1 0]
[ 0 0 1 -1 1 -1 0 1 -1 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + y*z-1 + 2*x-1*y + y-1*z + x-1*z + z-1 + x-1*y*z-1 + y-1 + 2*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Polytope 1515
Image of polytope 1515 PALP id: 1515
grdb id: 61943
Integer points: [ 1 0 0 -1 1 0 0 -1 0 -1 -1 -1 0]
[ 0 1 0 1 -1 0 -1 1 -1 0 -1 0 0]
[ 0 0 1 1 -1 -1 0 0 -1 1 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y*z + x-1*y + x-1*z + x*y-1*z-1 + z-1 + y-1 + 2*x-1 + y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 5 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1516
Image of polytope 1516 PALP id: 1516
grdb id: 61938
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 1 -1 1 0 -1 0 1 0 0]
[ 0 0 0 1 -1 0 0 -1 1 1 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + y*z-1 + x-1*y + x-1*z + x-1*y*z-1 + y-1 + 3*x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
107 rank 3, number 11 x + y + z + y*z-1 + x-1*y + x-1*z + x-1*y*z-1 + y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Polytope 1517
Image of polytope 1517 PALP id: 1517
grdb id: 61936
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 0 -1 1 0 1 -1 0 0]
[ 0 0 1 -1 0 -1 0 0 1 1 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
32 ? x + y + z + x-1*y*z + x-1*y + x-1*z + z-1 + y-1 + 3*x-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
8 ? x + y + z + x-1*y*z + x-1*y + x-1*z + z-1 + y-1 + 2*x-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Polytope 1518
Image of polytope 1518 PALP id: 1518
grdb id: 61940
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 0 -1 0 1 1 0 0]
[ 0 0 1 -1 0 1 -1 0 1 0 1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 y*z + x + y + z + x-1*y*z + x-1*y + x-1*z + z-1 + y-1 + x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 5 Lattice Minkowski decompositions of facet 3
Polytope 1519
Image of polytope 1519 PALP id: 1519
grdb id: 61942
Integer points: [ 1 0 0 0 0 0 0 1 1 -1 -1 -1 0]
[ 0 1 0 1 -1 -1 0 -1 0 -1 1 0 0]
[ 0 0 1 -1 1 0 -1 0 -1 1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + x*z-1 + y*z-1 + x*y-1 + y-1*z + z-1 + x-1*y*z-1 + y-1 + 2*x-1 + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 5 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1520
Image of polytope 1520 PALP id: 1520
grdb id: 61933
Integer points: [ 1 0 1 0 -1 0 0 -1 0 -1 -1 -1 0]
[ 0 1 -1 0 1 -1 0 0 -1 1 0 0 0]
[ 0 0 0 1 0 0 -1 1 -1 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x*y-1 + x-1*y + x-1*z + z-1 + x-1*y*z-1 + y-1 + 2*x-1 + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 5 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1521
Image of polytope 1521 PALP id: 1521
grdb id: 61945
Integer points: [ 1 0 1 0 -1 0 0 0 -1 -1 -1 -1 0]
[ 0 1 -1 0 1 -1 0 1 0 1 0 0 0]
[ 0 0 0 1 0 0 -1 -1 1 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + y*z-1 + x*y-1 + x-1*y + x-1*z + z-1 + x-1*y*z-1 + y-1 + 2*x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 6 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1522
Image of polytope 1522 PALP id: 1522
grdb id: 61941
Integer points: [ 1 0 1 0 0 0 -1 0 -1 -1 -2 -1 0]
[ 0 1 -1 0 0 -1 1 -1 1 0 1 0 0]
[ 0 0 0 1 -1 0 0 -1 1 1 1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y*z + x*y-1 + x-1*y + x-1*z + x-2*y*z + z-1 + y-1 + 2*x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 5 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1523
Image of polytope 1523 PALP id: 1523
grdb id: 61915
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 1 0 -1 1 -1 0 1 0 0]
[ 0 0 0 1 1 -1 -1 0 0 1 1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? y*z + x + y + z + x-1*y*z + x-1*y + x-1*z + y-1 + 2*x-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
122 ? y*z + x + y + z + x-1*y*z + x-1*y + x-1*z + y-1 + 3*x-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Polytope 1524
Image of polytope 1524 PALP id: 1524
grdb id: 61929
Integer points: [ 1 0 0 0 0 0 0 -1 -1 -1 -1 -1 0]
[ 0 1 0 1 -1 -1 0 0 -1 0 -1 -1 0]
[ 0 0 1 -1 1 0 -1 0 1 -1 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + y*z-1 + y-1*z + z-1 + y-1 + x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1525
Image of polytope 1525 PALP id: 1525
grdb id: 61930
Integer points: [ 1 0 1 0 0 -1 0 0 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 1 -1 -1 1 0 0 0 0]
[ 0 0 0 1 -1 0 0 -1 1 1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*y*z + x*y-1 + x-1*y + x-1*z + z-1 + y-1 + 2*x-1 + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1526
Image of polytope 1526 PALP id: 1526
grdb id: 61889
Integer points: [ 1 0 0 0 0 0 0 -1 -1 -1 -1 -1 0]
[ 0 1 0 1 -1 0 -1 -1 1 0 1 0 0]
[ 0 0 1 -1 1 -1 0 1 -1 1 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + y*z-1 + x-1*y + y-1*z + x-1*z + z-1 + x-1*y*z-1 + y-1 + 2*x-1 + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1527
Image of polytope 1527 PALP id: 1527
grdb id: 1521
Integer points: [ 1 0 0 1 1 -1 -1 0 -1 0 1 0 0]
[ 0 1 0 0 -1 1 0 -1 0 0 -1 -1 0]
[ 0 0 1 -1 0 0 1 0 0 -1 -1 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x*z-1 + x*y-1 + x-1*y + x-1*z + x*y-1*z-1 + z-1 + y-1 + x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 8 Lattice Minkowski decompositions of facet 3
Polytope 1528
Image of polytope 1528 PALP id: 1528
grdb id: 12648
Integer points: [ 1 0 0 1 -1 0 1 -1 0 -1 -1 0 0]
[ 0 1 0 -1 1 0 -1 1 -1 0 0 -1 0]
[ 0 0 1 0 0 -1 1 -1 0 0 -1 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + x*y-1*z + z + x*y-1 + x-1*y + y-1*z + z-1 + x-1*y*z-1 + y-1 + x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 7 Lattice Minkowski decompositions of facet 3
Polytope 1529
Image of polytope 1529 PALP id: 1529
grdb id: 12645
Integer points: [ 1 0 0 -1 1 1 -1 -1 1 0 0 -1 0]
[ 0 1 0 1 0 -1 1 0 -1 0 -1 0 0]
[ 0 0 1 1 -1 0 0 1 -1 -1 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
3 ? x + y + z + x-1*y*z + x*z-1 + x*y-1 + x-1*y + x-1*z + x*y-1*z-1 + z-1 + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 3 6 Lattice Minkowski decompositions of facet 3
Polytope 1530
Image of polytope 1530 PALP id: 1530
grdb id: 546304
Integer points: [ 1 1 0 -3 -3 -2 -1 -3 -2 -1 0 -1 0 1]
[ 0 2 0 -1 -3 -2 -1 -2 -1 0 1 -1 0 1]
[ 0 0 1 -1 1 1 1 0 0 0 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 4 1 none
Image of facet 101 1 none
Image of facet 9 1 irreducible and admissible
Polytope 1531
Image of polytope 1531 PALP id: 1531
grdb id: 546287
Integer points: [ 1 0 0 -2 -5 -3 -4 -1 -2 -3 -1 -1 -2 0]
[ 0 1 0 -2 -2 -2 -2 -1 -1 -1 0 -1 -1 0]
[ 0 0 1 1 -2 0 -1 1 0 -1 0 0 -1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 14 1 none
Image of facet 102 1 none
Polytope 1532
Image of polytope 1532 PALP id: 1532
grdb id: 546372
Integer points: [ 1 0 1 -4 1 0 -1 -2 -3 0 -1 -2 1 0]
[ 0 1 0 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 0 2 -2 3 2 1 0 -1 1 0 -1 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
25 ? x*z2 + x*y-1*z3 + 2*x*z + x + y + 4*z + 5*y-1*z2 + 5*x-1 + 10*x-1*y-1*z + 2*x-2*z-1 + 10*x-2*y-1 + 5*x-3*y-1*z-1 + x-4*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 43 1 irreducible and admissible
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Polytope 1533
Image of polytope 1533 PALP id: 1533
grdb id: 546365
Integer points: [ 1 0 0 -1 -6 -5 -4 -3 -2 -3 -2 -1 -1 0]
[ 0 1 0 1 -4 -3 -2 -1 0 -2 -1 0 -1 0]
[ 0 0 1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 43 1 irreducible and admissible
Image of facet 4 1 none
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Polytope 1534
Image of polytope 1534 PALP id: 1534
grdb id: 546293
Integer points: [ 1 0 1 -5 -6 -2 -3 -4 0 -1 -2 -2 1 0]
[ 0 1 0 -2 -2 -1 -1 -1 0 0 0 -1 0 0]
[ 0 0 2 -2 -3 0 -1 -2 1 0 -1 -1 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 104 1 none
Image of facet 9 1 irreducible and admissible
Polytope 1535
Image of polytope 1535 PALP id: 1535
grdb id: 546295
Integer points: [ 1 0 0 -8 -9 -6 -3 -5 -2 -4 -1 -4 -1 0]
[ 0 1 0 -5 -6 -4 -2 -3 -1 -2 0 -3 -1 0]
[ 0 0 1 -2 -2 -1 0 -1 0 -1 0 -1 0 0]
Degree: 50
Hilbert function: 1 + 28 t + 130 t2 + 357 t3 + 759 t4 + 1386 t5 + 2288 t6 + 3515 t7 + 5117 t8 + 7144 t9 + 9646 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 14 1 none
Image of facet 104 1 none
Polytope 1536
Image of polytope 1536 PALP id: 1536
grdb id: 537271
Integer points: [ 1 1 0 2 -1 -1 1 -1 -1 -1 0 0 0 1]
[ 0 2 0 2 -3 1 1 -2 -1 0 -1 0 1 1]
[ 0 0 1 1 -1 -1 0 -1 -1 -1 0 0 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 2 none
Image of facet 1 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 13 1 irreducible and admissible
Polytope 1537
Image of polytope 1537 PALP id: 1537
grdb id: 537263
Integer points: [ 1 1 0 -4 0 -2 -1 -3 -2 -1 0 -1 0 1]
[ 0 2 0 -3 1 -1 0 -2 -1 0 1 -1 0 1]
[ 0 0 1 -1 1 1 1 0 0 0 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 1 none
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 77 1 none
Polytope 1538
Image of polytope 1538 PALP id: 1538
grdb id: 537266
Integer points: [ 1 1 0 0 -3 -1 -2 -1 0 -1 0 1 0 1]
[ 0 3 0 -1 -4 -2 -3 -1 1 -2 0 2 -1 1]
[ 0 0 1 1 -1 1 0 0 0 0 0 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 26 2 none
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Polytope 1539
Image of polytope 1539 PALP id: 1539
grdb id: 537088
Integer points: [ 1 0 0 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 2 0 1 0 1 -1 0 1 0]
[ 0 0 0 1 -2 1 -1 0 -1 0 -1 0 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Polytope 1540
Image of polytope 1540 PALP id: 1540
grdb id: 537050
Integer points: [ 1 0 0 -3 -3 -2 -3 -2 -2 -1 -1 -1 -1 0]
[ 0 1 0 -2 0 1 -1 0 -1 1 0 0 -1 0]
[ 0 0 1 0 -2 -2 -1 -1 0 -1 0 -1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 105 1 none
Polytope 1541
Image of polytope 1541 PALP id: 1541
grdb id: 537109
Integer points: [ 1 0 0 -1 -2 -3 -2 -1 -1 -2 -1 -1 0 0]
[ 0 1 0 -2 1 0 0 0 1 -1 -1 0 0 -1]
[ 0 0 1 0 -2 -2 -1 0 -1 -1 0 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 14 1 none
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 1542
Image of polytope 1542 PALP id: 1542
grdb id: 536970
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -1 -3 -2 -1 -2 0 -1 0 -1 0]
[ 0 0 1 -1 1 -1 0 0 -1 0 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 13 1 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 1543
Image of polytope 1543 PALP id: 1543
grdb id: 537089
Integer points: [ 1 0 0 0 -1 -3 -2 -1 0 -2 -1 0 -1 0]
[ 0 1 0 -2 -2 0 -1 -1 -1 0 0 -1 0 0]
[ 0 0 1 -1 -2 -2 -2 -1 0 -1 0 -1 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
25 ? x + y + z + 2*y-1 + 3*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + y-2*z-1 + 4*x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2*z-2 + 2*x-2*y-1*z-2 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 9 1 irreducible and admissible
Polytope 1544
Image of polytope 1544 PALP id: 1544
grdb id: 537096
Integer points: [ 1 1 -1 0 1 -2 -1 0 -1 0 -1 0 1 0]
[ 0 2 -2 0 3 0 0 1 1 2 -1 0 1 -1]
[ 0 0 0 1 -1 -1 0 0 -1 -1 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 4 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1545
Image of polytope 1545 PALP id: 1545
grdb id: 537133
Integer points: [ 1 -1 0 1 0 1 1 1 1 0 0 0 0 0]
[ 0 0 1 0 -2 -2 -1 -1 0 -1 0 -1 0 0]
[ 0 0 0 2 -3 -2 -1 0 1 -2 -1 -1 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x*z2 + 2*x*z + x + y + 2*z + 2*x*y-1 + 2*x*y-1*z-1 + 3*z-1 + x-1 + 2*y-1*z-1 + x*y-2*z-2 + 3*y-1*z-2 + y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 9 1 irreducible and admissible
Polytope 1546
Image of polytope 1546 PALP id: 1546
grdb id: 537127
Integer points: [ 1 0 -1 1 -3 -3 0 -1 -2 -1 -2 1 0 -1]
[ 0 1 -1 0 0 1 0 0 0 1 1 0 0 0]
[ 0 0 0 2 -2 -3 1 0 -1 -1 -2 1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 13 1 irreducible and admissible
Image of facet 6 1 none
Image of facet 9 1 irreducible and admissible
Polytope 1547
Image of polytope 1547 PALP id: 1547
grdb id: 537113
Integer points: [ 1 0 0 -2 -2 0 -1 -1 -1 0 0 -1 0 0]
[ 0 1 0 2 1 -3 -1 0 1 -2 -1 1 -1 0]
[ 0 0 1 1 0 -2 -1 0 1 -1 0 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + 2*x-1*y*z + x-2*y2*z + 2*x-1*y + 3*y-1 + 4*x-1 + x-2*y + 2*y-1*z-1 + 3*y-2*z-1 + 2*x-1*y-1*z-1 + y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 9 1 irreducible and admissible
Polytope 1548
Image of polytope 1548 PALP id: 1548
grdb id: 536888
Integer points: [ 1 0 0 -2 -1 -3 -2 -2 -1 -1 -1 -1 0 0]
[ 0 1 0 -2 2 -2 0 -1 1 0 -1 -1 1 0]
[ 0 0 1 1 -2 0 -1 0 -1 0 1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 106 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1549
Image of polytope 1549 PALP id: 1549
grdb id: 536890
Integer points: [ 1 0 0 -2 -1 -2 -1 -1 -1 -2 -2 -2 0 0]
[ 0 1 0 -2 2 2 1 0 -1 1 0 -1 1 0]
[ 0 0 1 1 -2 -3 -1 0 1 -2 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
25 ? x + y + z + 2*y*z-1 + x-1*y2*z-2 + 4*x-1*y*z-1 + 5*x-1 + 2*x-1*y-1*z + x-2*y2*z-3 + 4*x-2*y*z-2 + 6*x-2*z-1 + 4*x-2*y-1 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 13 1 irreducible and admissible
Polytope 1550
Image of polytope 1550 PALP id: 1550
grdb id: 537123
Integer points: [ 1 0 0 -2 -1 -2 -1 -2 0 -1 -2 -1 0 0]
[ 0 1 1 -1 0 -1 0 -1 1 0 -1 0 0 0]
[ 0 0 2 0 -2 -3 -1 -2 1 0 -1 1 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
25 ? y*z2 + 2*y*z + x + y + 2*x-1*z + 2*z-1 + 5*x-1 + 4*x-1*z-1 + x-1*z-2 + x-2*y-1 + 3*x-2*y-1*z-1 + 3*x-2*y-1*z-2 + x-2*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 9 1 irreducible and admissible
Polytope 1551
Image of polytope 1551 PALP id: 1551
grdb id: 537092
Integer points: [ 1 0 0 -2 1 -3 -2 -1 -1 0 -1 -1 0 1]
[ 0 1 0 1 -2 0 0 0 -1 -1 1 0 0 -1]
[ 0 0 1 -2 2 -2 -1 0 0 1 -1 -1 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 14 1 none
Polytope 1552
Image of polytope 1552 PALP id: 1552
grdb id: 536941
Integer points: [ 1 0 0 -1 -2 -3 -1 -1 -2 -1 -2 0 -1 0]
[ 0 1 0 -2 2 2 1 0 1 -1 0 0 1 -1]
[ 0 0 1 0 -1 -2 0 0 -1 0 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 74 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1553
Image of polytope 1553 PALP id: 1553
grdb id: 537136
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 2 -3 -2 1 0 -1 -1 -2 1 0 -1]
[ 0 0 1 2 -2 -2 1 0 -1 0 -1 1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 9 1 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 5 1 none
Polytope 1554
Image of polytope 1554 PALP id: 1554
grdb id: 537119
Integer points: [ 1 0 1 -3 -3 0 -1 0 -2 -1 -2 1 0 -1]
[ 0 1 0 0 -1 -1 -1 0 -1 0 0 0 0 0]
[ 0 0 2 -2 -1 2 1 1 0 0 -1 1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x*z2 + 2*x*z + x + y + z + y-1*z2 + x-1 + 3*x-1*y-1*z + 2*x-1*z-1 + 2*x-2*z-1 + 3*x-2*y-1 + x-3*z-2 + x-3*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 109 1 Lattice Minkowski decompositions of facet 109
Image of facet 9 1 irreducible and admissible
Polytope 1555
Image of polytope 1555 PALP id: 1555
grdb id: 536973
Integer points: [ 1 0 -1 0 -2 -4 -3 -2 -1 -3 -2 -1 -1 0]
[ 0 1 1 0 0 -4 -2 -1 0 -3 -2 -1 -1 0]
[ 0 0 0 1 -1 -3 -2 -1 0 -2 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 8 1 none
Image of facet 13 1 irreducible and admissible
Image of facet 80 1 none
Polytope 1556
Image of polytope 1556 PALP id: 1556
grdb id: 537064
Integer points: [ 1 0 0 -2 -2 -4 -3 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 -2 0 -2 -1 -1 0 -2 -1 0 -1 0]
[ 0 0 1 -1 1 1 1 1 1 0 0 0 0 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 37 1 none
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1557
Image of polytope 1557 PALP id: 1557
grdb id: 537086
Integer points: [ 1 0 0 -1 -2 -4 -3 -1 -2 -3 -1 -2 -1 0]
[ 0 1 0 1 -2 -2 -2 -1 -1 -1 0 0 -1 0]
[ 0 0 1 -1 1 -1 0 1 0 -1 0 -1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 4 1 none
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 9 1 irreducible and admissible
Polytope 1558
Image of polytope 1558 PALP id: 1558
grdb id: 537117
Integer points: [ 1 0 0 0 -1 -2 -1 -1 0 0 -1 0 0 0]
[ 0 1 0 -3 2 3 0 1 -2 -1 2 -1 0 1]
[ 0 0 1 -2 2 2 0 1 -1 0 1 -1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x-1*y2*z2 + x-2*y3*z2 + 2*y*z + 2*x-1*y2*z + x + y + z + 3*x-1*y*z + 3*y-1 + 2*x-1 + 2*y-1*z-1 + 3*y-2*z-1 + y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1559
Image of polytope 1559 PALP id: 1559
grdb id: 537091
Integer points: [ 1 0 0 2 -3 3 -1 1 -2 0 0 2 -1 1]
[ 0 1 0 -1 0 -2 0 -1 0 -1 0 -1 0 0]
[ 0 0 1 -1 1 -3 1 -1 1 -1 0 -2 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 14 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1560
Image of polytope 1560 PALP id: 1560
grdb id: 537051
Integer points: [ 1 0 1 -3 -2 1 -1 -2 0 -1 0 -1 0 1]
[ 0 1 0 0 -1 -1 -1 0 -1 0 0 0 0 0]
[ 0 0 2 -2 0 3 1 -1 2 0 1 -1 0 1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
81 ? x*z2 + x*y-1*z3 + 2*x*z + x + y + z + 3*y-1*z2 + 3*x-1 + 3*x-1*y-1*z + 2*x-1*z-1 + 3*x-2*z-1 + x-2*y-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 110 1 Lattice Minkowski decompositions of facet 110
Image of facet 9 1 irreducible and admissible
Polytope 1561
Image of polytope 1561 PALP id: 1561
grdb id: 537094
Integer points: [ 1 0 -1 0 -2 -4 -1 -3 -2 -1 -3 -2 -1 0]
[ 0 1 -1 0 2 2 1 2 1 0 1 0 1 0]
[ 0 0 0 1 -1 -3 0 -2 -1 0 -2 -1 -1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Image of facet 8 1 none
Polytope 1562
Image of polytope 1562 PALP id: 1562
grdb id: 536829
Integer points: [ 1 0 0 -3 -4 -1 -2 -3 -1 -2 -1 0 -1 0]
[ 0 1 0 -1 -2 -2 -2 -2 -1 -1 0 -1 -1 0]
[ 0 0 1 -1 -1 2 1 0 1 0 0 1 0 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 14 1 none
Image of facet 111 1 none
Polytope 1563
Image of polytope 1563 PALP id: 1563
grdb id: 537090
Integer points: [ 1 0 1 0 -1 -4 -2 0 -3 -1 -2 1 0 -1]
[ 0 1 -2 0 -1 2 0 -1 1 0 1 -1 0 1]
[ 0 0 0 1 -1 -1 -1 0 -1 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 4 1 none
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 56 1 Lattice Minkowski decompositions of facet 56
Polytope 1564
Image of polytope 1564 PALP id: 1564
grdb id: 537105
Integer points: [ 1 0 0 -3 -4 -5 -2 -1 -4 -3 -2 -1 0 -2]
[ 0 1 0 -2 -3 -4 -1 0 -3 -2 -1 -1 0 -2]
[ 0 0 1 0 -2 -2 0 0 -1 -1 -1 0 0 -1]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
105 ? x + y + z + 3*x-1 + 2*x-1*y-1 + 3*x-2*y-1 + 2*x-2*y-1*z-1 + 2*x-2*y-2*z-1 + x-3*y-2 + 4*x-3*y-2*z-1 + 2*x-4*y-3*z-1 + x-4*y-3*z-2 + x-5*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 9 1 irreducible and admissible
Polytope 1565
Image of polytope 1565 PALP id: 1565
grdb id: 537075
Integer points: [ 1 0 0 -3 -4 -5 -4 -3 -2 -2 -1 -2 -1 0]
[ 0 1 0 -2 -1 -2 -2 -1 -1 0 0 -1 -1 0]
[ 0 0 1 0 -2 -2 -1 -1 0 -1 0 -1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
63 ? x + y + z + 2*x-1 + 2*x-1*y-1 + 2*x-2*z-1 + x-2*y-1 + 2*x-2*y-1*z-1 + 3*x-3*y-1*z-1 + x-3*y-2 + x-4*y-1*z-2 + 2*x-4*y-2*z-1 + x-5*y-2*z-2
57 ? x + y + z + x-1 + 2*x-1*y-1 + 2*x-2*z-1 + 2*x-2*y-1 + 2*x-2*y-1*z-1 + 3*x-3*y-1*z-1 + x-3*y-2 + x-4*y-1*z-2 + 2*x-4*y-2*z-1 + x-5*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 112 1 Lattice Minkowski decompositions of facet 112
Polytope 1566
Image of polytope 1566 PALP id: 1566
grdb id: 536823
Integer points: [ 1 0 0 -1 -2 -5 -3 -4 -2 -3 -1 -1 -2 0]
[ 0 1 0 0 -1 -4 -2 -3 -1 -2 0 -1 -2 0]
[ 0 0 1 1 1 -2 0 -1 0 -1 0 0 -1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 79 1 none
Polytope 1567
Image of polytope 1567 PALP id: 1567
grdb id: 536969
Integer points: [ 1 0 0 -1 -1 -5 -3 -2 -1 -4 -3 -2 -1 0]
[ 0 1 0 1 -1 -3 -2 -1 0 -2 -1 0 -1 0]
[ 0 0 1 -1 1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 4 1 none
Image of facet 13 1 irreducible and admissible
Polytope 1568
Image of polytope 1568 PALP id: 1568
grdb id: 536889
Integer points: [ 1 1 0 -3 -1 -5 -3 -2 -1 0 -4 -1 0 1]
[ 0 2 0 -1 -1 -3 -2 -1 0 1 -2 -1 0 1]
[ 0 0 1 -1 1 -1 0 0 0 0 -1 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 4 1 none
Image of facet 113 1 none
Polytope 1569
Image of polytope 1569 PALP id: 1569
grdb id: 536826
Integer points: [ 1 0 1 0 -2 -6 -4 -2 -3 -1 0 -3 -1 0]
[ 0 1 -1 0 -2 -3 -2 -1 -2 -1 -1 -1 0 0]
[ 0 0 0 1 -1 -2 -1 0 -1 0 0 -1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 75 1 none
Image of facet 14 1 none
Polytope 1570
Image of polytope 1570 PALP id: 1570
grdb id: 537053
Integer points: [ 1 0 0 -3 -6 -7 -5 -2 -4 -1 -3 -1 -3 0]
[ 0 1 0 -2 -3 -4 -3 -1 -2 0 -1 -1 -2 0]
[ 0 0 1 0 -2 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 105 1 none
Polytope 1571
Image of polytope 1571 PALP id: 1571
grdb id: 537111
Integer points: [ 1 0 0 0 -5 -6 -4 -2 -3 -1 -3 -1 -2 0]
[ 0 1 -1 0 2 3 2 1 1 0 2 1 1 0]
[ 0 0 0 1 -2 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 42 1 none
Image of facet 14 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1572
Image of polytope 1572 PALP id: 1572
grdb id: 535491
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 -1 -1 2 0 1 -1 0 1 -1 0 0]
[ 0 0 1 -1 2 -1 1 0 1 0 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
35 rank 2, number 15 x + y + z + x-1*y2*z-1 + 3*x-1*y + 3*x-1*z + x-1*y-1*z2 + 3*x-1*y*z-1 + 6*x-1 + 3*x-1*y-1*z + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Polytope 1573
Image of polytope 1573 PALP id: 1573
grdb id: 535773
Integer points: [ 1 0 0 -1 -2 -2 -1 -1 -2 -1 -2 -2 0 0]
[ 0 1 0 -2 2 -2 1 0 1 -1 0 -1 0 -1]
[ 0 0 1 0 -1 -1 0 0 -1 0 -1 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
88 ? x + y + z + 2*x-1*y + x-2*y2*z-1 + 2*y-1 + 4*x-1 + 4*x-2*y*z-1 + 3*x-1*y-1 + 6*x-2*z-1 + x-1*y-2 + 4*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Image of facet 13 1 irreducible and admissible
Polytope 1574
Image of polytope 1574 PALP id: 1574
grdb id: 535717
Integer points: [ 1 0 1 0 -2 -2 -1 -1 -2 -1 -2 -2 0 0]
[ 0 1 -1 0 2 -2 -1 0 -1 1 0 1 -1 0]
[ 0 0 0 1 -1 -1 0 0 -1 0 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 4 1 none
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Polytope 1575
Image of polytope 1575 PALP id: 1575
grdb id: 536190
Integer points: [ 1 0 0 -2 -3 -3 -2 -1 -3 -2 -1 -1 0 -1]
[ 0 1 0 -2 0 -2 0 0 -1 -1 -1 0 0 -1]
[ 0 0 1 -1 -2 -2 -1 0 -2 -1 0 -1 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
103 ? x + y + z + 3*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*z-1 + 4*x-2*y-1*z-1 + x-3*z-2 + x-2*y-2*z-1 + 2*x-3*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Polytope 1576
Image of polytope 1576 PALP id: 1576
grdb id: 536306
Integer points: [ 1 0 0 -1 0 -3 -2 -1 -2 -1 0 -1 0 0]
[ 0 1 0 -2 -2 0 0 0 -1 -1 -1 0 0 -1]
[ 0 0 1 0 1 -2 -1 0 -1 0 1 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + 2*y-1*z + 2*y-1 + 3*x-1 + y-2*z + 2*x-1*z-1 + 4*x-1*y-1 + 3*x-2*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Polytope 1577
Image of polytope 1577 PALP id: 1577
grdb id: 536192
Integer points: [ 1 0 0 0 -2 -2 -1 -1 -1 -2 -2 0 -1 -1]
[ 0 1 -1 0 0 -3 -2 -1 0 -2 -1 0 -1 0]
[ 0 0 0 1 1 -2 -1 0 1 -1 0 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 14 1 none
Polytope 1578
Image of polytope 1578 PALP id: 1578
grdb id: 536449
Integer points: [ 1 0 0 -3 1 -3 0 -1 -2 -1 -2 1 0 -1]
[ 0 1 0 -2 2 -3 1 0 -1 -1 -2 1 0 -1]
[ 0 0 1 -2 2 -2 1 0 -1 0 -1 1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
127 ? x*y2*z2 + 2*x*y*z + 4*y*z + x + y + z + 6*x-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + 4*x-2*y-1*z-1 + 3*x-2*y-2*z-1 + x-3*y-2*z-2 + x-3*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 13 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Polytope 1579
Image of polytope 1579 PALP id: 1579
grdb id: 535716
Integer points: [ 1 0 -1 0 -2 -2 -1 -2 -1 -2 -1 -2 0 0]
[ 0 1 1 0 0 -4 -2 -3 -1 -2 0 -1 -1 0]
[ 0 0 0 1 -1 -1 0 -1 0 -1 0 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 4 1 none
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Image of facet 13 1 irreducible and admissible
Polytope 1580
Image of polytope 1580 PALP id: 1580
grdb id: 535749
Integer points: [ 1 0 0 -2 0 -4 -1 -2 -3 -1 0 -1 -2 0]
[ 0 1 0 -2 1 -3 0 -1 -2 -1 1 0 -1 0]
[ 0 0 1 -1 2 -2 1 0 -1 0 1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
29 rank 2, number 23 y*z2 + 2*y*z + x + y + z + 4*x-1*z + 4*x-1 + 2*x-1*y-1 + 6*x-2*y-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1 + 4*x-3*y-2*z-1 + x-4*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 1581
Image of polytope 1581 PALP id: 1581
grdb id: 500508
Integer points: [ 1 0 0 -1 -2 -1 -2 -2 -1 -1 -1 -1 0 0]
[ 0 1 0 1 1 -2 -1 0 0 -1 1 0 0 -1]
[ 0 0 1 1 0 -2 -2 -1 0 -1 0 -1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
68 ? x + y + z + x-1*y*z + 2*x-1*y + x-1 + x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 47 1 Lattice Minkowski decompositions of facet 47
Polytope 1582
Image of polytope 1582 PALP id: 1582
grdb id: 500521
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 0 -1 0 0]
[ 0 1 0 -1 1 0 -2 0 -1 0 0 -1 -1 0]
[ 0 0 1 1 -1 -2 0 0 0 -1 0 -1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 83 1 none
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 1583
Image of polytope 1583 PALP id: 1583
grdb id: 500497
Integer points: [ 1 0 0 0 1 -2 -2 -2 -1 -1 0 -1 -1 0]
[ 0 1 0 0 -1 1 -1 0 0 -1 -1 1 0 0]
[ 0 0 1 -1 1 0 -2 -1 0 -1 0 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + x*y-1*z + z + 2*x-1*y + z-1 + 3*y-1 + 3*x-1 + x-2*y + 2*x-1*z-1 + 3*x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1584
Image of polytope 1584 PALP id: 1584
grdb id: 500523
Integer points: [ 1 0 0 -1 1 -2 2 1 0 1 0 -1 0 -1]
[ 0 1 0 2 -2 1 -1 0 1 -1 0 1 -1 0]
[ 0 0 1 -1 0 0 -1 -1 -1 0 0 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 6 2 none
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 1585
Image of polytope 1585 PALP id: 1585
grdb id: 500520
Integer points: [ 1 0 0 0 -2 1 0 -1 -1 0 -1 0 0 1]
[ 0 1 0 0 2 -2 -2 0 1 -1 1 -1 0 -1]
[ 0 0 1 -1 -1 2 1 0 -1 0 0 1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
23 ? x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*x-1*y + 2*y-1*z + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 2*x-1 + y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1586
Image of polytope 1586 PALP id: 1586
grdb id: 500522
Integer points: [ 1 1 -1 0 0 0 -2 -1 -1 0 -1 0 0 1]
[ 0 2 -2 0 1 1 -1 0 -1 1 0 0 -1 1]
[ 0 0 0 1 -1 1 -1 0 0 0 -1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 1 none
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1587
Image of polytope 1587 PALP id: 1587
grdb id: 500492
Integer points: [ 1 0 1 0 -1 -1 -3 -2 -2 -1 0 -1 0 1]
[ 0 1 -2 0 1 -1 1 1 0 0 -1 1 0 -1]
[ 0 0 0 1 1 -1 -1 0 -1 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 4 1 none
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Polytope 1588
Image of polytope 1588 PALP id: 1588
grdb id: 500519
Integer points: [ 1 1 -1 0 -1 1 -1 -1 0 0 -1 0 1 0]
[ 0 2 -2 0 -1 3 1 0 1 2 -1 0 1 -1]
[ 0 0 0 1 1 -1 -1 0 0 -1 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 4 1 none
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1589
Image of polytope 1589 PALP id: 1589
grdb id: 500507
Integer points: [ 1 0 -1 1 -3 -2 0 -1 0 -1 -2 1 0 -1]
[ 0 1 -1 0 0 1 1 1 0 0 0 0 0 0]
[ 0 0 0 2 -2 -1 1 0 1 0 -1 1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 89 1 none
Polytope 1590
Image of polytope 1590 PALP id: 1590
grdb id: 500464
Integer points: [ 1 0 0 -2 -1 -3 1 -1 0 -2 -1 0 1 -1]
[ 0 1 0 1 1 0 -2 0 -1 0 -1 0 -1 0]
[ 0 0 1 -1 0 -2 2 0 1 -1 0 0 1 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 85 1 none
Polytope 1591
Image of polytope 1591 PALP id: 1591
grdb id: 500518
Integer points: [ 1 0 0 0 1 -2 -3 -1 0 -1 -2 1 0 -1]
[ 0 1 -1 0 2 -1 -2 0 1 0 -1 1 0 -1]
[ 0 0 0 1 -2 2 2 1 -1 0 1 -1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x*y2*z-2 + 2*x*y*z-1 + x + y + z + 4*y*z-1 + 2*x-1*z + y-1 + 6*x-1 + x-1*y-1*z + x-2*y-1*z2 + 4*x-2*y-1*z + x-3*y-2*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 13 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Polytope 1592
Image of polytope 1592 PALP id: 1592
grdb id: 500500
Integer points: [ 1 0 0 1 -3 -2 0 -1 0 -1 -2 1 0 -1]
[ 0 1 0 2 -2 0 2 1 1 0 -1 1 0 -1]
[ 0 0 1 2 -2 -1 1 0 1 0 -1 1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 88 1 none
Image of facet 1 3 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1593
Image of polytope 1593 PALP id: 1593
grdb id: 500473
Integer points: [ 1 1 -3 0 1 -2 0 -1 0 -1 -2 1 0 -1]
[ 0 2 -2 0 2 -1 1 0 1 0 -1 1 0 -1]
[ 0 0 0 1 -1 1 1 1 0 0 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 1 3 irreducible and admissible
Image of facet 91 1 none
Polytope 1594
Image of polytope 1594 PALP id: 1594
grdb id: 500514
Integer points: [ 1 1 0 0 -2 -3 -2 -1 0 -1 -2 1 0 -1]
[ 0 2 0 1 -2 -2 -1 0 1 0 -1 1 0 -1]
[ 0 0 1 1 -1 0 1 1 0 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
94 ? x*y2 + 2*x*y + y*z + x + 4*y + z + 2*x-1*z + 6*x-1 + x-1*y-1 + x-2*y-1*z + 4*x-2*y-1 + x-2*y-2*z-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 13 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Polytope 1595
Image of polytope 1595 PALP id: 1595
grdb id: 500496
Integer points: [ 1 0 0 0 -1 -1 -4 -2 -3 -1 -2 -1 -2 0]
[ 0 1 -1 0 1 1 1 1 1 0 0 1 1 0]
[ 0 0 0 1 -1 1 -2 0 -1 0 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 95 1 none
Polytope 1596
Image of polytope 1596 PALP id: 1596
grdb id: 500516
Integer points: [ 1 0 0 -2 1 -1 -1 -1 0 -1 0 1 0 1]
[ 0 1 0 3 -3 0 2 1 -1 2 0 -2 1 -1]
[ 0 0 1 -3 3 -1 -1 -1 1 -2 0 2 -1 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 28 1 none
Polytope 1597
Image of polytope 1597 PALP id: 1597
grdb id: 500506
Integer points: [ 1 1 -2 0 -1 1 0 0 -1 1 0 -1 1 0]
[ 0 3 -3 0 -1 3 1 1 -1 2 0 -2 1 -1]
[ 0 0 0 1 1 -1 1 0 0 0 0 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 29 1 none
Polytope 1598
Image of polytope 1598 PALP id: 1598
grdb id: 500361
Integer points: [ 1 0 0 -1 1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 -1 -1 1 -1 0 -1 0 -1 0 -1 0]
[ 0 0 1 1 -1 -1 -1 -1 0 0 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
35 rank 2, number 15 x + y + z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + 2*y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 16 3 Lattice Minkowski decompositions of facet 16
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 1599
Image of polytope 1599 PALP id: 1599
grdb id: 500267
Integer points: [ 1 0 0 0 -2 -1 -2 -2 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 1 -2 -1 0 -1 0 0 1 -1 0]
[ 0 0 0 1 0 -2 -2 -1 -1 0 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 46 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1600
Image of polytope 1600 PALP id: 1600
grdb id: 500362
Integer points: [ 1 0 0 0 -1 -2 -2 0 -1 -1 -1 -2 0 -1]
[ 0 1 0 -2 -1 0 -2 -1 -2 -1 0 -1 0 0]
[ 0 0 1 -1 -1 1 -1 0 -1 0 1 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 8 1 none
Polytope 1601
Image of polytope 1601 PALP id: 1601
grdb id: 500037
Integer points: [ 1 0 0 0 -1 -2 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 0 -1 1 1 -2 0 -1 0 -1 0 -1 0]
[ 0 0 1 -1 0 -1 -1 -1 -1 0 0 -1 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Polytope 1602
Image of polytope 1602 PALP id: 1602
grdb id: 500337
Integer points: [ 1 0 0 0 0 -2 -2 -1 -1 -1 0 -1 0 0]
[ 0 1 0 0 -2 0 1 0 1 -1 -1 0 0 -1]
[ 0 0 1 -1 1 -1 -2 0 -1 0 1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + 2*y-1*z + z-1 + 2*x-1*y*z-1 + 2*y-1 + 2*x-1 + y-2*z + 2*x-1*z-1 + 2*x-1*y-1 + x-2*y*z-2 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1603
Image of polytope 1603 PALP id: 1603
grdb id: 500036
Integer points: [ 1 0 0 0 1 -2 -2 -2 -1 -1 0 -1 -1 0]
[ 0 1 0 0 -1 -1 1 0 0 -1 -1 1 0 0]
[ 0 0 1 -1 0 0 -2 -1 -1 0 0 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*y-1 + z-1 + 2*x-1*y*z-1 + 3*y-1 + 2*x-1 + 3*x-1*z-1 + 3*x-1*y-1 + x-2*y*z-2 + 2*x-2*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1604
Image of polytope 1604 PALP id: 1604
grdb id: 500379
Integer points: [ 1 -1 0 1 1 -2 1 1 1 0 0 0 -1 -1]
[ 0 0 1 1 1 1 -2 -1 0 -1 0 1 0 1]
[ 0 0 0 2 1 -1 -1 0 1 -1 0 1 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
154 ? x*y*z2 + x*y*z + 3*x*z + 3*y*z + x + y + 3*x*y-1 + 3*x-1*y + x-1 + x*y-2*z-1 + 3*y-1*z-1 + 3*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 9 3 irreducible and admissible
Image of facet 20 3 Lattice Minkowski decompositions of facet 20
Polytope 1605
Image of polytope 1605 PALP id: 1605
grdb id: 500012
Integer points: [ 1 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 -1 2 2 1 0 1 0 -1 1 0]
[ 0 0 0 1 2 -1 -2 0 1 -1 0 1 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
80 ? x + y + z + 2*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 3*x-1*z + x-1*y-1*z2 + x-1*y2*z-2 + 3*x-1*y*z-1 + 3*x-1 + 2*x-1*y-1*z + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 56 1 Lattice Minkowski decompositions of facet 56
Polytope 1606
Image of polytope 1606 PALP id: 1606
grdb id: 500002
Integer points: [ 1 0 0 -2 0 -1 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 1 2 2 0 1 0 1 0 1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Polytope 1607
Image of polytope 1607 PALP id: 1607
grdb id: 500133
Integer points: [ 1 0 0 -1 -1 -2 -2 -2 -1 -1 -1 0 0 0]
[ 0 1 0 2 -2 -1 1 0 1 0 -1 1 0 -1]
[ 0 0 1 -2 2 0 -2 -1 -1 0 1 -1 0 1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + x-1*y*z-1 + x-1 + 2*x-1*y-1*z + x-1*y-2*z2 + x-2*y*z-2 + 2*x-2*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 5 irreducible and admissible
Image of facet 114 1 Lattice Minkowski decompositions of facet 114
Polytope 1608
Image of polytope 1608 PALP id: 1608
grdb id: 500349
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 2 -2 2 -1 0 1 1 -1 0 1]
[ 0 0 1 -1 2 -2 1 -1 0 1 0 -1 0 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
127 ? x-1*y2*z2 + 2*y*z + x-1*y2*z + x + y + z + 4*x-1*y*z + 2*x-1*y + 6*x-1 + 2*y-1*z-1 + x-1*z-1 + 4*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 13 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Polytope 1609
Image of polytope 1609 PALP id: 1609
grdb id: 499963
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 -2 2 2 0 -1 1 0 0 -1 1]
[ 0 0 1 0 0 -1 -2 0 0 -1 -1 0 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
128 ? x + y + z + 2*y*z-1 + x-1*y2*z-1 + x-1*y + x-1*y2*z-2 + 3*x-1*y*z-1 + 2*y-1 + 3*x-1 + 2*x-1*z-1 + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1610
Image of polytope 1610 PALP id: 1610
grdb id: 500022
Integer points: [ 1 0 0 0 -1 -2 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 -1 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 0 1 -1 -1 2 1 0 1 0 1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Polytope 1611
Image of polytope 1611 PALP id: 1611
grdb id: 500331
Integer points: [ 1 0 0 0 -1 -2 -2 -1 -1 -1 -1 0 0 0]
[ 0 1 0 2 -2 0 -1 0 -1 1 0 1 0 -1]
[ 0 0 1 1 -2 -1 -2 0 -1 0 -1 1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 8 1 none
Polytope 1612
Image of polytope 1612 PALP id: 1612
grdb id: 500383
Integer points: [ 1 0 0 0 -1 0 -1 0 0 -1 -1 0 0 0]
[ 0 1 0 1 1 -2 -2 0 -1 0 -1 1 0 -1]
[ 0 0 1 -2 -1 1 2 -1 0 0 1 -1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 5 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 1613
Image of polytope 1613 PALP id: 1613
grdb id: 500348
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 0 -2 2 -2 1 0 -1 -1 1 0 -1]
[ 0 0 1 -1 1 -2 2 -1 0 1 0 -1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 5 1 none
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Polytope 1614
Image of polytope 1614 PALP id: 1614
grdb id: 500387
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 1 -1 -1 1 -2 -1 0 0 -1 0 1 0]
[ 0 0 2 -2 0 1 -2 -1 0 1 -1 0 1 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 5 1 none
Polytope 1615
Image of polytope 1615 PALP id: 1615
grdb id: 500364
Integer points: [ 1 0 0 0 1 -2 0 -1 0 -1 1 0 -1 0]
[ 0 1 0 0 -2 2 -2 1 -1 0 -1 0 1 -1]
[ 0 0 1 -1 0 -1 1 -1 0 0 0 0 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + 2*x*y-1 + 2*x-1*y + 2*y-1*z + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + x*y-2 + 2*y-1 + 2*x-1 + y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1616
Image of polytope 1616 PALP id: 1616
grdb id: 500366
Integer points: [ 1 0 1 0 -2 -2 0 -1 0 -1 -2 -1 0 0]
[ 0 1 -1 0 2 0 -2 1 -1 0 1 -1 0 -1]
[ 0 0 0 1 -1 -1 1 0 1 0 -1 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 4 1 none
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Polytope 1617
Image of polytope 1617 PALP id: 1617
grdb id: 500038
Integer points: [ 1 0 1 0 -2 0 -2 -1 -1 -2 -1 -2 0 0]
[ 0 1 -1 0 2 -1 -1 1 0 1 -1 0 0 -1]
[ 0 0 0 1 -1 1 -1 0 0 -1 0 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 4 1 none
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Polytope 1618
Image of polytope 1618 PALP id: 1618
grdb id: 500350
Integer points: [ 1 0 1 0 0 -1 -1 0 -1 -1 -1 0 0 0]
[ 0 1 -1 0 -2 -2 2 -1 -1 0 1 -1 0 1]
[ 0 0 0 1 -1 -2 2 0 -1 0 1 -1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? x-1*y2*z2 + 2*y*z + x + y + z + 4*x-1*y*z + x*y-1 + 2*y-1 + 6*x-1 + 2*y-1*z-1 + y-2*z-1 + 4*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 13 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Polytope 1619
Image of polytope 1619 PALP id: 1619
grdb id: 500080
Integer points: [ 1 0 -2 1 0 -2 1 0 0 -1 -1 1 0 -1]
[ 0 1 1 -2 0 0 -3 -1 -2 0 -1 -1 0 1]
[ 0 0 0 0 1 -1 -1 0 -1 0 -1 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
94 ? x + y + z + 2*x*y-1 + 2*x-1*y + x*y-2 + 2*y-1 + 2*x-1 + x-2*y + x*y-3*z-1 + 3*y-2*z-1 + 3*x-1*y-1*z-1 + x-2*z-1
91 ? x + y + z + 2*x*y-1 + 2*x-1*y + x*y-2 + 4*y-1 + 3*x-1 + x-2*y + x*y-3*z-1 + 3*y-2*z-1 + 3*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Polytope 1620
Image of polytope 1620 PALP id: 1620
grdb id: 499918
Integer points: [ 1 0 -1 0 -2 -1 -3 -2 -2 -1 -1 -1 0 0]
[ 0 1 1 0 0 -2 -2 -2 -1 -1 0 -1 -1 0]
[ 0 0 0 1 -1 0 -2 -1 -1 0 0 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 87 1 none
Polytope 1621
Image of polytope 1621 PALP id: 1621
grdb id: 499968
Integer points: [ 1 0 0 -3 0 -1 -3 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 -1 -1 -2 -3 -2 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 1 1 1 1 1 0 0 0 0 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 8 1 none
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 56 1 Lattice Minkowski decompositions of facet 56
Polytope 1622
Image of polytope 1622 PALP id: 1622
grdb id: 499686
Integer points: [ 1 0 0 -1 -3 -2 -3 -2 -3 -1 -2 -1 0 -1]
[ 0 1 0 0 -2 -1 -2 -1 -2 0 -1 -1 0 -1]
[ 0 0 1 1 0 1 -2 0 -1 0 -1 0 0 -1]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 92 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1623
Image of polytope 1623 PALP id: 1623
grdb id: 499983
Integer points: [ 1 0 0 -1 -2 -3 -1 -2 -1 -2 -1 -1 0 0]
[ 0 1 0 0 -1 -2 -2 -1 0 -2 -1 -1 0 -1]
[ 0 0 1 1 1 0 -2 0 0 -1 -1 0 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 14 1 none
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 1624
Image of polytope 1624 PALP id: 1624
grdb id: 500308
Integer points: [ 1 0 0 -1 -2 0 -3 -1 -1 -2 -2 0 0 -1]
[ 0 1 0 -2 0 -1 -2 0 -1 -1 -2 0 -1 -1]
[ 0 0 1 0 -1 1 -2 0 0 -1 -1 0 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
29 rank 2, number 23 x + y + z + y-1*z + 2*y-1 + 2*x-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + x-1*y-2 + x-2*y-1*z-1 + 2*x-2*y-2*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 71 1 Lattice Minkowski decompositions of facet 71
Polytope 1625
Image of polytope 1625 PALP id: 1625
grdb id: 499868
Integer points: [ 1 0 0 -1 -1 -3 -3 -3 -2 -2 -1 -1 -1 0]
[ 0 1 0 -1 1 -2 0 -1 0 -1 0 0 -1 0]
[ 0 0 1 1 -1 0 -2 -1 -1 0 0 -1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
28 rank 2, number 25 x + y + z + x-1*y*z-1 + 2*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + x-2*z-1 + x-2*y-1 + x-3*z-2 + 2*x-3*y-1*z-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 115 1 Lattice Minkowski decompositions of facet 115
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1626
Image of polytope 1626 PALP id: 1626
grdb id: 499967
Integer points: [ 1 0 0 -1 -1 -3 -3 -2 -1 -3 -2 -1 0 -1]
[ 0 1 0 0 -1 -2 -2 -1 0 -2 -1 -1 0 -1]
[ 0 0 1 -1 1 0 -2 0 0 -1 -1 0 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + 3*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*y-1 + 3*x-2*y-1*z-1 + x-3*y-2 + 2*x-3*y-2*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1627
Image of polytope 1627 PALP id: 1627
grdb id: 499909
Integer points: [ 1 0 0 -1 -1 -2 -3 -1 -2 -1 -2 0 -1 0]
[ 0 1 0 1 -2 1 0 0 0 -1 -1 0 0 -1]
[ 0 0 1 0 0 -1 -2 0 -1 0 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 84 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1628
Image of polytope 1628 PALP id: 1628
grdb id: 500363
Integer points: [ 1 0 0 -1 -1 -1 -3 -2 -2 -1 -2 -1 -1 0]
[ 0 1 0 -1 1 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 -1 1 1 1 0 1 0 1 0 1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
37 rank 3, number 17 x + y + z + x-1*y*z + 2*x-1*z + 2*x-1 + x-1*y-1*z + 2*x-2*z + 2*x-1*y-1 + 2*x-2*y-1*z + x-1*y-1*z-1 + 2*x-2*y-1 + x-3*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1629
Image of polytope 1629 PALP id: 1629
grdb id: 500365
Integer points: [ 1 0 0 0 -2 -1 -2 -1 -1 -2 0 0 -1 -1]
[ 0 1 -1 0 -1 -2 -3 -2 -1 -2 -1 0 -1 0]
[ 0 0 0 1 0 -2 -2 -1 0 -1 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + y-1 + 2*x-1 + 2*y-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + 2*x-1*y-2*z-1 + x-1*y-2*z-2 + 2*x-2*y-2*z-1 + x-2*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1630
Image of polytope 1630 PALP id: 1630
grdb id: 500319
Integer points: [ 1 0 -1 1 -1 -3 -3 0 -1 -2 -2 1 0 -1]
[ 0 1 -1 0 1 0 -1 0 0 0 -1 0 0 0]
[ 0 0 0 2 -1 -2 -2 1 0 -1 -1 1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 6 1 none
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Polytope 1631
Image of polytope 1631 PALP id: 1631
grdb id: 500025
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 0 -1 -3 0 -1 -2 -1 -2 0 -1]
[ 0 0 1 -1 1 2 2 0 1 2 0 1 0 1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 8 1 none
Image of facet 9 1 irreducible and admissible
Polytope 1632
Image of polytope 1632 PALP id: 1632
grdb id: 500353
Integer points: [ 1 0 0 0 -2 -3 1 0 -1 -2 -1 1 0 -1]
[ 0 1 -1 0 2 2 -2 -1 0 1 1 -1 0 1]
[ 0 0 0 1 -1 -2 2 1 0 -1 0 1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
91 ? x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*x-1*y + 4*y-1*z + 2*x-1*y*z-1 + x-2*y2*z-1 + y-1 + 6*x-1 + 4*x-2*y*z-1 + x-3*y2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 13 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Polytope 1633
Image of polytope 1633 PALP id: 1633
grdb id: 500125
Integer points: [ 1 0 0 0 -2 -2 -3 -1 0 -1 -2 -1 0 -1]
[ 0 1 0 2 0 -2 -2 1 1 0 -1 -1 0 -1]
[ 0 0 1 1 -1 -1 -2 0 1 0 -1 0 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? y2*z + 2*y*z + x + y + z + 2*x-1*y + 5*x-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + 4*x-2*y-1*z-1 + x-2*y-2*z-1 + x-3*y-2*z-2
46 ? y2*z + 2*y*z + x + y + z + 2*x-1*y + 4*x-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + 3*x-2*y-1*z-1 + x-2*y-2*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Polytope 1634
Image of polytope 1634 PALP id: 1634
grdb id: 500046
Integer points: [ 1 0 0 0 0 -1 -3 -2 -1 0 -2 -1 -1 0]
[ 0 1 0 -1 -1 0 2 1 0 -1 1 0 1 0]
[ 0 0 1 -1 1 1 -1 0 0 0 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 8 1 none
Polytope 1635
Image of polytope 1635 PALP id: 1635
grdb id: 500356
Integer points: [ 1 0 0 1 0 -2 -3 0 -1 -1 -2 1 0 -1]
[ 0 1 0 -2 -1 1 2 -1 0 0 1 -1 0 1]
[ 0 0 1 0 -1 0 -1 0 0 -1 -1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 6 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 1636
Image of polytope 1636 PALP id: 1636
grdb id: 499833
Integer points: [ 1 0 1 -3 -2 1 0 0 -1 -1 -2 1 0 -1]
[ 0 1 0 0 -1 1 -1 0 -1 0 0 0 0 0]
[ 0 0 2 -2 0 1 2 1 1 0 -1 1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
81 ? x*y*z + x*z2 + 2*x*z + x + y + z + y-1*z2 + 3*x-1 + 2*x-1*y-1*z + 2*x-1*z-1 + 3*x-2*z-1 + x-2*y-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 5 irreducible and admissible
Image of facet 116 1 Lattice Minkowski decompositions of facet 116
Polytope 1637
Image of polytope 1637 PALP id: 1637
grdb id: 500386
Integer points: [ 1 1 -1 -1 0 1 -2 0 -1 0 -1 0 1 0]
[ 0 2 0 -2 0 0 -3 -1 -2 -1 -1 0 1 1]
[ 0 0 0 0 1 -1 -1 0 -1 -1 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 6 1 none
Polytope 1638
Image of polytope 1638 PALP id: 1638
grdb id: 499593
Integer points: [ 1 0 -1 -1 0 -2 -3 -2 -1 -2 -1 0 -1 0]
[ 0 1 1 -2 0 -1 -4 -3 -1 -2 0 -1 -2 0]
[ 0 0 0 0 1 -1 -2 -1 0 -1 0 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 86 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1639
Image of polytope 1639 PALP id: 1639
grdb id: 499960
Integer points: [ 1 0 0 -2 0 -2 -4 -1 -3 -2 -1 -3 -1 0]
[ 0 1 0 0 -1 -2 -2 -1 -2 -1 0 -1 -1 0]
[ 0 0 1 -1 1 1 -1 1 0 0 0 -1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 8 1 none
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Polytope 1640
Image of polytope 1640 PALP id: 1640
grdb id: 500236
Integer points: [ 1 0 0 -1 -2 -3 -4 -3 -2 -1 -2 -1 -1 0]
[ 0 1 0 -1 0 -2 -2 -1 -1 0 -1 0 -1 0]
[ 0 0 1 -1 1 0 1 1 0 0 1 1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
63 ? x + y + z + 2*x-1*z + 2*x-1 + x-2*z + 2*x-1*y-1 + 2*x-2*y-1*z + x-1*y-1*z-1 + x-2*y-1 + 2*x-3*y-1*z + x-3*y-2 + x-4*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 47 1 Lattice Minkowski decompositions of facet 47
Polytope 1641
Image of polytope 1641 PALP id: 1641
grdb id: 499924
Integer points: [ 1 0 0 -1 -2 -3 -4 -3 -2 -1 -2 -1 -1 0]
[ 0 1 0 0 -2 -2 -3 -2 -1 -1 -1 0 -1 0]
[ 0 0 1 1 -1 -2 -2 -1 0 0 -1 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 42 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1642
Image of polytope 1642 PALP id: 1642
grdb id: 500031
Integer points: [ 1 0 0 -1 -1 -2 -4 -3 -2 -1 -1 0 -3 -2]
[ 0 1 0 0 0 -1 -3 -2 -1 0 -1 0 -2 -1]
[ 0 0 1 -1 1 1 -1 0 0 0 0 0 -1 -1]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 8 1 none
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 9 1 irreducible and admissible
Polytope 1643
Image of polytope 1643 PALP id: 1643
grdb id: 500333
Integer points: [ 1 0 0 0 -2 -3 -4 -3 -1 -2 -1 -2 0 -1]
[ 0 1 -1 0 -1 -2 -3 -2 -1 -2 0 -1 0 -1]
[ 0 0 0 1 0 -2 -2 -1 0 -1 0 -1 0 -1]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
76 ? x + y + z + y-1 + 2*x-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + 2*x-2*y-1*z-1 + 2*x-2*y-2*z-1 + 2*x-3*y-2*z-1 + x-3*y-2*z-2 + x-4*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1644
Image of polytope 1644 PALP id: 1644
grdb id: 500326
Integer points: [ 1 0 0 0 -2 -3 -4 -3 -1 -2 -1 -2 0 -1]
[ 0 1 -1 0 1 0 1 1 0 0 1 1 0 0]
[ 0 0 0 1 0 -2 -2 -1 0 -1 0 -1 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
28 rank 2, number 25 x + y + z + 2*x-1*y + y-1 + x-1 + x-2*y + 2*x-1*z-1 + 2*x-2*y*z-1 + x-2*z-1 + 2*x-3*y*z-1 + x-3*z-2 + x-4*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 48 1 Lattice Minkowski decompositions of facet 48
Polytope 1645
Image of polytope 1645 PALP id: 1645
grdb id: 500327
Integer points: [ 1 0 0 0 -2 -3 -4 -3 -1 -2 -1 -2 0 -1]
[ 0 1 0 -1 -1 -3 -3 -2 -1 -2 0 -1 0 -1]
[ 0 0 1 -1 0 -2 -2 -1 0 -1 0 -1 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 8 1 none
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1646
Image of polytope 1646 PALP id: 1646
grdb id: 500334
Integer points: [ 1 0 0 0 -2 -3 -4 -3 -1 -2 -1 -2 0 -1]
[ 0 1 0 -1 -1 0 -1 -1 -1 -1 0 0 0 0]
[ 0 0 1 -1 1 1 1 1 0 0 1 1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 8 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1647
Image of polytope 1647 PALP id: 1647
grdb id: 500332
Integer points: [ 1 0 0 0 -2 -3 -4 -3 -2 -1 -2 -1 -1 0]
[ 0 1 0 -1 0 -2 -2 -1 -1 0 -1 0 -1 0]
[ 0 0 1 -1 1 0 1 1 1 1 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + 2*x-1*z + 3*x-1 + x-2*z + y-1*z-1 + 2*x-1*y-1 + 2*x-2*y-1*z + 3*x-2*y-1 + 2*x-3*y-1*z + x-3*y-2 + x-4*y-2*z
103 ? x + y + z + 2*x-1*z + 3*x-1 + x-2*z + y-1*z-1 + 3*x-1*y-1 + 2*x-2*y-1*z + 3*x-2*y-1 + 2*x-3*y-1*z + x-3*y-2 + x-4*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 9 1 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1648
Image of polytope 1648 PALP id: 1648
grdb id: 500035
Integer points: [ 1 0 0 0 -1 -1 -4 -2 -3 -1 -2 -1 -2 0]
[ 0 1 -1 0 -2 0 -3 -1 -2 -1 -2 0 -1 0]
[ 0 0 0 1 -1 1 -2 0 -1 0 -1 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 66 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Polytope 1649
Image of polytope 1649 PALP id: 1649
grdb id: 499995
Integer points: [ 1 0 1 0 -1 -2 -4 -1 0 -3 -2 -1 0 -2]
[ 0 1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 0 1 -1 0 -2 0 0 -1 -1 0 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
159 ? x + y + z + x*y-1 + 3*y-1 + 2*x-1 + 3*x-1*y-1 + x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1 + 3*x-2*y-1*z-1 + 2*x-3*y-1*z-1 + x-4*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1650
Image of polytope 1650 PALP id: 1650
grdb id: 500380
Integer points: [ 1 0 1 0 -2 1 1 -1 0 -1 0 1 0 1]
[ 0 1 1 -1 0 0 1 0 0 0 0 0 0 0]
[ 0 0 2 -1 -3 3 1 -1 1 -2 0 2 -1 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
96 ? x*y*z2 + x*z3 + x*y*z + 3*x*z2 + 3*x*z + x + y + 3*z + 3*z-1 + y-1*z-1 + 3*x-1*z-1 + 3*x-1*z-2 + x-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 9 3 irreducible and admissible
Image of facet 20 3 Lattice Minkowski decompositions of facet 20
Polytope 1651
Image of polytope 1651 PALP id: 1651
grdb id: 499997
Integer points: [ 1 0 -1 0 -1 -3 -4 -2 -3 -2 -1 -2 0 -1]
[ 0 1 -1 0 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 0 1 -1 2 2 0 1 1 0 1 0 1]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 14 1 none
Polytope 1652
Image of polytope 1652 PALP id: 1652
grdb id: 499542
Integer points: [ 1 0 0 -2 -1 -3 -5 -4 -2 -3 -1 -1 -2 0]
[ 0 1 0 0 -1 -2 -2 -2 -1 -1 0 -1 -1 0]
[ 0 0 1 -1 1 0 -2 -1 0 -1 0 0 -1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
105 ? x + y + z + 3*x-1 + x-1*y-1*z + 2*x-1*y-1 + x-2*z-1 + 2*x-2*y-1 + 2*x-2*y-1*z-1 + 2*x-3*y-1*z-1 + x-3*y-2 + 2*x-4*y-2*z-1 + x-5*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 117 1 Lattice Minkowski decompositions of facet 117
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1653
Image of polytope 1653 PALP id: 1653
grdb id: 498796
Integer points: [ 1 0 -1 0 -2 0 -2 -1 -2 -1 -1 0 -1 0]
[ 0 1 1 0 0 -2 -2 -1 -1 0 -2 -1 -1 0]
[ 0 0 0 1 -1 -1 -1 0 -1 0 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + x-1*y + 2*y-1 + 2*x-1 + 2*x-1*y-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-2*z-1 + 2*x-1*y-2*z-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 1654
Image of polytope 1654 PALP id: 1654
grdb id: 497952
Integer points: [ 1 0 -1 0 -2 0 -2 -1 0 -1 -2 -1 0 0]
[ 0 1 1 0 0 -2 -2 -2 -1 -1 -1 0 -1 0]
[ 0 0 0 1 -1 1 -1 0 1 0 -1 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 4 1 none
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Polytope 1655
Image of polytope 1655 PALP id: 1655
grdb id: 498894
Integer points: [ 1 0 0 -2 1 -2 1 0 -1 0 -1 1 0 -1]
[ 0 1 0 1 -2 1 -2 -1 0 -1 0 -1 0 1]
[ 0 0 1 0 0 -1 -1 0 0 -1 -1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
101 ? x + y + z + 2*x*y-1 + 2*x-1*y + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + 3*y-1*z-1 + 3*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 1656
Image of polytope 1656 PALP id: 1656
grdb id: 497346
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 0 -2 -2 -1 0 -2 -1 -1 0 -1]
[ 0 0 1 0 -1 0 -2 0 0 -1 -1 0 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
143 ? x + y + z + x-1*y + 2*y-1 + 3*x-1 + 2*y-1*z-1 + x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1657
Image of polytope 1657 PALP id: 1657
grdb id: 498815
Integer points: [ 1 0 0 0 -2 -1 -2 -1 -2 -1 -1 0 -1 0]
[ 0 1 0 0 0 -2 -2 0 -1 -1 0 0 -1 -1]
[ 0 0 1 -1 1 0 1 0 1 0 1 0 1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
32 ? x + y + z + 2*x-1*z + z-1 + 2*y-1 + 2*x-1 + 2*x-1*y-1*z + x-2*z + 2*x-1*y-1 + 2*x-2*y-1*z + x-1*y-2 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1658
Image of polytope 1658 PALP id: 1658
grdb id: 497552
Integer points: [ 1 0 0 0 -1 -2 0 0 -1 0 -1 0 -1 0]
[ 0 1 0 -1 0 1 -1 -1 0 -1 0 0 1 0]
[ 0 0 1 1 1 0 -2 0 0 -1 -1 0 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + 2*x-1*y + y-1*z + x-1*z + 2*z-1 + 3*y-1 + 3*x-1 + x-2*y + 3*y-1*z-1 + 2*x-1*z-1 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1659
Image of polytope 1659 PALP id: 1659
grdb id: 498690
Integer points: [ 1 0 0 0 0 -2 -2 -1 -1 0 -1 -1 0 0]
[ 0 1 0 0 -2 1 0 -1 0 -1 0 1 -1 0]
[ 0 0 1 -1 1 0 1 1 0 0 1 0 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + 2*x-1*y + 2*y-1*z + 2*x-1*z + z-1 + 2*y-1 + 2*x-1 + x-2*y + y-2*z + 2*x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1660
Image of polytope 1660 PALP id: 1660
grdb id: 497546
Integer points: [ 1 0 0 1 1 -2 0 0 -1 0 -1 0 -1 0]
[ 0 1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 1 0 -1 0 -2 0 0 -1 -1 0 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
100 ? x + y + z + x*y-1 + x*y-1*z-1 + 2*z-1 + 3*y-1 + 2*x-1 + 3*y-1*z-1 + 3*x-1*y-1 + y-1*z-2 + 2*x-1*y-1*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1661
Image of polytope 1661 PALP id: 1661
grdb id: 498805
Integer points: [ 1 0 -1 0 0 -1 -1 -1 -1 0 -1 0 0 0]
[ 0 1 0 0 -2 2 -2 1 -1 -1 0 0 1 -1]
[ 0 0 0 1 1 -2 0 -1 0 1 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 2*x-1*y*z-1 + 2*y-1 + x-1 + y-2*z + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1662
Image of polytope 1662 PALP id: 1662
grdb id: 497198
Integer points: [ 1 0 0 -2 -2 0 -1 -1 0 -1 -2 -1 0 0]
[ 0 1 0 2 0 -2 -2 1 -1 0 1 -1 0 -1]
[ 0 0 1 -1 -1 1 0 0 1 0 -1 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
88 ? x + y + z + 2*x-1*y + 2*y-1*z + x-2*y2*z-1 + 2*y-1 + 4*x-1 + y-2*z + 2*x-2*y*z-1 + 3*x-1*y-1 + x-2*z-1 + x-1*y-2
81 ? x + y + z + 2*x-1*y + 2*y-1*z + x-2*y2*z-1 + 2*y-1 + 5*x-1 + y-2*z + 2*x-2*y*z-1 + 4*x-1*y-1 + x-2*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 5 irreducible and admissible
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Polytope 1663
Image of polytope 1663 PALP id: 1663
grdb id: 497452
Integer points: [ 1 0 0 -1 -2 -1 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 -1 2 2 1 0 1 0 1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 14 1 none
Polytope 1664
Image of polytope 1664 PALP id: 1664
grdb id: 498868
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 1 -2 2 1 0 -1 0 1 0 -1]
[ 0 0 1 0 -2 2 -2 -1 0 1 -1 -1 0 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
127 ? x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 4*x-1*y*z-1 + 6*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + x-1*y*z-2 + 2*x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 5 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Polytope 1665
Image of polytope 1665 PALP id: 1665
grdb id: 498855
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -2 2 -2 0 -1 1 0 -1 0 -1]
[ 0 0 1 0 0 -1 -1 0 0 -1 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
128 ? x + y + z + x-1*y2*z-1 + x-1*y + 4*x-1*y*z-1 + 2*y-1 + 3*x-1 + 6*x-1*z-1 + 3*x-1*y-1 + 4*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 13 1 irreducible and admissible
Polytope 1666
Image of polytope 1666 PALP id: 1666
grdb id: 498739
Integer points: [ 1 0 0 0 -2 0 -2 -2 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 0 2 2 1 2 1 1 0 1 0]
[ 0 0 0 1 -1 1 1 0 1 0 1 0 1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
69 ? y2*z + 2*y*z + 2*x-1*y2*z + x + y + z + 2*x-1*y*z + x-2*y2*z + 2*x-1*y + y-1 + 2*x-1 + 2*x-2*y + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1667
Image of polytope 1667 PALP id: 1667
grdb id: 497674
Integer points: [ 1 0 0 0 -1 -2 -2 -1 -1 -2 -1 -2 0 0]
[ 0 1 0 -1 -2 2 -1 1 0 1 -1 0 0 -1]
[ 0 0 1 1 0 -1 -1 0 0 -1 0 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
88 ? x + y + z + 2*x-1*y + y-1*z + x-2*y2*z-1 + 2*y-1 + 4*x-1 + 3*x-2*y*z-1 + 3*x-1*y-1 + 3*x-2*z-1 + x-1*y-2 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 9 1 irreducible and admissible
Polytope 1668
Image of polytope 1668 PALP id: 1668
grdb id: 495904
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 2 -2 -1 0 -1 1 0 1 0]
[ 0 0 0 1 1 -1 -1 0 0 -1 0 -1 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + x-1*y2*z-1 + 2*x-1*y + x-1*z + 4*x-1*y*z-1 + y-1 + 4*x-1 + 6*x-1*z-1 + 2*x-1*y-1 + 4*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 13 1 irreducible and admissible
Polytope 1669
Image of polytope 1669 PALP id: 1669
grdb id: 497352
Integer points: [ 1 0 -1 0 -2 0 -2 -1 -1 -2 -1 -2 0 0]
[ 0 1 1 0 0 -1 -3 -2 -1 -2 0 -1 -1 0]
[ 0 0 0 1 -1 1 -1 0 0 -1 0 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 4 1 none
Polytope 1670
Image of polytope 1670 PALP id: 1670
grdb id: 496119
Integer points: [ 1 0 -1 0 -1 -2 -2 -2 -1 -2 -1 -2 0 0]
[ 0 1 1 0 -2 1 -3 -2 -1 -1 0 0 -1 0]
[ 0 0 0 1 0 -1 -1 -1 0 -1 0 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
82 ? x + y + z + x-1*y + 2*y-1 + 4*x-1 + x-2*y*z-1 + 4*x-1*y-1 + 4*x-2*z-1 + x-1*y-2 + 6*x-2*y-1*z-1 + 4*x-2*y-2*z-1 + x-2*y-3*z-1
159 ? x + y + z + x-1*y + 2*y-1 + 3*x-1 + x-2*y*z-1 + 3*x-1*y-1 + 4*x-2*z-1 + x-1*y-2 + 6*x-2*y-1*z-1 + 4*x-2*y-2*z-1 + x-2*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 93 1 Lattice Minkowski decompositions of facet 93
Polytope 1671
Image of polytope 1671 PALP id: 1671
grdb id: 498770
Integer points: [ 1 0 0 -1 -1 -1 -3 -2 -2 -1 -2 -1 -1 0]
[ 0 1 0 -1 -1 1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 -1 1 -1 -1 0 -1 0 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + x-1*y*z-1 + 3*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + 2*x-2*z-1 + 2*x-2*y-1 + 2*x-2*y-1*z-1 + x-3*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 1672
Image of polytope 1672 PALP id: 1672
grdb id: 497484
Integer points: [ 1 0 0 -1 0 -2 -3 -1 -2 -1 -1 -2 0 -1]
[ 0 1 -1 1 0 -3 -3 -1 -2 -2 0 -1 0 -1]
[ 0 0 0 0 1 -2 -2 0 -1 -1 0 -1 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 14 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1673
Image of polytope 1673 PALP id: 1673
grdb id: 497292
Integer points: [ 1 0 0 0 -1 -1 -3 -2 -1 -2 -1 -1 0 0]
[ 0 1 0 -1 1 -2 0 0 0 -1 -1 0 0 -1]
[ 0 0 1 1 -1 0 -2 -1 0 -1 0 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + y-1*z + x-1*y*z-1 + 2*y-1 + 3*x-1 + 2*x-1*z-1 + 3*x-1*y-1 + 3*x-2*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1674
Image of polytope 1674 PALP id: 1674
grdb id: 497278
Integer points: [ 1 0 0 0 0 -1 -3 -2 -1 0 -1 0 -2 -1]
[ 0 1 0 -1 -1 -1 -1 -1 -1 -1 0 0 -1 -1]
[ 0 0 1 -1 1 1 -1 0 0 0 0 0 -1 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 8 1 none
Image of facet 9 1 irreducible and admissible
Polytope 1675
Image of polytope 1675 PALP id: 1675
grdb id: 497409
Integer points: [ 1 0 1 -1 0 -1 -3 -2 -1 -2 -1 -1 0 0]
[ 0 1 -1 1 0 -1 -3 -2 -1 -1 0 -2 -1 0]
[ 0 0 0 0 1 -1 -2 -1 0 -1 0 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 14 2 none
Polytope 1676
Image of polytope 1676 PALP id: 1676
grdb id: 497286
Integer points: [ 1 0 1 0 -2 1 0 0 0 -1 -1 0 0 -1]
[ 0 1 -1 0 1 -2 -3 -1 -2 0 -1 0 -1 1]
[ 0 0 0 1 0 -1 -2 0 -1 0 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Polytope 1677
Image of polytope 1677 PALP id: 1677
grdb id: 498747
Integer points: [ 1 0 1 0 -1 -3 -3 -2 -1 -2 0 -1 0 -1]
[ 0 1 -1 0 -1 0 -1 -1 0 0 -1 -1 0 0]
[ 0 0 0 1 0 -2 -2 -1 0 -1 0 -1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + x*y-1 + 2*y-1 + 3*x-1 + 2*x-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*z-1 + 2*x-2*y-1*z-1 + x-3*z-2 + x-3*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1678
Image of polytope 1678 PALP id: 1678
grdb id: 498844
Integer points: [ 1 0 1 0 1 -2 -3 -1 0 -2 -1 0 -1 0]
[ 0 1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 0 0 1 -1 0 -1 0 0 -1 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 13 1 irreducible and admissible
Image of facet 6 1 none
Polytope 1679
Image of polytope 1679 PALP id: 1679
grdb id: 498737
Integer points: [ 1 0 0 0 -2 2 2 1 1 -1 0 0 1 -1]
[ 0 1 -1 0 1 -2 -3 -2 -1 0 -1 0 -1 1]
[ 0 0 0 1 0 -1 -2 -1 0 0 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + 2*x*y-1 + 2*x-1*y + x2*y-2*z-1 + 2*x*y-1*z-1 + y-1 + 2*x-1 + x-2*y + 2*x*y-2*z-1 + 2*y-1*z-1 + x2*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1680
Image of polytope 1680 PALP id: 1680
grdb id: 497408
Integer points: [ 1 0 0 0 -1 -1 -4 -3 -2 -2 -1 -2 -1 0]
[ 0 1 -1 0 -1 0 -3 -2 -1 -2 -1 -1 0 0]
[ 0 0 0 1 -1 1 -2 -1 0 -1 0 -1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1681
Image of polytope 1681 PALP id: 1681
grdb id: 497571
Integer points: [ 1 0 0 0 0 -1 -4 -2 -3 -1 -2 -1 -2 0]
[ 0 1 -1 0 1 1 1 1 1 1 1 0 0 0]
[ 0 0 0 1 1 1 -2 0 -1 0 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
147 ? y*z + x + y + z + x-1*y*z + 3*x-1*y + y-1 + 3*x-1 + 3*x-2*y + 2*x-2*y*z-1 + 2*x-2*z-1 + 3*x-3*y*z-1 + x-4*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Polytope 1682
Image of polytope 1682 PALP id: 1682
grdb id: 402568
Integer points: [ 1 0 0 -1 2 0 -2 1 1 -1 0 1 -1 0]
[ 0 1 0 1 -1 1 1 -2 0 1 0 -1 0 -1]
[ 0 0 1 1 -1 -1 0 0 -1 0 0 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 6 2 none
Polytope 1683
Image of polytope 1683 PALP id: 1683
grdb id: 402540
Integer points: [ 1 0 0 -1 1 -1 1 0 1 0 0 0 0 -1]
[ 0 1 0 1 -1 -1 -2 -2 -1 -1 0 -1 0 0]
[ 0 0 1 -1 -1 1 0 1 0 0 -1 1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + 2*x*y-1 + 2*y-1*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + x*y-2 + 3*y-1 + 2*x-1 + y-2*z + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1684
Image of polytope 1684 PALP id: 1684
grdb id: 402536
Integer points: [ 1 0 0 0 0 -2 -1 -2 -2 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 -1 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 0 1 -1 0 1 -2 -1 0 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 46 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1685
Image of polytope 1685 PALP id: 1685
grdb id: 402562
Integer points: [ 1 0 0 1 -1 1 -1 -2 0 0 -1 1 0 -1]
[ 0 1 0 -1 1 -2 1 1 0 -1 0 -1 0 1]
[ 0 0 1 -1 1 0 -1 0 -1 0 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 5 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1686
Image of polytope 1686 PALP id: 1686
grdb id: 402543
Integer points: [ 1 0 1 0 0 -1 -2 -2 0 -1 -1 1 0 -1]
[ 0 1 -2 0 -1 1 1 1 -1 0 0 -1 0 1]
[ 0 0 0 1 -1 1 0 -1 0 0 -1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 6 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1687
Image of polytope 1687 PALP id: 1687
grdb id: 402466
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 1 -2 0 0 1 1 1 0 -1 1 0 -1]
[ 0 0 2 -2 1 -1 2 0 1 0 -1 1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 45 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1688
Image of polytope 1688 PALP id: 1688
grdb id: 402548
Integer points: [ 1 0 0 0 0 -1 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 1 -1 0 0 -1 1 0 0]
[ 0 0 1 -1 0 -1 0 2 1 0 1 0 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
25 ? x + y + z + 2*x-1*y + 2*x-1*z + z-1 + x-1*y*z-1 + y-1 + 3*x-1 + x-2*y + 2*x-1*y-1*z + 2*x-2*z + x-2*y-1*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 1689
Image of polytope 1689 PALP id: 1689
grdb id: 402566
Integer points: [ 1 0 0 1 -1 0 0 -1 0 0 0 0 -1 0]
[ 0 1 1 -1 1 -1 -1 -1 0 -1 0 1 0 0]
[ 0 0 2 -1 1 -2 0 -1 -1 -1 0 1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 5 1 none
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1690
Image of polytope 1690 PALP id: 1690
grdb id: 402559
Integer points: [ 1 0 1 1 -1 0 -2 0 0 -1 0 1 -1 0]
[ 0 1 0 -1 1 -1 0 1 0 0 0 0 0 0]
[ 0 0 2 0 -1 -1 -1 -1 -1 -1 0 1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 8 1 none
Polytope 1691
Image of polytope 1691 PALP id: 1691
grdb id: 402539
Integer points: [ 1 1 -1 -1 0 -1 -1 -1 -1 -1 0 0 0 1]
[ 0 2 -2 0 0 0 -2 -1 -1 -1 -1 0 1 1]
[ 0 0 0 0 1 -1 -1 1 0 -1 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x*y2 + 2*x*y + x + 2*y + z + 2*y-1 + x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
151 ? x*y2 + 2*x*y + x + 2*y + z + 2*y-1 + x-1 + x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 1 3 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1692
Image of polytope 1692 PALP id: 1692
grdb id: 402565
Integer points: [ 1 1 -1 -1 0 -1 1 -1 0 -1 0 0 1 0]
[ 0 2 -2 0 0 -1 0 -2 -1 -1 -1 0 1 1]
[ 0 0 0 0 1 1 -1 -1 0 0 -1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 6 1 none
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1693
Image of polytope 1693 PALP id: 1693
grdb id: 402557
Integer points: [ 1 1 -1 0 -1 -1 0 -1 -1 0 -1 0 1 0]
[ 0 2 -2 0 0 -1 1 0 0 1 -1 0 1 -1]
[ 0 0 0 1 -1 1 1 1 0 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 2 none
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1694
Image of polytope 1694 PALP id: 1694
grdb id: 402564
Integer points: [ 1 1 0 0 -1 -1 0 -2 0 -1 -1 0 1 0]
[ 0 2 0 0 0 -2 -1 -2 -1 -1 -1 0 1 1]
[ 0 0 1 -1 0 0 -1 1 0 0 1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x*y2 + 2*x*y + x + 2*y + z + z-1 + 2*y-1 + x-1 + 2*x-1*y-1*z + y-1*z-1 + x-1*y-1 + x-1*y-2 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1695
Image of polytope 1695 PALP id: 1695
grdb id: 402551
Integer points: [ 1 0 0 0 -1 -1 -2 -3 -2 -2 -1 -1 -1 0]
[ 0 1 0 -1 -1 1 -1 -1 -1 0 0 -1 0 0]
[ 0 0 1 -1 0 0 -2 -2 -1 -1 0 -1 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1696
Image of polytope 1696 PALP id: 1696
grdb id: 402508
Integer points: [ 1 0 1 -2 0 -1 1 -1 0 0 -1 1 0 -1]
[ 0 1 -2 1 0 1 -3 -1 -2 -1 0 -1 0 1]
[ 0 0 0 0 1 1 -1 -1 -1 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
94 ? x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + x*y-2 + 2*y-1 + 2*x-1 + x-2*y + x*y-3*z-1 + 2*y-2*z-1 + x-1*y-1*z-1
91 ? x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + x*y-2 + 4*y-1 + 3*x-1 + x-2*y + x*y-3*z-1 + 2*y-2*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 1 4 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Polytope 1697
Image of polytope 1697 PALP id: 1697
grdb id: 402552
Integer points: [ 1 0 1 0 -1 1 0 -1 0 0 -1 -1 0 0]
[ 0 1 -1 0 1 -2 -3 -2 -2 -1 -1 0 -1 0]
[ 0 0 0 1 1 -1 -2 -2 -1 0 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
35 rank 2, number 15 x + y + z + x-1*y*z + x*y-1 + 3*y-1 + 3*x-1 + x*y-2*z-1 + y-1*z-1 + 3*y-2*z-1 + 3*x-1*y-1*z-1 + y-3*z-2 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 1698
Image of polytope 1698 PALP id: 1698
grdb id: 402476
Integer points: [ 1 0 1 0 0 -2 -3 -1 -2 -1 0 -1 0 1]
[ 0 1 -2 0 -1 1 2 0 1 0 -1 1 0 -1]
[ 0 0 0 1 1 -1 -1 1 0 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 45 1 none
Polytope 1699
Image of polytope 1699 PALP id: 1699
grdb id: 402281
Integer points: [ 1 0 0 -1 1 0 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 -1 0 -1 -1 0 -1 0 -1 0 -1]
[ 0 0 1 1 -1 -1 1 -1 0 0 1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y*z + 2*x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + 2*y-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 1700
Image of polytope 1700 PALP id: 1700
grdb id: 402368
Integer points: [ 1 0 0 1 -1 0 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 1 1 1 -1 0 1 0 0 -1 0]
[ 0 0 1 -1 1 1 -1 1 1 0 0 0 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
56 rank 2, number 11 y*z + x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Polytope 1701
Image of polytope 1701 PALP id: 1701
grdb id: 401730
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 2 1 2 1 1 0 0 1 0]
[ 0 0 1 -1 0 1 2 2 0 1 0 1 1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
57 ? x-1*y2*z2 + 2*y*z + x-1*y2*z + x-1*y*z2 + x + y + z + 2*x-1*y*z + 2*x-1*y + 2*x-1*z + x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 71 1 Lattice Minkowski decompositions of facet 71
Polytope 1702
Image of polytope 1702 PALP id: 1702
grdb id: 401568
Integer points: [ 1 0 0 -1 0 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -1 -1 -1 -1 -1 -1 0 0 -1 0]
[ 0 0 1 0 -1 1 -1 2 1 0 1 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 14 1 none
Polytope 1703
Image of polytope 1703 PALP id: 1703
grdb id: 401402
Integer points: [ 1 0 -1 0 -1 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 1 0 -2 0 -1 -2 -1 -2 -1 0 -1 0]
[ 0 0 0 1 -1 1 1 1 1 0 0 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 37 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1704
Image of polytope 1704 PALP id: 1704
grdb id: 402420
Integer points: [ 1 0 0 -1 -2 0 -2 -1 -1 -1 0 -1 0 0]
[ 0 1 0 1 0 -2 -1 -2 0 -1 -1 0 0 -1]
[ 0 0 1 0 -1 -1 -2 -2 0 -1 0 -1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y + 2*y-1 + 2*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + y-2*z-1 + 3*x-1*y-1*z-1 + x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1705
Image of polytope 1705 PALP id: 1705
grdb id: 402373
Integer points: [ 1 0 0 -1 -1 -2 -1 -2 -1 -2 -1 -1 0 0]
[ 0 1 0 1 -1 0 -2 -2 0 -1 -1 0 0 -1]
[ 0 0 1 -1 -1 -1 0 -1 0 -1 0 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + x-1*y*z-1 + 2*y-1 + 2*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-2*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1706
Image of polytope 1706 PALP id: 1706
grdb id: 401283
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 -2 -1 1 0 1 0 -1 0 -1]
[ 0 0 1 -1 -1 0 1 1 1 0 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
143 ? x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Polytope 1707
Image of polytope 1707 PALP id: 1707
grdb id: 401566
Integer points: [ 1 0 0 -1 -1 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 1 -2 -1 -2 0 -1 0 -1 0 -1]
[ 0 0 1 -1 1 0 1 1 1 1 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
147 ? x + y + z + x-1*y*z + y-1*z + 3*x-1*z + 2*y-1 + 2*x-1 + 3*x-1*y-1*z + 3*x-1*y-1 + x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1708
Image of polytope 1708 PALP id: 1708
grdb id: 401403
Integer points: [ 1 0 0 -1 -1 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -2 -1 1 1 0 1 0 -1 0 -1]
[ 0 0 1 -1 0 1 1 1 1 0 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 37 1 none
Polytope 1709
Image of polytope 1709 PALP id: 1709
grdb id: 402259
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 -1 0 -1 0 0]
[ 0 1 0 0 1 -1 0 -2 0 -1 0 -1 0 -1]
[ 0 0 1 0 -1 1 -2 0 -1 0 0 -1 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + y*z-1 + 2*z-1 + 2*y-1 + x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1710
Image of polytope 1710 PALP id: 1710
grdb id: 402432
Integer points: [ 1 0 0 -1 1 1 -2 -1 -1 0 0 -1 0 1]
[ 0 1 0 1 -2 -2 1 0 0 -1 -1 1 0 -1]
[ 0 0 1 1 0 -1 0 -1 0 0 -1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
101 ? x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 1 4 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1711
Image of polytope 1711 PALP id: 1711
grdb id: 402347
Integer points: [ 1 0 0 0 -1 -1 0 -1 -1 0 -1 -1 0 0]
[ 0 1 0 0 1 1 -2 -1 0 -1 0 1 -1 0]
[ 0 0 1 -1 -1 1 1 1 0 0 1 0 1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + x-1*y*z + 2*x-1*y + 2*y-1*z + 2*x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + y-2*z + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1712
Image of polytope 1712 PALP id: 1712
grdb id: 402267
Integer points: [ 1 0 0 0 -1 1 0 -2 0 -1 -1 0 0 -1]
[ 0 1 0 0 1 -1 -2 0 -1 0 -1 0 -1 0]
[ 0 0 1 -1 0 1 1 -1 1 0 0 0 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
128 ? x + y + x*y-1*z + z + x-1*y + 2*y-1*z + z-1 + 2*y-1 + 2*x-1 + y-2*z + 2*x-1*z-1 + 2*x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1713
Image of polytope 1713 PALP id: 1713
grdb id: 402294
Integer points: [ 1 0 0 0 0 -1 -2 -2 -1 -2 -1 -1 0 -1]
[ 0 1 -1 0 1 0 1 1 1 1 0 1 0 0]
[ 0 0 0 1 -1 1 0 -2 0 -1 0 -1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + y*z-1 + 2*x-1*y + x-1*z + 2*x-1*y*z-1 + y-1 + 2*x-1 + x-2*y + 2*x-1*z-1 + 2*x-2*y*z-1 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Polytope 1714
Image of polytope 1714 PALP id: 1714
grdb id: 401597
Integer points: [ 1 0 1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 1 0 1 0 -2 -1 0 -1 0 -1 0]
[ 0 0 0 0 1 -1 1 -1 0 0 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1715
Image of polytope 1715 PALP id: 1715
grdb id: 402297
Integer points: [ 1 0 1 -1 0 0 -2 0 0 -1 -1 0 0 -1]
[ 0 1 -1 1 0 0 0 -2 -1 0 -1 0 -1 0]
[ 0 0 0 0 1 -1 -1 1 1 0 0 0 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*y-1 + x-1*y + 2*y-1*z + z-1 + 2*y-1 + 2*x-1 + y-2*z + 2*x-1*z-1 + 2*x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Polytope 1716
Image of polytope 1716 PALP id: 1716
grdb id: 401569
Integer points: [ 1 0 1 0 -2 -1 1 -2 0 -1 0 -1 0 -1]
[ 0 1 -1 0 1 0 -2 1 -1 0 -1 0 0 1]
[ 0 0 0 1 0 1 -1 -1 0 0 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*y-1 + 2*x-1*y + x-1*z + 2*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + 3*y-1*z-1 + 3*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1717
Image of polytope 1717 PALP id: 1717
grdb id: 401296
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 0 -1 -2 2 1 0 -1 1 0 -1]
[ 0 0 1 -1 1 1 0 -1 0 0 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*y2*z-1 + 2*x-1*y + x-1*z + 2*x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Polytope 1718
Image of polytope 1718 PALP id: 1718
grdb id: 401839
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 -2 -1 -2 0 -1 0 -1 -1 0]
[ 0 0 1 -1 0 1 2 2 1 1 0 0 1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
148 ? x + y + z + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + x-1 + 2*x-1*y-1*z + x-1*y-2*z2 + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 71 1 Lattice Minkowski decompositions of facet 71
Polytope 1719
Image of polytope 1719 PALP id: 1719
grdb id: 402387
Integer points: [ 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 1 2 -2 2 -1 0 1 -1 0 1]
[ 0 0 1 -1 1 1 -2 1 -1 0 0 -1 0 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? y2*z + 2*y*z + x-1*y2*z + x + y + z + x-1*y*z + 2*x-1*y + 3*x-1 + 2*y-1*z-1 + x-1*z-1 + 3*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 9 1 irreducible and admissible
Polytope 1720
Image of polytope 1720 PALP id: 1720
grdb id: 402296
Integer points: [ 1 0 0 -1 0 -2 -2 1 -1 0 -1 -1 0 1]
[ 0 1 -1 1 0 1 1 -2 0 -1 0 1 0 -1]
[ 0 0 0 0 1 -1 -2 2 0 1 -1 -1 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + 2*x*y-1*z + z + x*y-2*z2 + x-1*y + 3*y-1*z + 2*x-1*y*z-1 + y-1 + 3*x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1721
Image of polytope 1721 PALP id: 1721
grdb id: 402434
Integer points: [ 1 0 0 -1 1 -2 0 -2 -1 -1 -1 0 0 1]
[ 0 1 -1 0 0 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 0 0 2 -2 1 -1 -1 0 -1 0 1 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x*z2 + 2*x*z + x + y + 2*z + y-1*z + y-1 + x-1 + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1722
Image of polytope 1722 PALP id: 1722
grdb id: 402266
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 0 -1 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 0 1 -1 0 -1 0 2 1 0 1 0 1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + 2*y-1*z + z-1 + 2*y-1 + x-1 + 2*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*y-1 + 2*x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1723
Image of polytope 1723 PALP id: 1723
grdb id: 402265
Integer points: [ 1 0 0 0 0 -1 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 -1 0 1 0 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 0 1 -1 -1 0 2 1 0 1 0 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + y*z-1 + 2*x-1*z + y-1 + 3*x-1 + 2*x-1*y-1*z + x-2*y-1*z2 + x-1*z-1 + 2*x-1*y-1 + 2*x-2*y-1*z + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 1724
Image of polytope 1724 PALP id: 1724
grdb id: 402440
Integer points: [ 1 0 0 0 0 1 -1 -1 0 0 0 0 -1 0]
[ 0 1 1 -1 -1 1 0 0 0 -1 0 1 0 0]
[ 0 0 2 -2 0 1 1 -1 -1 -1 0 1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? x*y*z + y*z2 + 2*y*z + x + y + 2*z + x-1*z + 2*z-1 + y-1 + 2*x-1 + 2*y-1*z-1 + x-1*z-1 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1725
Image of polytope 1725 PALP id: 1725
grdb id: 402427
Integer points: [ 1 0 0 0 1 0 -1 -1 0 0 0 0 -1 -1]
[ 0 1 0 0 -1 -2 -1 2 -1 0 1 -1 0 1]
[ 0 0 1 -1 0 1 1 -2 1 0 -1 0 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + z + 2*y*z-1 + x*y-1 + 2*y-1*z + x-1*y2*z-2 + z-1 + 3*x-1*y*z-1 + 2*y-1 + 3*x-1 + y-2*z + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1726
Image of polytope 1726 PALP id: 1726
grdb id: 402269
Integer points: [ 1 0 0 2 -1 -2 0 0 0 1 1 -1 0 -1]
[ 0 1 0 -1 0 1 -1 -1 -1 -1 -1 0 0 1]
[ 0 0 1 -1 1 0 -1 1 0 0 -1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 8 1 none
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1727
Image of polytope 1727 PALP id: 1727
grdb id: 402299
Integer points: [ 1 0 1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 1 0 -1 2 -2 0 -1 0 1 -1 0]
[ 0 0 0 0 1 0 -1 -1 0 -1 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 6 1 none
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Polytope 1728
Image of polytope 1728 PALP id: 1728
grdb id: 401473
Integer points: [ 1 0 -1 0 -2 -1 0 -2 -2 -1 -1 -1 0 0]
[ 0 1 1 0 -1 -2 -1 -3 -2 -2 -1 0 -1 0]
[ 0 0 0 1 -1 -1 1 -1 -1 0 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Polytope 1729
Image of polytope 1729 PALP id: 1729
grdb id: 401485
Integer points: [ 1 0 0 -2 -1 -1 -3 -3 -2 -3 -2 -1 -1 0]
[ 0 1 0 -1 0 -1 -2 -2 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 1 1 -1 1 1 0 0 0 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Polytope 1730
Image of polytope 1730 PALP id: 1730
grdb id: 401519
Integer points: [ 1 0 0 -2 0 -3 -1 -3 -2 -1 -2 -1 -1 0]
[ 0 1 0 0 -1 -2 -2 -3 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 1 0 1 1 1 1 0 0 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
102 ? x + y + z + y-1*z + 2*x-1 + 3*x-1*y-1*z + 2*x-1*y-1 + x-1*y-2*z + x-2*z-1 + 2*x-2*y-1 + 3*x-2*y-2*z + x-3*y-2 + x-3*y-3*z
92 ? x + y + z + y-1*z + 3*x-1 + 3*x-1*y-1*z + 2*x-1*y-1 + x-1*y-2*z + x-2*z-1 + 4*x-2*y-1 + 3*x-2*y-2*z + x-3*y-2 + x-3*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Polytope 1731
Image of polytope 1731 PALP id: 1731
grdb id: 402183
Integer points: [ 1 0 0 -1 0 -2 -3 -3 -1 -2 -1 -2 -1 0]
[ 0 1 0 -1 1 1 -1 0 1 0 0 -1 0 0]
[ 0 0 1 0 1 -1 -2 -2 0 -1 0 -1 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
147 ? y*z + x + y + z + 2*x-1*y + 4*x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + 4*x-2*z-1 + 2*x-2*y-1*z-1 + x-3*z-2 + x-3*y-1*z-2
112 rank 3, number 15 y*z + x + y + z + 2*x-1*y + 3*x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + 3*x-2*z-1 + 2*x-2*y-1*z-1 + x-3*z-2 + x-3*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 96 1 Lattice Minkowski decompositions of facet 96
Polytope 1732
Image of polytope 1732 PALP id: 1732
grdb id: 401340
Integer points: [ 1 0 0 -1 0 -2 -3 -3 -2 -1 -2 -1 -1 0]
[ 0 1 0 1 -1 1 0 -1 0 0 -1 -1 0 0]
[ 0 0 1 0 1 -1 -2 -2 -1 0 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + x-1*y + y-1*z + 3*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 3*x-1*y-1 + 3*x-2*z-1 + 3*x-2*y-1*z-1 + x-3*z-2 + x-3*y-1*z-2
144 rank 3, number 12 x + y + z + x-1*y + y-1*z + 4*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 3*x-1*y-1 + 4*x-2*z-1 + 3*x-2*y-1*z-1 + x-3*z-2 + x-3*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Image of facet 9 1 irreducible and admissible
Polytope 1733
Image of polytope 1733 PALP id: 1733
grdb id: 401407
Integer points: [ 1 0 0 -1 0 -1 -3 -3 -2 -1 -2 -1 -1 0]
[ 0 1 0 -1 1 1 0 1 1 1 0 0 0 0]
[ 0 0 1 0 1 -1 -2 -2 -1 0 -1 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? y*z + x + y + z + 3*x-1*y + x-1*y*z-1 + 2*x-1 + 2*x-1*z-1 + 3*x-2*y*z-1 + x-1*y-1 + 2*x-2*z-1 + x-3*y*z-2 + x-3*z-2
95 ? y*z + x + y + z + 3*x-1*y + x-1*y*z-1 + 4*x-1 + 2*x-1*z-1 + 3*x-2*y*z-1 + x-1*y-1 + 3*x-2*z-1 + x-3*y*z-2 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Polytope 1734
Image of polytope 1734 PALP id: 1734
grdb id: 402413
Integer points: [ 1 0 0 -1 0 -1 -3 -3 -2 -1 -2 -1 -1 0]
[ 0 1 0 0 -1 -2 -2 -3 -1 0 -2 -1 -1 0]
[ 0 0 1 -1 1 1 0 1 0 0 1 1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
47 ? x + y + z + y-1*z + 3*x-1 + 3*x-1*y-1*z + x-1*z-1 + x-1*y-1 + x-1*y-2*z + 3*x-2*y-1 + 3*x-2*y-2*z + x-3*y-2 + x-3*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 1735
Image of polytope 1735 PALP id: 1735
grdb id: 401582
Integer points: [ 1 0 0 0 -1 -1 -2 -3 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 -2 1 1 0 0 0 -1 -1 0 0]
[ 0 0 0 1 -1 1 1 1 1 1 0 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1736
Image of polytope 1736 PALP id: 1736
grdb id: 402414
Integer points: [ 1 0 0 0 -1 -1 -2 -3 -2 -2 -1 -1 -1 0]
[ 0 1 -1 0 -1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 0 0 1 -1 1 1 1 0 1 0 0 1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 8 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1737
Image of polytope 1737 PALP id: 1737
grdb id: 402402
Integer points: [ 1 0 0 0 -1 -1 -2 -3 -2 -2 -1 -1 -1 0]
[ 0 1 -1 0 0 0 -2 -2 -1 -1 0 -1 -1 0]
[ 0 0 0 1 -1 1 1 1 0 1 0 0 1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1738
Image of polytope 1738 PALP id: 1738
grdb id: 401607
Integer points: [ 1 0 1 0 -1 0 -1 -3 -2 -1 0 -1 0 -2]
[ 0 1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 -1]
[ 0 0 0 1 -1 1 1 -1 0 0 0 0 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Polytope 1739
Image of polytope 1739 PALP id: 1739
grdb id: 402411
Integer points: [ 1 0 0 0 0 -2 -2 -3 -1 -2 -1 -1 0 -1]
[ 0 1 -1 0 -1 2 1 2 1 1 0 1 0 0]
[ 0 0 0 1 1 -1 -2 -2 0 -1 0 -1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
55 rank 2, number 19 x + y + z + 2*x-1*y + y-1*z + x-1*y*z-1 + x-2*y2*z-1 + y-1 + 3*x-1 + 2*x-1*z-1 + 3*x-2*y*z-1 + x-2*y*z-2 + x-3*y2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Polytope 1740
Image of polytope 1740 PALP id: 1740
grdb id: 401280
Integer points: [ 1 0 0 -2 0 -3 -4 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 -1 -1 -1 -2 -2 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 1 -1 -1 1 1 0 0 0 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
140 ? x + y + z + y-1*z + 3*x-1 + 2*x-1*y-1*z + 3*x-1*y-1 + 3*x-2*y-1 + x-2*y-2*z + x-2*y-1*z-1 + x-3*y-1*z-1 + 2*x-3*y-2 + x-4*y-2*z-1
123 ? x + y + z + y-1*z + 3*x-1 + 2*x-1*y-1*z + 2*x-1*y-1 + 3*x-2*y-1 + x-2*y-2*z + x-2*y-1*z-1 + x-3*y-1*z-1 + 2*x-3*y-2 + x-4*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Polytope 1741
Image of polytope 1741 PALP id: 1741
grdb id: 402346
Integer points: [ 1 0 0 -1 -2 -2 -3 -4 -3 -1 -1 -2 0 -1]
[ 0 1 0 0 -1 -2 -2 -3 -2 -1 0 -1 0 -1]
[ 0 0 1 -1 0 -1 -2 -2 -1 0 0 -1 0 -1]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? x + y + z + 2*x-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + 3*x-2*y-1*z-1 + x-2*y-2*z-1 + 2*x-3*y-2*z-1 + x-3*y-2*z-2 + x-4*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1742
Image of polytope 1742 PALP id: 1742
grdb id: 401416
Integer points: [ 1 0 -1 0 -2 -1 -3 -3 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 0 2 2 3 2 1 1 0 1 0]
[ 0 0 0 1 -1 -1 -2 -2 -1 0 -1 0 -1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 66 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Polytope 1743
Image of polytope 1743 PALP id: 1743
grdb id: 401404
Integer points: [ 1 0 0 0 -2 -1 -3 -3 -1 -2 -1 -2 0 -1]
[ 0 1 -1 0 0 2 2 3 1 2 0 1 0 1]
[ 0 0 0 1 -1 -1 -2 -2 0 -1 0 -1 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + x-1*y2*z-1 + 3*x-1*y + 2*x-1*y*z-1 + 3*x-2*y2*z-1 + y-1 + 2*x-1 + x-3*y3*z-2 + 3*x-2*y*z-1 + x-3*y2*z-2 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1744
Image of polytope 1744 PALP id: 1744
grdb id: 400004
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 1 -1 -1 1 -1 0 0 0 1 0]
[ 0 0 0 1 -1 -1 1 1 0 1 0 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + x-1*y*z-1 + y-1 + 4*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Polytope 1745
Image of polytope 1745 PALP id: 1745
grdb id: 397635
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 -1 -1 2 -1 0 1 0 1 0]
[ 0 0 0 1 1 1 -1 -1 0 0 0 -1 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y2*z-1 + 2*x-1*y + x-1*z + 3*x-1*y*z-1 + y-1 + 4*x-1 + x-1*y-1*z + 3*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1746
Image of polytope 1746 PALP id: 1746
grdb id: 398434
Integer points: [ 1 0 -1 0 -2 -1 0 -2 -1 0 -2 -1 0 0]
[ 0 1 1 0 1 -2 -2 -1 0 -1 0 -1 0 -1]
[ 0 0 0 1 -1 0 1 -1 0 1 -1 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
159 ? x + y + z + x-1*y + 2*y-1*z + 2*y-1 + 3*x-1 + y-2*z + x-2*y*z-1 + 3*x-1*y-1 + 2*x-2*z-1 + x-1*y-2 + x-2*y-1*z-1
82 ? x + y + z + x-1*y + 2*y-1*z + 2*y-1 + 4*x-1 + y-2*z + x-2*y*z-1 + 4*x-1*y-1 + 2*x-2*z-1 + x-1*y-2 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 96 1 Lattice Minkowski decompositions of facet 96
Polytope 1747
Image of polytope 1747 PALP id: 1747
grdb id: 398237
Integer points: [ 1 0 -1 0 0 -2 -1 -2 -1 -2 -1 -2 0 0]
[ 0 1 1 0 -1 1 -2 -2 -1 -1 0 0 -1 0]
[ 0 0 0 1 1 -1 0 -1 0 -1 0 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
82 ? x + y + z + x-1*y + y-1*z + 2*y-1 + 4*x-1 + x-2*y*z-1 + 4*x-1*y-1 + 3*x-2*z-1 + x-1*y-2 + 3*x-2*y-1*z-1 + x-2*y-2*z-1
159 ? x + y + z + x-1*y + y-1*z + 2*y-1 + 3*x-1 + x-2*y*z-1 + 3*x-1*y-1 + 3*x-2*z-1 + x-1*y-2 + 3*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Image of facet 9 1 irreducible and admissible
Polytope 1748
Image of polytope 1748 PALP id: 1748
grdb id: 397686
Integer points: [ 1 0 0 -1 -1 -1 -2 -2 -2 -2 -1 -1 -1 0]
[ 0 1 0 1 -1 1 1 -2 -1 0 -1 0 0 0]
[ 0 0 1 0 -1 -1 -1 -1 -1 -1 0 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + x-1*y + x-1*y*z-1 + 3*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + 3*x-2*z-1 + 3*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1749
Image of polytope 1749 PALP id: 1749
grdb id: 400168
Integer points: [ 1 0 0 -1 -1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 1 -1 -2 -2 -1 0 0 -1 -1 0]
[ 0 0 1 0 -1 -1 1 0 0 0 -1 1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 6 1 none
Polytope 1750
Image of polytope 1750 PALP id: 1750
grdb id: 400210
Integer points: [ 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 1 -1 -2 -2 -1 0 -1 0 -1 0]
[ 0 0 1 0 -1 1 0 -1 0 0 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 6 1 none
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 1751
Image of polytope 1751 PALP id: 1751
grdb id: 400226
Integer points: [ 1 0 0 -1 0 0 -2 -2 -1 -1 0 -1 -1 0]
[ 0 1 0 1 -1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 0 1 0 -1 1 1 1 0 1 0 0 1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1752
Image of polytope 1752 PALP id: 1752
grdb id: 397711
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 -1 1 0 -2 1 0 -1 1 0 -1 0]
[ 0 0 1 1 -1 -1 1 1 1 1 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + x-1*y*z + 2*x-1*y + y-1*z + 3*x-1*z + x-1*y*z-1 + 4*x-1 + 3*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Polytope 1753
Image of polytope 1753 PALP id: 1753
grdb id: 400224
Integer points: [ 1 0 0 0 0 -2 -1 -2 -1 -2 -1 -1 0 -1]
[ 0 1 -1 0 -1 -1 -1 -1 0 -1 0 -1 0 -1]
[ 0 0 0 1 1 0 1 -2 0 -1 -1 0 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + y-1*z + y-1 + 2*x-1 + x-1*y-1*z + 2*x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + 2*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1754
Image of polytope 1754 PALP id: 1754
grdb id: 400122
Integer points: [ 1 0 0 0 0 -1 -2 -2 -1 -2 -1 -1 0 -1]
[ 0 1 -1 0 -1 0 1 1 1 1 0 1 0 0]
[ 0 0 0 1 1 1 0 -2 0 -1 0 -1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + 2*x-1*y + y-1*z + x-1*z + 2*x-1*y*z-1 + y-1 + 3*x-1 + x-2*y + 2*x-1*z-1 + 2*x-2*y*z-1 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1755
Image of polytope 1755 PALP id: 1755
grdb id: 400493
Integer points: [ 1 0 0 0 0 -1 -2 -2 -1 -2 -1 -1 0 -1]
[ 0 1 0 -1 0 0 -1 -1 -1 -1 0 -1 0 0]
[ 0 0 1 0 -1 1 0 -2 0 -1 0 -1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + x-1*z + z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + 2*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1756
Image of polytope 1756 PALP id: 1756
grdb id: 400558
Integer points: [ 1 0 0 0 0 -1 0 -2 -1 -1 0 -1 0 0]
[ 0 1 0 1 -1 1 -1 1 0 0 -1 1 0 0]
[ 0 0 1 -1 1 1 -1 1 0 1 0 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y*z + y*z-1 + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + 2*z-1 + 2*y-1 + 2*x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 1757
Image of polytope 1757 PALP id: 1757
grdb id: 397770
Integer points: [ 1 0 0 -1 -1 -2 -1 -2 -2 -2 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 2 2 1 0 1 0 1 0]
[ 0 0 1 -1 0 -1 -1 -1 -1 -1 0 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
47 ? x + y + z + x-1*y2*z-1 + 2*x-1*y + 2*x-1*y*z-1 + x-2*y2*z-1 + 3*x-1 + x-1*z-1 + 3*x-2*y*z-1 + x-1*y-1 + 3*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1758
Image of polytope 1758 PALP id: 1758
grdb id: 397760
Integer points: [ 1 0 0 -1 -1 -1 -2 -2 -2 -2 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 -1 -1 -1 -1 0 0 -1 0]
[ 0 0 1 -1 -1 1 -1 2 0 1 0 1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + 2*x-1*z + 3*x-1 + x-1*y-1*z + x-2*y-1*z2 + x-1*z-1 + 2*x-1*y-1 + 3*x-2*y-1*z + x-1*y-1*z-1 + 3*x-2*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1759
Image of polytope 1759 PALP id: 1759
grdb id: 400520
Integer points: [ 1 0 0 -1 -1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 1 0 2 0 1 -2 -2 -1 0 1 -1 -1 0]
[ 0 0 1 -1 -1 0 1 0 0 0 -1 1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
128 ? x + y + z + x-1*y2*z-1 + x-1*y + 2*y-1*z + 2*x-1*y*z-1 + 2*y-1 + 3*x-1 + y-2*z + x-1*z-1 + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Polytope 1760
Image of polytope 1760 PALP id: 1760
grdb id: 400262
Integer points: [ 1 0 0 0 -1 -2 -1 -2 -2 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 0 2 2 1 0 1 0 1 0]
[ 0 0 0 1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + x-1*y2*z-1 + 2*x-1*y + 3*x-1*y*z-1 + x-2*y2*z-1 + y-1 + 2*x-1 + 3*x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1761
Image of polytope 1761 PALP id: 1761
grdb id: 400230
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 -1 0 0 -2 2 1 -1 0 1 -1 0]
[ 0 0 1 1 -1 1 1 -1 0 1 0 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
55 rank 2, number 19 x + y + z + x-1*y2*z-1 + 2*x-1*y + y-1*z + x-1*z + 2*x-1*y*z-1 + 4*x-1 + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Polytope 1762
Image of polytope 1762 PALP id: 1762
grdb id: 400554
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 1 2 -2 -1 -1 0 0 1 -1 0]
[ 0 0 1 1 0 -1 0 -1 0 0 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
128 ? x + y + z + x-1*y2*z-1 + x-1*y + y-1*z + 3*x-1*y*z-1 + 2*y-1 + 3*x-1 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 1763
Image of polytope 1763 PALP id: 1763
grdb id: 400195
Integer points: [ 1 0 0 0 0 0 -2 -2 -1 0 -1 0 -1 -1]
[ 0 1 0 0 -1 -1 1 2 0 -1 1 0 0 1]
[ 0 0 1 -1 1 -1 -1 -1 -1 0 -1 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + 2*x-1*y + y-1*z + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1764
Image of polytope 1764 PALP id: 1764
grdb id: 400494
Integer points: [ 1 0 -1 0 -1 0 -1 -3 -2 -1 -2 0 -1 0]
[ 0 1 0 0 0 -1 -2 -2 -1 -1 -2 0 -1 -1]
[ 0 0 0 1 -1 1 0 -2 -1 0 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + y-1*z + 2*y-1 + x-1 + x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + 2*x-2*y-2*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1765
Image of polytope 1765 PALP id: 1765
grdb id: 400086
Integer points: [ 1 0 0 0 -1 -2 -1 -3 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 0 -1 -2 -2 -2 -1 -1 0 -1 0]
[ 0 0 0 1 -1 0 -1 -1 -1 0 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + y-1 + 2*x-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + x-1*y-2*z-1 + 2*x-2*y-1*z-1 + 2*x-2*y-2*z-1 + x-3*y-2*z-1
103 ? x + y + z + y-1 + 2*x-1 + x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + x-1*y-2*z-1 + 2*x-2*y-1*z-1 + 2*x-2*y-2*z-1 + x-3*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1766
Image of polytope 1766 PALP id: 1766
grdb id: 400145
Integer points: [ 1 0 0 0 -1 -1 -2 -3 -2 -1 -2 -1 0 -1]
[ 0 1 -1 0 -1 1 1 1 1 0 0 1 0 0]
[ 0 0 0 1 0 0 -2 -2 -1 0 -1 -1 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + x-1*y + 2*x-1*y*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1 + x-2*y*z-2 + 2*x-2*z-1 + x-3*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1767
Image of polytope 1767 PALP id: 1767
grdb id: 400227
Integer points: [ 1 0 0 0 -1 -1 -2 -3 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 1 -1 1 1 0 0 1 0 1 0]
[ 0 0 0 1 -1 -1 0 -1 -1 0 -1 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? x + y + z + 2*x-1*y + x-1*y*z-1 + y-1 + 3*x-1 + x-2*y + 2*x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1*z-1 + 2*x-2*z-1 + x-3*y*z-1
16 ? x + y + z + 2*x-1*y + x-1*y*z-1 + y-1 + 2*x-1 + x-2*y + 2*x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1*z-1 + 2*x-2*z-1 + x-3*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1768
Image of polytope 1768 PALP id: 1768
grdb id: 400139
Integer points: [ 1 0 0 0 0 -2 -2 -3 -1 -2 -1 -1 0 -1]
[ 0 1 -1 0 -1 0 -1 -1 0 -1 -1 0 0 -1]
[ 0 0 0 1 1 -1 -2 -2 0 -1 0 -1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + y-1*z + y-1 + 2*x-1 + 2*x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + 3*x-2*y-1*z-1 + x-2*y-1*z-2 + x-3*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Polytope 1769
Image of polytope 1769 PALP id: 1769
grdb id: 400552
Integer points: [ 1 0 0 0 0 -1 -3 -3 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 1 1 0 1 1 1 0 0 0 0]
[ 0 0 0 1 1 -1 -2 -2 -1 0 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 y*z + x + y + z + 3*x-1*y + x-1*y*z-1 + y-1 + 3*x-1 + 2*x-1*z-1 + 3*x-2*y*z-1 + 3*x-2*z-1 + x-3*y*z-2 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 1770
Image of polytope 1770 PALP id: 1770
grdb id: 400426
Integer points: [ 1 0 1 -1 0 -1 -1 -3 -2 -1 -2 0 -1 0]
[ 0 1 -1 1 0 0 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 0 0 1 -1 0 -2 -1 0 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + x*y-1 + x-1*y + 2*y-1 + 2*x-1 + x-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + 2*x-2*y-1*z-1 + x-3*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1771
Image of polytope 1771 PALP id: 1771
grdb id: 400378
Integer points: [ 1 0 1 -1 0 -1 -1 -3 -2 -1 -2 0 -1 0]
[ 0 1 -1 1 0 1 -1 1 1 0 0 0 0 -1]
[ 0 0 0 0 1 -1 0 -2 -1 0 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x*y-1 + x-1*y + x-1*y*z-1 + 2*y-1 + 2*x-1 + 2*x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1 + 2*x-2*z-1 + x-3*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1772
Image of polytope 1772 PALP id: 1772
grdb id: 408682
Integer points: [ 1 0 0 0 0 -1 0 -2 0 -1 0 -1 0 -1]
[ 0 1 0 1 -1 1 -1 1 0 0 -1 1 0 0]
[ 0 0 1 -1 1 0 -1 -1 -1 -1 0 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + y*z-1 + x-1*y + y-1*z + 2*z-1 + 2*x-1*y*z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 1773
Image of polytope 1773 PALP id: 1773
grdb id: 408230
Integer points: [ 1 0 0 0 0 0 -2 -2 -1 -1 0 -1 -1 0]
[ 0 1 0 0 -1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 -1 1 1 1 0 1 0 0 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + y-1*z + 2*x-1*z + z-1 + 2*y-1 + 2*x-1 + 2*x-1*y-1*z + x-2*z + y-1*z-1 + 2*x-1*y-1 + x-2*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1774
Image of polytope 1774 PALP id: 1774
grdb id: 408626
Integer points: [ 1 0 0 1 -1 0 -2 0 0 -1 -1 0 0 -1]
[ 0 1 0 -1 1 0 0 -2 -1 0 -1 0 -1 0]
[ 0 0 1 0 0 -1 -1 -1 0 0 -1 0 -1 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
3 ? x + y + z + x*y-1 + x-1*y + z-1 + 2*y-1 + 2*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 1775
Image of polytope 1775 PALP id: 1775
grdb id: 408716
Integer points: [ 1 0 0 1 -1 0 -1 -1 -1 0 -1 0 -1 0]
[ 0 1 0 -1 1 0 -1 -1 0 -1 -1 0 0 -1]
[ 0 0 1 0 0 -1 0 -2 0 0 -1 0 -1 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
85 rank 3, number 8 x + y + z + x*y-1 + x-1*y + z-1 + 2*y-1 + 2*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 1776
Image of polytope 1776 PALP id: 1776
grdb id: 236731
Integer points: [ 1 0 1 -1 0 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 1 0 2 -1 -1 -1 0 0 1 -1 0]
[ 0 0 0 0 1 -1 1 0 -1 0 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 6 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1777
Image of polytope 1777 PALP id: 1777
grdb id: 236718
Integer points: [ 1 0 0 -1 0 -1 0 -2 -2 -1 -1 0 -1 0]
[ 0 1 0 1 -1 0 -1 1 1 0 0 -1 1 0]
[ 0 0 1 1 -1 -1 1 0 1 1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y*z + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + 2*y-1 + 3*x-1 + x-2*y + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1778
Image of polytope 1778 PALP id: 1778
grdb id: 236706
Integer points: [ 1 0 0 -1 1 0 -2 -1 -2 -1 0 -1 -1 0]
[ 0 1 0 1 -1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 0 1 0 -1 -1 1 1 1 0 0 0 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1779
Image of polytope 1779 PALP id: 1779
grdb id: 236656
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 1 0 0 -2 -2 -1 -1 0 -1 0]
[ 0 0 0 1 0 -1 1 -1 -2 0 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 46 1 none
Polytope 1780
Image of polytope 1780 PALP id: 1780
grdb id: 236710
Integer points: [ 1 0 0 0 -1 0 -2 -1 -2 -2 -1 -1 -1 0]
[ 0 1 -1 0 0 -1 1 1 1 1 0 0 1 0]
[ 0 0 0 1 -1 1 -1 1 1 0 1 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1781
Image of polytope 1781 PALP id: 1781
grdb id: 236696
Integer points: [ 1 0 0 0 0 -1 -1 -2 -2 -2 -1 -1 0 -1]
[ 0 1 -1 0 1 -1 0 -1 -1 -1 0 -1 0 0]
[ 0 0 0 1 -1 1 1 1 -1 0 0 0 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1782
Image of polytope 1782 PALP id: 1782
grdb id: 236727
Integer points: [ 1 0 0 0 0 1 -2 -1 -2 -1 0 -1 0 -1]
[ 0 1 0 0 -1 -1 1 -1 0 0 -1 0 0 1]
[ 0 0 1 -1 0 -1 0 -1 -1 0 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
60 rank 2, number 18 x + y + z + 2*x-1*y + x*y-1*z-1 + z-1 + y-1 + x-1 + x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1783
Image of polytope 1783 PALP id: 1783
grdb id: 236732
Integer points: [ 1 0 0 0 0 1 -1 -1 -2 1 0 -1 0 -1]
[ 0 1 0 0 1 -2 1 1 1 -1 0 1 -1 0]
[ 0 0 1 -1 1 0 -1 1 0 0 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 y*z + x + y + z + x-1*y*z + 2*x*y-1 + x-1*y + z-1 + x-1*y*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1784
Image of polytope 1784 PALP id: 1784
grdb id: 236686
Integer points: [ 1 0 0 0 1 0 -1 -2 -2 -1 0 -1 0 -1]
[ 0 1 0 0 -1 -1 -1 0 1 0 -1 0 0 1]
[ 0 0 1 -1 0 1 0 -1 -2 0 0 -1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + x*y-1 + y-1*z + z-1 + 2*x-1*y*z-1 + 2*y-1 + 2*x-1 + 2*x-1*z-1 + x-1*y-1 + x-2*y*z-2 + x-2*z-1
128 ? x + y + z + x*y-1 + y-1*z + z-1 + 2*x-1*y*z-1 + 2*y-1 + 2*x-1 + 3*x-1*z-1 + x-1*y-1 + x-2*y*z-2 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1785
Image of polytope 1785 PALP id: 1785
grdb id: 236692
Integer points: [ 1 0 0 1 -2 0 -1 0 -1 0 -1 1 0 -1]
[ 0 1 0 -2 1 -1 0 -1 0 -1 0 -1 0 1]
[ 0 0 1 0 0 -1 -1 1 1 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + x*y-2 + y-1 + x-1 + x-2*y + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 50 1 Lattice Minkowski decompositions of facet 50
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1786
Image of polytope 1786 PALP id: 1786
grdb id: 236704
Integer points: [ 1 0 0 1 -2 0 -1 1 0 0 1 -1 0 -1]
[ 0 1 0 -1 1 -1 0 -1 -1 -1 -1 0 0 1]
[ 0 0 1 -1 0 -1 1 1 1 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1787
Image of polytope 1787 PALP id: 1787
grdb id: 236658
Integer points: [ 1 0 0 1 -2 0 0 1 -1 0 -1 1 0 -1]
[ 0 1 0 -2 1 -1 -1 -2 0 -1 0 -1 0 1]
[ 0 0 1 0 0 -1 1 -1 1 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + x*y-2 + y-1 + 2*x-1 + x-2*y + x*y-2*z-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 51 1 Lattice Minkowski decompositions of facet 51
Polytope 1788
Image of polytope 1788 PALP id: 1788
grdb id: 236729
Integer points: [ 1 0 0 1 -1 0 1 -1 -2 -1 0 -1 0 0]
[ 0 1 0 -1 1 1 0 -1 0 0 0 0 0 -1]
[ 0 0 1 0 0 1 -1 0 -1 -1 -1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
56 rank 2, number 11 y*z + x + y + z + x*z-1 + x*y-1 + x-1*y + 3*z-1 + 2*y-1 + x-1 + 3*x-1*z-1 + x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1789
Image of polytope 1789 PALP id: 1789
grdb id: 236721
Integer points: [ 1 0 0 1 0 -1 -2 -2 -1 -1 0 -1 0 1]
[ 0 1 0 -2 -1 1 1 2 0 0 -1 1 0 -1]
[ 0 0 1 0 1 -1 0 -1 1 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + 2*x*y-1 + x-1*y + y-1*z + x-1*z + x-1*y*z-1 + x-2*y2*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1790
Image of polytope 1790 PALP id: 1790
grdb id: 236728
Integer points: [ 1 0 1 -1 0 2 0 -2 -1 0 1 -1 -1 0]
[ 0 1 -1 1 0 -1 -1 0 -1 -1 -1 0 0 0]
[ 0 0 0 0 1 -1 -1 1 0 0 -1 0 1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 6 1 none
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1791
Image of polytope 1791 PALP id: 1791
grdb id: 236722
Integer points: [ 1 0 0 0 1 1 -1 -1 -3 1 0 -1 -1 -2]
[ 0 1 -1 0 1 -1 -1 1 0 0 0 0 0 0]
[ 0 0 0 1 -1 -1 0 0 1 -1 0 1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x*y*z-1 + x + y + z + 2*x*z-1 + x-1*y + 3*x-1*z + x*y-1*z-1 + y-1 + 3*x-1 + 3*x-2*z + x-1*y-1 + x-3*z
10 rank 1, V18 x*y*z-1 + x + y + z + 2*x*z-1 + x-1*y + 3*x-1*z + x*y-1*z-1 + y-1 + 2*x-1 + 3*x-2*z + x-1*y-1 + x-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1792
Image of polytope 1792 PALP id: 1792
grdb id: 236615
Integer points: [ 1 0 1 0 -2 -2 0 -1 -3 -2 -1 0 -1 0]
[ 0 1 -1 0 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 0 0 1 -1 -1 1 1 -1 0 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 45 1 none
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1793
Image of polytope 1793 PALP id: 1793
grdb id: 236734
Integer points: [ 1 1 -1 -1 0 -1 -1 -2 -2 -1 0 0 0 1]
[ 0 2 -2 0 0 -1 -2 -2 -3 -1 -1 0 1 1]
[ 0 0 0 0 1 -1 -1 -1 -1 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x*y2 + 2*x*y + x + 2*y + z + 2*y-1 + x-1 + x-1*y-1 + x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1 + x-2*y-2*z-1 + x-2*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 1 3 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 1794
Image of polytope 1794 PALP id: 1794
grdb id: 236254
Integer points: [ 1 0 0 -1 0 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -1 1 -1 -1 -1 -1 0 0 -1 0]
[ 0 0 1 0 -1 1 1 -1 1 0 1 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y*z + x-1*y + y-1*z + 2*x-1*z + 2*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1795
Image of polytope 1795 PALP id: 1795
grdb id: 236314
Integer points: [ 1 0 0 0 -1 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 0 -1 0 -1 -1 -1 -1 0 -1 0]
[ 0 0 1 -1 -1 1 1 -1 2 0 1 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
55 rank 2, number 19 x + y + z + y-1*z + x-1*z + x-1*y-1*z2 + 2*y-1 + 2*x-1 + 3*x-1*y-1*z + y-1*z-1 + x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Polytope 1796
Image of polytope 1796 PALP id: 1796
grdb id: 235986
Integer points: [ 1 0 -1 0 -1 -2 -1 0 -2 -2 -1 -1 0 0]
[ 0 1 1 0 -1 0 -2 -1 -2 -1 -1 0 -1 0]
[ 0 0 0 1 -1 -1 0 1 -1 -1 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? x + y + z + x-1*y + y-1*z + 2*y-1 + 2*x-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-2*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
129 ? x + y + z + x-1*y + y-1*z + 2*y-1 + 3*x-1 + 4*x-1*y-1 + x-1*y-1*z-1 + x-2*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Polytope 1797
Image of polytope 1797 PALP id: 1797
grdb id: 235630
Integer points: [ 1 0 -1 0 -1 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 1 0 -1 -2 -1 0 -2 -1 -1 0 -1 0]
[ 0 0 0 1 -1 0 1 1 1 1 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
147 ? x + y + z + x-1*y + y-1*z + x-1*z + 2*y-1 + 2*x-1 + 2*x-1*y-1*z + x-1*y-1 + x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 47 1 Lattice Minkowski decompositions of facet 47
Polytope 1798
Image of polytope 1798 PALP id: 1798
grdb id: 235966
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 -1]
[ 0 1 0 1 0 0 -2 -1 -2 -1 0 -1 0 -1]
[ 0 0 1 0 -1 1 0 1 -1 0 0 0 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
114 ? x + y + z + x-1*y + x-1*z + 2*y-1 + 3*x-1 + x-1*y-1*z + x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
144 rank 3, number 12 x + y + z + x-1*y + x-1*z + 2*y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Polytope 1799
Image of polytope 1799 PALP id: 1799
grdb id: 236106
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 1 0 -1 -1 -2 -1 0 0 -1 0]
[ 0 0 1 0 -1 1 -1 1 0 0 0 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
88 ? x + y + z + x-1*y + x-1*z + x-1*y*z-1 + 2*y-1 + 4*x-1 + x-1*y-1*z + 2*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
46 ? x + y + z + x-1*y + x-1*z + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Polytope 1800
Image of polytope 1800 PALP id: 1800
grdb id: 236110
Integer points: [ 1 0 0 -1 -1 0 -2 -1 -2 -2 -1 -1 0 0]
[ 0 1 0 1 0 -1 1 -2 -1 0 0 -1 0 -1]
[ 0 0 1 0 -1 1 -1 0 -1 -1 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + x-1*y + y-1*z + 2*y-1 + 2*x-1 + x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + 2*x-2*z-1 + x-1*y-2 + x-2*y-1*z-1
82 ? x + y + z + x-1*y + y-1*z + 2*y-1 + 4*x-1 + x-1*z-1 + x-2*y*z-1 + 3*x-1*y-1 + 2*x-2*z-1 + x-1*y-2 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Polytope 1801
Image of polytope 1801 PALP id: 1801
grdb id: 236235
Integer points: [ 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 0 -1 0 -2 -2 -1 0 -1 0 -1]
[ 0 0 1 0 -1 1 1 0 1 1 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + x-1*y + y-1*z + x-1*z + 2*y-1 + x-1 + 2*x-1*y-1*z + x-1*z-1 + x-1*y-1 + x-1*y-2*z + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 48 1 Lattice Minkowski decompositions of facet 48
Polytope 1802
Image of polytope 1802 PALP id: 1802
grdb id: 235719
Integer points: [ 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 0 1 -2 1 -1 0 0 -1 0 -1]
[ 0 0 1 0 -1 1 0 1 1 1 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 y*z + x + y + z + x-1*y*z + x-1*y + 2*x-1*z + 2*y-1 + x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 47 1 Lattice Minkowski decompositions of facet 47
Polytope 1803
Image of polytope 1803 PALP id: 1803
grdb id: 236389
Integer points: [ 1 0 0 -1 0 -1 0 -2 -2 -1 -1 -1 0 0]
[ 0 1 0 1 -1 0 -1 0 -1 -1 0 -1 -1 0]
[ 0 0 1 0 -1 -1 1 -1 -1 0 0 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y + y-1*z + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-1
67 ? x + y + z + x-1*y + y-1*z + 2*y-1 + 3*x-1 + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1804
Image of polytope 1804 PALP id: 1804
grdb id: 236599
Integer points: [ 1 0 0 -1 1 -1 0 1 -1 1 0 0 0 -1]
[ 0 1 0 1 -1 0 1 -2 1 -1 0 0 -1 1]
[ 0 0 1 1 -1 0 1 0 -1 0 -1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 y*z + x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + x*y-2 + 2*y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1805
Image of polytope 1805 PALP id: 1805
grdb id: 236353
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 0 0 -1]
[ 0 1 0 -1 0 0 -2 -1 -2 -1 0 -1 0 -1]
[ 0 0 1 -1 -1 1 0 1 -1 0 0 0 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + x-1*z + 2*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1806
Image of polytope 1806 PALP id: 1806
grdb id: 236322
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 1 -1 -1 -2 -2 -1 0 0 -1 0]
[ 0 0 1 1 -1 -1 1 0 1 0 -1 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + y-1*z + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + 2*x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1807
Image of polytope 1807 PALP id: 1807
grdb id: 236580
Integer points: [ 1 0 0 0 -1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 1 0 -2 -1 -2 -1 0 -1 0 -1]
[ 0 0 1 -1 -1 -1 1 1 1 0 0 0 0 1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + 2*y-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + y-2*z + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1808
Image of polytope 1808 PALP id: 1808
grdb id: 236266
Integer points: [ 1 0 0 0 -1 0 -2 -1 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 0 -1 0 -2 -2 -1 -1 0 -1 0]
[ 0 0 0 1 -1 1 -1 1 1 1 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
103 ? x + y + z + y-1*z + y-1 + 2*x-1 + 2*x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z + x-2*z-1 + 2*x-2*y-1 + x-2*y-2*z
112 rank 3, number 15 x + y + z + y-1*z + y-1 + 2*x-1 + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z + x-2*z-1 + 2*x-2*y-1 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1809
Image of polytope 1809 PALP id: 1809
grdb id: 236272
Integer points: [ 1 0 0 0 -1 0 -1 -2 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 0 -1 0 -1 -1 -1 -1 0 -1 0]
[ 0 0 0 1 -1 1 1 -1 1 1 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
147 ? x + y + z + y-1*z + x-1*z + y-1 + 3*x-1 + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-2*y-1*z + 2*x-2*y-1 + x-2*y-1*z-1
112 rank 3, number 15 x + y + z + y-1*z + x-1*z + y-1 + 2*x-1 + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-2*y-1*z + 2*x-2*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1810
Image of polytope 1810 PALP id: 1810
grdb id: 236286
Integer points: [ 1 0 0 0 -1 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 0 -1 -1 0 -1 -1 -1 0 0 0]
[ 0 0 1 0 0 -1 1 -2 -2 0 -1 -1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + 2*z-1 + y-1 + x-1 + x-1*y-1*z + y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + x-1*z-2 + 3*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1811
Image of polytope 1811 PALP id: 1811
grdb id: 236421
Integer points: [ 1 0 0 0 0 -1 -2 -1 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 -1 0 0 -2 -2 -1 -1 0 -1 0]
[ 0 0 0 1 -1 -1 -1 -1 -1 0 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + y-1 + 2*x-1 + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + x-1*y-2*z-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
16 ? x + y + z + y-1 + 2*x-1 + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + x-2*z-1 + x-1*y-2*z-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1812
Image of polytope 1812 PALP id: 1812
grdb id: 236242
Integer points: [ 1 0 0 0 0 -1 -2 -1 -2 -1 -1 -1 0 0]
[ 0 1 0 0 1 0 -1 -2 -2 0 -1 -1 0 -1]
[ 0 0 1 -1 -1 1 1 0 1 0 0 1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + y*z-1 + x-1*z + z-1 + 2*y-1 + 2*x-1 + 2*x-1*y-1*z + 3*x-1*y-1 + x-2*y-1*z + x-1*y-2 + x-2*y-2*z
38 ? x + y + z + y*z-1 + x-1*z + z-1 + 2*y-1 + 2*x-1 + 2*x-1*y-1*z + 2*x-1*y-1 + x-2*y-1*z + x-1*y-2 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1813
Image of polytope 1813 PALP id: 1813
grdb id: 236452
Integer points: [ 1 0 0 0 0 -1 -1 -2 -2 -2 -1 -1 0 -1]
[ 0 1 -1 0 -1 0 -1 -1 -1 -1 0 -1 0 -1]
[ 0 0 0 1 -1 1 1 -1 1 0 0 0 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 8 1 none
Polytope 1814
Image of polytope 1814 PALP id: 1814
grdb id: 236280
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 -1 1 -1 -2 0 0 -1 0 -1]
[ 0 0 1 -1 1 -1 1 1 0 0 1 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? y*z + x + y + z + x-1*y*z + 2*x-1*z + z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + 2*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 1815
Image of polytope 1815 PALP id: 1815
grdb id: 236477
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 1 -1 1 -2 0 -1 0 0 -1]
[ 0 0 1 -1 -1 0 1 1 0 0 0 1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y*z + y*z-1 + x-1*y + 2*x-1*z + z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1816
Image of polytope 1816 PALP id: 1816
grdb id: 236554
Integer points: [ 1 0 0 0 0 1 -2 -1 -2 -1 0 0 -1 -1]
[ 0 1 0 0 -1 0 -1 -2 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 0 -1 0 -1 -1 0 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
55 rank 2, number 19 x + y + z + x*z-1 + z-1 + y-1 + 2*x-1 + 2*y-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + x-1*y-2*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1817
Image of polytope 1817 PALP id: 1817
grdb id: 236578
Integer points: [ 1 0 0 0 0 1 -1 -2 -2 -1 -1 0 -1 0]
[ 0 1 0 0 1 -1 1 0 -1 0 -1 -1 0 0]
[ 0 0 1 -1 -1 0 -1 -1 0 -1 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + y*z-1 + x*y-1 + z-1 + x-1*y*z-1 + 3*y-1 + x-1 + 2*x-1*z-1 + 3*x-1*y-1 + x-2*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1818
Image of polytope 1818 PALP id: 1818
grdb id: 236285
Integer points: [ 1 0 0 0 1 0 -1 -2 -2 -1 0 -1 0 -1]
[ 0 1 0 0 -1 -1 -1 0 -1 -1 -1 0 0 0]
[ 0 0 1 -1 0 1 1 -1 0 0 0 0 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x*y-1 + y-1*z + z-1 + 3*y-1 + x-1 + x-1*y-1*z + 2*x-1*z-1 + 3*x-1*y-1 + x-2*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1819
Image of polytope 1819 PALP id: 1819
grdb id: 236593
Integer points: [ 1 0 0 0 1 0 -1 1 -2 0 -1 1 0 -1]
[ 0 1 0 0 -1 -1 0 -2 1 -1 0 -1 0 1]
[ 0 0 1 -1 -1 1 1 0 0 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
109 ? x + y + z + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + x*y-1*z-1 + z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1820
Image of polytope 1820 PALP id: 1820
grdb id: 236194
Integer points: [ 1 0 0 1 -1 0 0 -1 -2 0 -1 0 0 -1]
[ 0 1 0 0 0 -1 -1 0 1 -1 0 0 0 1]
[ 0 0 1 -1 1 1 -1 -1 0 0 0 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + x*z-1 + 2*x-1*y + y-1*z + x-1*z + 2*z-1 + 2*y-1 + 3*x-1 + x-2*y + y-1*z-1 + x-1*z-1
52 rank 2, number 52 x + y + z + x*z-1 + 2*x-1*y + y-1*z + x-1*z + 2*z-1 + 2*y-1 + 2*x-1 + x-2*y + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1821
Image of polytope 1821 PALP id: 1821
grdb id: 236574
Integer points: [ 1 0 0 1 -1 1 0 -1 -2 -1 0 0 -1 0]
[ 0 1 0 -1 1 0 -1 -1 0 0 0 -1 0 0]
[ 0 0 1 0 0 -1 1 0 -1 0 0 0 -1 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + x*z-1 + x*y-1 + x-1*y + y-1*z + 3*z-1 + 2*y-1 + x-1 + 3*x-1*z-1 + x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1822
Image of polytope 1822 PALP id: 1822
grdb id: 236592
Integer points: [ 1 0 0 1 0 -1 1 -2 1 1 0 -1 0 -1]
[ 0 1 0 -1 0 1 0 1 -2 -1 0 1 -1 0]
[ 0 0 1 1 -1 -1 1 0 0 0 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? x*z + x + y + x*y-1*z + z + 2*x*y-1 + 2*x-1*y + z-1 + x-1*y*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1823
Image of polytope 1823 PALP id: 1823
grdb id: 236588
Integer points: [ 1 0 0 1 1 0 -1 0 -1 0 -1 -1 0 0]
[ 0 1 0 -1 -1 -1 0 -1 0 -1 0 0 0 0]
[ 0 0 1 1 0 1 1 -1 -2 0 0 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + x*y-1*z + z + x*y-1 + y-1*z + x-1*z + 2*z-1 + 2*y-1 + 3*x-1 + y-1*z-1 + 3*x-1*z-1 + x-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1824
Image of polytope 1824 PALP id: 1824
grdb id: 236258
Integer points: [ 1 0 1 -1 0 -2 -1 -1 -2 -1 -2 -1 0 0]
[ 0 1 -1 1 0 0 -1 -2 -2 -1 -1 0 -1 0]
[ 0 0 0 0 1 -1 -1 -1 -1 0 -1 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1825
Image of polytope 1825 PALP id: 1825
grdb id: 236465
Integer points: [ 1 0 1 -1 0 0 1 0 -2 -1 -1 0 0 -1]
[ 0 1 -1 1 0 -1 -1 -1 -1 -1 0 -1 0 -1]
[ 0 0 0 0 1 -1 1 1 -1 0 0 0 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1826
Image of polytope 1826 PALP id: 1826
grdb id: 236600
Integer points: [ 1 0 1 -1 0 1 0 -1 -1 -1 0 0 0 0]
[ 0 1 -1 1 0 1 -2 1 -1 0 1 0 -1 -1]
[ 0 0 0 0 1 -1 1 -1 0 0 -1 0 1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x*y*z-1 + x + y + z + 2*y*z-1 + x*y-1 + x-1*y + 2*y-1*z + x-1*y*z-1 + 2*y-1 + 2*x-1 + y-2*z + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1827
Image of polytope 1827 PALP id: 1827
grdb id: 236416
Integer points: [ 1 0 1 0 -1 0 -1 -2 -2 -1 0 -1 -1 0]
[ 0 1 -1 0 0 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 0 0 1 -1 1 1 0 1 0 0 1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + x*y-1 + y-1*z + x-1*z + 3*y-1 + x-1 + 2*x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-2*y-1*z + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1828
Image of polytope 1828 PALP id: 1828
grdb id: 236366
Integer points: [ 1 0 1 0 0 -2 0 -1 -2 0 -1 -1 0 -1]
[ 0 1 -1 0 -1 1 -1 0 1 -1 0 0 0 1]
[ 0 0 0 1 -1 0 1 1 -1 0 0 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + x*y-1 + 2*x-1*y + y-1*z + x-1*z + 2*y-1 + 3*x-1 + x-2*y + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1829
Image of polytope 1829 PALP id: 1829
grdb id: 236336
Integer points: [ 1 0 1 0 0 -1 -2 0 -2 0 -1 -1 0 -1]
[ 0 1 -1 0 -1 0 1 -2 0 -1 -1 0 0 1]
[ 0 0 0 1 -1 -1 0 -1 -1 0 -1 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
85 rank 3, number 8 x + y + z + x*y-1 + 2*x-1*y + 2*y-1 + 2*x-1 + x-2*y + y-1*z-1 + x-1*z-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1830
Image of polytope 1830 PALP id: 1830
grdb id: 236259
Integer points: [ 1 0 1 0 0 -1 -1 -2 -2 -1 0 -1 -1 0]
[ 0 1 -1 0 -1 0 0 -1 -1 -1 -1 -1 0 0]
[ 0 0 0 1 -1 -1 1 0 -1 0 0 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x*y-1 + x-1*z + 3*y-1 + x-1 + y-1*z-1 + x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1831
Image of polytope 1831 PALP id: 1831
grdb id: 236323
Integer points: [ 1 0 1 0 1 -2 1 0 -1 0 -1 0 0 -1]
[ 0 1 -1 0 -1 1 -2 -2 -1 -1 0 -1 0 1]
[ 0 0 0 1 -1 0 -1 -1 -1 0 0 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1832
Image of polytope 1832 PALP id: 1832
grdb id: 236598
Integer points: [ 1 0 0 -1 0 2 0 -2 2 1 1 0 -1 -1]
[ 0 1 -1 0 0 0 -1 1 -1 0 -1 0 1 0]
[ 0 0 0 0 1 1 1 -2 1 1 1 0 -1 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x2*z + x2*y-1*z + 2*x*z + x + y + 2*x*y-1*z + z + y-1*z + 2*x-1*y*z-1 + y-1 + x-1 + 2*x-1*z-1 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1833
Image of polytope 1833 PALP id: 1833
grdb id: 236550
Integer points: [ 1 0 0 0 -2 2 0 2 1 1 1 -1 0 -1]
[ 0 1 -1 0 1 -1 -1 -2 -2 -1 -1 0 0 1]
[ 0 0 0 1 0 -1 -1 -1 -1 0 -1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x2*y-1*z-1 + 2*x*y-1 + 2*x-1*y + x2*y-2*z-1 + 2*x*y-1*z-1 + y-1 + 2*x-1 + x-2*y + x*y-2*z-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1834
Image of polytope 1834 PALP id: 1834
grdb id: 236585
Integer points: [ 1 0 0 0 -1 -1 -1 0 -1 0 0 0 -1 0]
[ 0 1 0 0 0 2 1 -2 2 -1 0 1 1 -1]
[ 0 0 1 -1 0 -1 0 1 -2 1 0 -1 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + 2*y*z-1 + x-1*y2*z-1 + x-1*y + 2*y-1*z + x-1*y2*z-2 + z-1 + 2*x-1*y*z-1 + 2*y-1 + x-1 + y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1835
Image of polytope 1835 PALP id: 1835
grdb id: 236594
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 1 1 -1 -2 -1 0 0 -1 0]
[ 0 0 1 -1 0 0 -1 2 2 1 0 1 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + z-1 + x-1*y*z-1 + y-1 + 3*x-1 + 3*x-1*y-1*z + x-1*y-2*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1836
Image of polytope 1836 PALP id: 1836
grdb id: 236602
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 1 -1 -1 0 0 1 1 0 -1 0 1 0]
[ 0 0 2 -2 0 0 -1 1 0 -1 -1 0 1 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
109 ? y*z2 + 2*y*z + x + y + 2*z + x-1*y*z + x-1*y + 2*z-1 + y-1 + x-1 + 2*y-1*z-1 + x-1*z-1 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 1 4 irreducible and admissible
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Polytope 1837
Image of polytope 1837 PALP id: 1837
grdb id: 236224
Integer points: [ 1 0 -1 0 -1 -1 -1 0 -1 -1 -1 0 0 0]
[ 0 1 0 0 0 -2 -1 -2 -3 -2 -1 -1 0 -1]
[ 0 0 0 1 -1 0 1 1 1 1 0 1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
103 ? x + y + z + 2*y-1*z + 2*y-1 + x-1 + y-2*z + x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-2*z + x-1*y-2 + x-1*y-3*z
112 rank 3, number 15 x + y + z + 2*y-1*z + 2*y-1 + x-1 + y-2*z + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-2*z + x-1*y-2 + x-1*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1838
Image of polytope 1838 PALP id: 1838
grdb id: 235624
Integer points: [ 1 0 0 -1 -1 -1 -2 -3 -3 -2 -1 -2 0 -1]
[ 0 1 0 -1 1 1 -1 0 1 1 0 0 0 0]
[ 0 0 1 0 0 -1 -1 -2 -2 -1 0 -1 0 -1]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
87 ? x + y + z + x-1*y + x-1*y*z-1 + 3*x-1 + 2*x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1 + 4*x-2*z-1 + x-3*y*z-2 + x-2*y-1*z-1 + x-3*z-2
160 ? x + y + z + x-1*y + x-1*y*z-1 + 2*x-1 + 2*x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1 + 2*x-2*z-1 + x-3*y*z-2 + x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Polytope 1839
Image of polytope 1839 PALP id: 1839
grdb id: 235629
Integer points: [ 1 0 0 -1 -1 -1 -2 -3 -3 -2 -1 -1 0 -2]
[ 0 1 0 0 -1 0 -1 -2 -2 -1 0 -1 0 -1]
[ 0 0 1 -1 -1 1 1 0 -1 0 0 0 0 -1]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? x + y + z + x-1*z + 2*x-1 + x-1*z-1 + 2*x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + 2*x-2*y-1 + 2*x-2*y-1*z-1 + x-3*y-2 + x-3*y-2*z-1
126 ? x + y + z + x-1*z + 3*x-1 + x-1*z-1 + 2*x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + 4*x-2*y-1 + 2*x-2*y-1*z-1 + x-3*y-2 + x-3*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Polytope 1840
Image of polytope 1840 PALP id: 1840
grdb id: 236250
Integer points: [ 1 0 0 -1 -1 0 -1 -2 -3 -2 -2 -1 -1 0]
[ 0 1 0 0 -1 -1 0 -2 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 0 1 1 1 1 0 1 0 1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
111 ? x + y + z + y-1*z + x-1*z + 2*x-1 + 3*x-1*y-1*z + x-1*z-1 + x-1*y-1 + 2*x-2*y-1*z + 2*x-2*y-1 + x-2*y-2*z + x-3*y-2*z
37 rank 3, number 17 x + y + z + y-1*z + x-1*z + 2*x-1 + 2*x-1*y-1*z + x-1*z-1 + x-1*y-1 + 2*x-2*y-1*z + 2*x-2*y-1 + x-2*y-2*z + x-3*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1841
Image of polytope 1841 PALP id: 1841
grdb id: 236296
Integer points: [ 1 0 0 -1 0 -1 -1 -3 -3 -1 -2 -2 0 -1]
[ 0 1 -1 0 0 0 -2 -2 -3 -1 -2 -1 0 -1]
[ 0 0 0 0 1 -1 -1 -2 -2 0 -1 -1 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
28 rank 2, number 25 x + y + z + y-1 + x-1 + x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2*z-1 + 2*x-2*y-1*z-1 + 3*x-2*y-2*z-1 + x-3*y-2*z-2 + x-3*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1842
Image of polytope 1842 PALP id: 1842
grdb id: 236237
Integer points: [ 1 0 0 0 -1 -2 -2 -3 -3 -1 -1 -2 0 -1]
[ 0 1 -1 0 0 0 -2 -1 -2 -1 0 -1 0 -1]
[ 0 0 0 1 -1 -1 -1 -2 -2 0 0 -1 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + y-1 + 2*x-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + 3*x-2*y-1*z-1 + x-2*y-2*z-1 + x-3*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1843
Image of polytope 1843 PALP id: 1843
grdb id: 236397
Integer points: [ 1 0 0 0 -1 -2 0 -1 -3 -2 -1 -2 -1 0]
[ 0 1 -1 0 1 0 1 1 1 1 1 1 0 0]
[ 0 0 0 1 -1 -1 1 1 -1 0 0 -1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
147 ? y*z + x + y + z + x-1*y*z + 3*x-1*y + x-1*y*z-1 + y-1 + 3*x-1 + 2*x-2*y + 2*x-2*y*z-1 + x-2*z-1 + x-3*y*z-1
112 rank 3, number 15 y*z + x + y + z + x-1*y*z + 3*x-1*y + x-1*y*z-1 + y-1 + 2*x-1 + 2*x-2*y + 2*x-2*y*z-1 + x-2*z-1 + x-3*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1844
Image of polytope 1844 PALP id: 1844
grdb id: 236253
Integer points: [ 1 0 0 0 -1 -1 -1 -3 -3 -1 -2 -2 0 -1]
[ 0 1 -1 0 1 1 -1 0 1 0 0 1 0 0]
[ 0 0 0 1 0 -1 -1 -2 -2 0 -1 -1 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
29 rank 2, number 23 x + y + z + x-1*y + x-1*y*z-1 + y-1 + 3*x-1 + x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1*z-1 + 3*x-2*z-1 + x-3*y*z-2 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1845
Image of polytope 1845 PALP id: 1845
grdb id: 235643
Integer points: [ 1 0 0 0 -1 -1 -1 -3 -3 -2 -1 -2 0 -1]
[ 0 1 0 1 0 -1 1 -2 -1 0 0 -1 0 -1]
[ 0 0 1 1 -1 0 0 -2 -2 -1 0 -1 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
66 rank 2, number 24 y*z + x + y + z + x-1*y + 2*x-1 + x-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + 2*x-2*y-1*z-1 + x-3*y-1*z-2 + x-3*y-2*z-2
122 ? y*z + x + y + z + x-1*y + 4*x-1 + x-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + 3*x-2*y-1*z-1 + x-3*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Polytope 1846
Image of polytope 1846 PALP id: 1846
grdb id: 236262
Integer points: [ 1 0 0 0 -1 0 -2 -2 -3 -2 -1 -1 -1 0]
[ 0 1 -1 0 -1 1 -1 1 0 0 0 1 0 0]
[ 0 0 0 1 0 -1 -1 -2 -2 -1 0 -1 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + y*z-1 + 2*x-1*y*z-1 + y-1 + 3*x-1 + 2*x-1*z-1 + x-1*y-1 + x-2*y*z-2 + 3*x-2*z-1 + x-2*y-1*z-1 + x-3*z-2
144 rank 3, number 12 x + y + z + y*z-1 + 2*x-1*y*z-1 + y-1 + 3*x-1 + 3*x-1*z-1 + x-1*y-1 + x-2*y*z-2 + 3*x-2*z-1 + x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1847
Image of polytope 1847 PALP id: 1847
grdb id: 235606
Integer points: [ 1 0 0 0 -1 0 -2 -2 -3 -1 -2 -1 0 -1]
[ 0 1 -1 0 1 -1 1 -1 0 0 0 -1 0 0]
[ 0 0 0 1 0 1 -1 -1 -2 0 -1 0 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
159 ? x + y + z + x-1*y + y-1*z + y-1 + 4*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + 3*x-2*z-1 + x-2*y-1*z-1 + x-3*z-2
107 rank 3, number 11 x + y + z + x-1*y + y-1*z + y-1 + 2*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + 2*x-2*z-1 + x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Polytope 1848
Image of polytope 1848 PALP id: 1848
grdb id: 236548
Integer points: [ 1 0 0 0 -1 0 -1 -2 -2 0 -1 -1 0 -1]
[ 0 1 0 0 0 -1 -2 -2 -3 -1 -1 -2 0 -1]
[ 0 0 1 -1 0 1 0 1 1 0 0 1 0 1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
29 rank 2, number 23 x + y + z + y-1*z + z-1 + 2*y-1 + x-1 + 2*x-1*y-1*z + x-1*y-1 + 2*x-1*y-2*z + x-1*y-2 + x-2*y-2*z + x-2*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1849
Image of polytope 1849 PALP id: 1849
grdb id: 236213
Integer points: [ 1 0 0 0 0 -1 -2 -2 -3 -2 -1 -1 0 -1]
[ 0 1 -1 0 -1 -1 1 1 1 0 0 0 0 1]
[ 0 0 0 1 -1 -1 0 -1 -1 -1 0 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + 2*x-1*y + y-1 + 3*x-1 + x-2*y + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1*z-1 + 2*x-2*z-1 + x-3*y*z-1
107 rank 3, number 11 x + y + z + 2*x-1*y + y-1 + 2*x-1 + x-2*y + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1*z-1 + 2*x-2*z-1 + x-3*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1850
Image of polytope 1850 PALP id: 1850
grdb id: 236271
Integer points: [ 1 0 0 0 0 -1 -2 -2 -3 -1 -2 -1 -1 0]
[ 0 1 -1 0 1 -1 1 -1 0 1 0 0 0 0]
[ 0 0 0 1 -1 1 0 1 1 0 1 1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
66 rank 2, number 24 x + y + z + y*z-1 + 2*x-1*y + 3*x-1*z + y-1 + x-1 + x-2*y + x-1*y-1*z + 3*x-2*z + x-2*y-1*z + x-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1851
Image of polytope 1851 PALP id: 1851
grdb id: 236231
Integer points: [ 1 0 0 0 0 -1 -2 -2 -3 -2 -1 -1 0 -1]
[ 0 1 -1 0 1 1 0 1 1 1 0 1 0 0]
[ 0 0 0 1 -1 0 -1 -2 -2 -1 0 -1 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + y*z-1 + x-1*y + 2*x-1*y*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + 2*x-2*y*z-1 + x-2*y*z-2 + x-2*z-1 + x-3*y*z-2
16 ? x + y + z + y*z-1 + x-1*y + 3*x-1*y*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + 2*x-2*y*z-1 + x-2*y*z-2 + x-2*z-1 + x-3*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1852
Image of polytope 1852 PALP id: 1852
grdb id: 236551
Integer points: [ 1 0 0 0 0 -1 -2 -2 -3 -1 -1 -2 0 -1]
[ 0 1 0 0 -1 1 0 1 1 1 0 1 0 0]
[ 0 0 1 -1 0 1 1 0 1 0 0 1 0 1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + 2*x-2*y*z + z-1 + y-1 + x-1 + x-2*y + x-2*z + x-3*y*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1853
Image of polytope 1853 PALP id: 1853
grdb id: 236555
Integer points: [ 1 0 0 0 0 -1 -1 -2 -2 -1 -1 -1 0 0]
[ 0 1 0 0 -1 0 -2 -1 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 0 0 -2 -2 -3 -1 -2 -1 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + z-1 + y-1 + x-1 + 2*y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1*z-1 + 2*x-1*y-1*z-2 + x-1*y-2*z-2 + x-2*y-1*z-2 + x-2*y-2*z-3
16 ? x + y + z + z-1 + y-1 + x-1 + 2*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1*z-1 + 2*x-1*y-1*z-2 + x-1*y-2*z-2 + x-2*y-1*z-2 + x-2*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1854
Image of polytope 1854 PALP id: 1854
grdb id: 236595
Integer points: [ 1 0 1 -1 0 -1 1 -1 0 -1 0 0 0 0]
[ 0 1 -1 1 0 1 -2 -1 -3 0 -2 -1 -1 0]
[ 0 0 0 0 1 1 -1 -1 -2 0 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y*z + x*y-1 + x-1*y + 3*y-1 + 2*x-1 + x*y-2*z-1 + 2*y-1*z-1 + 3*y-2*z-1 + x-1*y-1*z-1 + y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1855
Image of polytope 1855 PALP id: 1855
grdb id: 245234
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 0 -1 -1 0]
[ 0 1 0 0 -1 -1 1 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 1 -1 -1 1 -1 0 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + y-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1856
Image of polytope 1856 PALP id: 1856
grdb id: 245021
Integer points: [ 1 0 0 -1 0 -1 -2 -1 -2 -1 -2 -1 -1 0]
[ 0 1 0 -1 1 0 -1 -1 -1 0 -1 0 -1 0]
[ 0 0 1 -1 1 -1 -1 1 1 1 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? y*z + x + y + z + 2*x-1*z + 3*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + 2*x-2*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1857
Image of polytope 1857 PALP id: 1857
grdb id: 244786
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 -1 0 -2 -2 -1 0 -1 0 -1]
[ 0 0 1 -1 1 -1 1 0 1 1 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? x + y + z + y-1*z + x-1*z + 2*y-1 + 2*x-1 + 2*x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 1858
Image of polytope 1858 PALP id: 1858
grdb id: 245022
Integer points: [ 1 0 0 0 -1 -1 -2 -1 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 1 0 0 -2 -2 -1 -1 0 -1 0]
[ 0 0 0 1 0 -1 -1 -1 -1 0 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + x-1*y + y-1 + 2*x-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + x-1*y-2*z-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1859
Image of polytope 1859 PALP id: 1859
grdb id: 242713
Integer points: [ 1 0 0 0 -1 -1 -1 -2 -2 -2 -2 -1 -1 0]
[ 0 1 -1 0 0 1 -1 1 -2 -1 0 -1 0 0]
[ 0 0 0 1 -1 0 -1 -1 -1 -1 -1 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? x + y + z + x-1*y + y-1 + 3*x-1 + x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + 3*x-2*z-1 + 3*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1860
Image of polytope 1860 PALP id: 1860
grdb id: 245700
Integer points: [ 1 0 0 0 -1 -1 -1 0 -1 -1 -1 0 0 0]
[ 0 1 0 -1 0 1 1 -1 0 0 0 -1 0 0]
[ 0 0 1 1 1 0 -1 -1 -2 0 -1 0 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + x-1*y + y-1*z + x-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + y-1*z-1 + 3*x-1*z-1 + x-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1861
Image of polytope 1861 PALP id: 1861
grdb id: 245758
Integer points: [ 1 0 0 0 -1 -1 -1 0 -1 0 -1 -1 0 0]
[ 0 1 0 0 1 0 -1 -2 -2 -1 0 -1 0 -1]
[ 0 0 1 -1 0 -1 0 -1 -1 0 0 -1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + x-1*y + z-1 + 2*y-1 + 2*x-1 + 2*y-1*z-1 + x-1*z-1 + x-1*y-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1862
Image of polytope 1862 PALP id: 1862
grdb id: 245344
Integer points: [ 1 0 0 0 -1 0 -1 -2 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 -1 -1 0 -1 -1 -1 -1 0 -1 0]
[ 0 0 0 1 -1 1 1 -1 1 1 0 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 1863
Image of polytope 1863 PALP id: 1863
grdb id: 245713
Integer points: [ 1 0 0 0 -1 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 -1 0 -2 -2 -1 0 -1 -1 0]
[ 0 0 1 -1 0 1 1 0 1 0 0 1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
88 ? x + y + z + x-1*y + y-1*z + x-1*z + z-1 + 2*y-1 + 3*x-1 + 2*x-1*y-1*z + 3*x-1*y-1 + x-1*y-2*z + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1864
Image of polytope 1864 PALP id: 1864
grdb id: 245247
Integer points: [ 1 0 0 0 0 -1 -1 -2 -2 -2 -1 -1 0 -1]
[ 0 1 -1 0 1 -1 1 1 -1 0 0 0 0 1]
[ 0 0 0 1 -1 0 0 -1 -1 -1 0 -1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + y*z-1 + x-1*y + 2*x-1*y*z-1 + y-1 + 3*x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + 2*x-2*z-1 + x-2*y-1*z-1
107 rank 3, number 11 x + y + z + y*z-1 + x-1*y + 2*x-1*y*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + 2*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1865
Image of polytope 1865 PALP id: 1865
grdb id: 245697
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 1 1 -1 -2 0 -1 0 -1 0]
[ 0 0 1 -1 1 0 -1 -1 0 -1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
85 rank 3, number 8 x + y + z + x-1*y + y-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + 2*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1866
Image of polytope 1866 PALP id: 1866
grdb id: 245712
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 1 1 -1 -2 0 -1 0 -1 0]
[ 0 0 1 -1 -1 0 -1 -1 0 -1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
85 rank 3, number 8 x + y + z + y*z-1 + x-1*y + z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + 2*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1867
Image of polytope 1867 PALP id: 1867
grdb id: 245168
Integer points: [ 1 0 0 0 0 -1 0 -1 -1 -1 -1 0 -1 0]
[ 0 1 0 0 -1 1 -1 -1 -1 0 -1 -1 0 0]
[ 0 0 1 -1 1 0 -1 0 -2 0 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y + y-1*z + z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + 2*x-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1868
Image of polytope 1868 PALP id: 1868
grdb id: 245226
Integer points: [ 1 0 1 -1 0 -1 1 -2 0 0 -1 -1 0 0]
[ 0 1 -1 1 0 0 -2 0 -2 -1 -1 0 -1 0]
[ 0 0 0 0 1 -1 -1 -1 -1 0 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x*y-1 + x-1*y + 2*y-1 + 2*x-1 + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1869
Image of polytope 1869 PALP id: 1869
grdb id: 242735
Integer points: [ 1 0 0 0 -1 -1 0 -1 -3 -2 -1 -2 -1 0]
[ 0 1 -1 0 0 1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 0 1 -1 0 1 -1 -2 -1 0 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + x-1*y + y-1*z + y-1 + 3*x-1 + x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + 2*x-2*z-1 + 3*x-2*y-1*z-1 + x-3*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1870
Image of polytope 1870 PALP id: 1870
grdb id: 669490
Integer points: [ 1 0 0 1 -1 0 1 1 0 -1 0 -1 0 0]
[ 0 1 0 -1 1 0 -1 -2 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 1 -1 0 -1 -1 -1 0 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
35 rank 2, number 15 x + y + z + x-1*y*z + x*y-1 + x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + x*y-2*z-1 + y-1*z-1 + y-2*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1871
Image of polytope 1871 PALP id: 1871
grdb id: 669468
Integer points: [ 1 0 1 -1 0 0 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 1 0 -1 -1 0 -1 -1 -1 0 -1 0]
[ 0 0 0 0 1 -1 1 1 -1 1 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1872
Image of polytope 1872 PALP id: 1872
grdb id: 669437
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -1 -1 0 -2 -2 -1 -1 0 -1 0]
[ 0 0 1 0 -1 -1 1 0 -1 1 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + x-1*y + x-1*z + 2*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + x-1*y-1 + x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 51 1 Lattice Minkowski decompositions of facet 51
Polytope 1873
Image of polytope 1873 PALP id: 1873
grdb id: 669485
Integer points: [ 1 0 0 -1 0 0 -1 -2 -1 1 -1 0 0 1]
[ 0 1 0 1 0 -1 0 1 1 -2 0 -1 0 -1]
[ 0 0 1 1 -1 0 1 1 0 -2 0 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y*z + x-1*y + x-1*z + x-2*y*z + 2*x*y-1*z-1 + z-1 + y-1 + 3*x-1 + 3*y-1*z-1 + x*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Polytope 1874
Image of polytope 1874 PALP id: 1874
grdb id: 669448
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 0 0 -1 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 0 -1 1 -1 1 0 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
55 rank 2, number 19 x + y + z + x-1*y + x-1*z + z-1 + 2*y-1 + x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 50 1 Lattice Minkowski decompositions of facet 50
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1875
Image of polytope 1875 PALP id: 1875
grdb id: 669445
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 1 0 -1 1 0 -2 0 -1 0 -1]
[ 0 0 1 -1 0 -1 1 -1 1 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
60 rank 2, number 18 x + y + z + y*z-1 + x-1*y + x-1*z + x-1*y*z-1 + 2*y-1 + x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 51 1 Lattice Minkowski decompositions of facet 51
Polytope 1876
Image of polytope 1876 PALP id: 1876
grdb id: 669474
Integer points: [ 1 0 0 0 0 0 -1 -1 -2 -2 -1 -1 -1 0]
[ 0 1 0 0 -1 1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 0 1 -1 1 0 1 0 0 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
55 rank 2, number 19 y*z + x + y + z + 2*x-1*z + z-1 + y-1 + 2*x-1 + x-1*y-1*z + x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1877
Image of polytope 1877 PALP id: 1877
grdb id: 669486
Integer points: [ 1 0 0 0 0 1 1 -2 -1 0 1 -1 0 -1]
[ 0 1 0 0 -1 -1 -1 1 0 -1 -1 0 0 1]
[ 0 0 1 -1 0 -1 1 0 1 1 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + x*y-1*z + z + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + x*y-1*z-1 + z-1 + y-1 + 2*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 1 2 irreducible and admissible
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Polytope 1878
Image of polytope 1878 PALP id: 1878
grdb id: 669466
Integer points: [ 1 0 1 0 -1 -1 0 -2 -1 -2 -1 0 -1 0]
[ 0 1 -1 0 1 0 -1 0 -1 -1 -1 -1 0 0]
[ 0 0 0 1 -1 -1 1 -1 1 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x*y-1 + y-1*z + x-1*y*z-1 + 3*y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-2*z-1 + x-2*y-1
85 rank 3, number 8 x + y + z + x*y-1 + y-1*z + x-1*y*z-1 + 3*y-1 + 3*x-1 + x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-2*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Polytope 1879
Image of polytope 1879 PALP id: 1879
grdb id: 669463
Integer points: [ 1 0 1 0 -1 1 0 -2 -1 -2 0 -1 0 -1]
[ 0 1 -1 0 1 -2 -1 1 0 1 -1 0 0 1]
[ 0 0 0 1 1 -1 -1 0 1 1 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + x-1*y*z + x*y-1 + 2*x-1*y + x-1*z + x-2*y*z + 2*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + y-1*z-1
17 rank 1, V22 x + y + z + x-1*y*z + x*y-1 + 2*x-1*y + x-1*z + x-2*y*z + 2*y-1 + 2*x-1 + x-2*y + x*y-2*z-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1880
Image of polytope 1880 PALP id: 1880
grdb id: 672834
Integer points: [ 1 0 0 -1 0 -1 0 -1 -1 -1 -1 0 -1 0]
[ 0 1 0 1 -1 0 -1 0 -1 -1 -1 -1 0 0]
[ 0 0 1 0 -1 -1 1 1 -1 1 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + x-1*y + y-1*z + x-1*z + 2*y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
46 ? x + y + z + x-1*y + y-1*z + x-1*z + 2*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1881
Image of polytope 1881 PALP id: 1881
grdb id: 672698
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 0 1 -1 1 -1 -1 0 0 0]
[ 0 0 1 -1 0 1 0 1 -1 -1 0 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + x-1*y + x-1*z + z-1 + x-1*y*z-1 + y-1 + 3*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 1882
Image of polytope 1882 PALP id: 1882
grdb id: 672912
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 -1 0 -1 0]
[ 0 1 0 0 -1 -1 1 1 0 0 0 -1 1 0]
[ 0 0 1 -1 1 -1 -1 1 1 -1 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + x-1*y*z + 2*x-1*y + y-1*z + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1883
Image of polytope 1883 PALP id: 1883
grdb id: 672884
Integer points: [ 1 0 0 0 0 1 1 -1 -1 0 0 -1 0 0]
[ 0 1 0 1 -1 -1 -1 0 0 -1 -1 0 0 0]
[ 0 0 1 -1 1 1 0 1 -1 -1 0 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + x*y-1*z + z + y*z-1 + x*y-1 + y-1*z + x-1*z + 2*z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1884
Image of polytope 1884 PALP id: 1884
grdb id: 672737
Integer points: [ 1 0 0 0 0 1 1 -1 -1 1 0 0 0 -1]
[ 0 1 0 1 -1 0 -1 -1 1 -1 -1 0 0 0]
[ 0 0 1 -1 1 -1 0 1 -1 -1 0 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + x*z-1 + y*z-1 + x*y-1 + y-1*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1885
Image of polytope 1885 PALP id: 1885
grdb id: 672886
Integer points: [ 1 0 0 1 -1 0 1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 1 0 -1 0 -1 -1 0 -1 -1 0]
[ 0 0 1 -1 1 -1 0 1 0 -1 0 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y*z + x*y-1 + x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + 2*y-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1886
Image of polytope 1886 PALP id: 1886
grdb id: 672906
Integer points: [ 1 0 0 1 0 -1 -1 0 -1 -1 0 -1 0 0]
[ 0 1 0 0 -1 1 -1 -1 0 -1 -1 0 0 0]
[ 0 0 1 -1 1 0 0 -1 -1 -1 0 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*z-1 + x-1*y + y-1*z + 2*z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 11 6 Lattice Minkowski decompositions of facet 11
Polytope 1887
Image of polytope 1887 PALP id: 1887
grdb id: 672861
Integer points: [ 1 0 0 1 1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 -1 0 1 1 -1 0 0 0 0 -1]
[ 0 0 1 -1 0 1 0 1 0 -1 0 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + x-1*y*z + x*z-1 + x*y-1 + x-1*y + x-1*z + 2*z-1 + 2*y-1 + x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1888
Image of polytope 1888 PALP id: 1888
grdb id: 672877
Integer points: [ 1 0 0 1 -1 0 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 0 -1 -1 0 -1 -1 0 -1 0 0]
[ 0 0 1 -1 1 0 1 -1 0 2 0 1 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*z-1 + y-1*z + x-1*z + x-1*y-1*z2 + 2*z-1 + y-1 + 2*x-1 + 2*x-1*y-1*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1889
Image of polytope 1889 PALP id: 1889
grdb id: 672831
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -2 -2 -2 -1 -1 0]
[ 0 1 -1 0 0 -1 0 -1 -1 -1 -1 0 -1 0]
[ 0 0 0 1 -1 -1 1 1 -1 1 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
147 ? x + y + z + x-1*z + y-1 + 3*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + 2*x-2*y-1 + x-2*y-1*z-1
145 ? x + y + z + x-1*z + y-1 + 3*x-1 + x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + 2*x-2*y-1 + x-2*y-1*z-1
103 ? x + y + z + x-1*z + y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + 2*x-2*y-1 + x-2*y-1*z-1
112 rank 3, number 15 x + y + z + x-1*z + y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + 2*x-2*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 23 2 Lattice Minkowski decompositions of facet 23
Polytope 1890
Image of polytope 1890 PALP id: 1890
grdb id: 672704
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 1 1 0 0 -2 -1 0 -1 0]
[ 0 0 0 1 -1 0 1 -1 1 -1 0 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y*z + x-1*y + x-1*z + y-1 + 3*x-1 + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1891
Image of polytope 1891 PALP id: 1891
grdb id: 672641
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 0 -1 0 -1 -2 0 -1 0 -1]
[ 0 0 1 -1 -1 1 1 -1 -1 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + y*z-1 + x-1*z + z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
36 rank 3, number 7 x + y + z + y*z-1 + x-1*z + z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1892
Image of polytope 1892 PALP id: 1892
grdb id: 672913
Integer points: [ 1 0 0 0 0 0 -1 -2 -1 -2 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 0 -1 -2 -2 0 -1 -1 0]
[ 0 0 1 -1 0 1 -1 0 1 1 0 0 1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + y-1*z + z-1 + y-1 + 2*x-1 + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z + x-2*y-1 + x-2*y-2*z
144 rank 3, number 12 x + y + z + y-1*z + z-1 + y-1 + 2*x-1 + 2*x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z + x-2*y-1 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1893
Image of polytope 1893 PALP id: 1893
grdb id: 672826
Integer points: [ 1 0 0 0 0 0 -1 -1 -2 -2 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 0 1 -1 0 1 1 -1 0 1 1 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + y-1*z + x-1*z + z-1 + y-1 + 2*x-1 + 2*x-1*y-1*z + 2*x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + x-2*y-1
144 rank 3, number 12 x + y + z + y-1*z + x-1*z + z-1 + y-1 + 2*x-1 + 2*x-1*y-1*z + 3*x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1894
Image of polytope 1894 PALP id: 1894
grdb id: 672796
Integer points: [ 1 0 0 0 0 0 -1 -1 -2 -2 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 1 -1 0 -1 -1 0 0 0]
[ 0 0 1 -1 0 -1 0 1 1 1 0 0 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y + 2*x-1*z + z-1 + y-1 + 2*x-1 + x-1*y-1*z + x-2*z + y-1*z-1 + 2*x-1*y-1 + x-2*y-1*z
67 ? x + y + z + x-1*y + 2*x-1*z + z-1 + y-1 + 3*x-1 + x-1*y-1*z + x-2*z + y-1*z-1 + 2*x-1*y-1 + x-2*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1895
Image of polytope 1895 PALP id: 1895
grdb id: 672899
Integer points: [ 1 0 0 0 0 0 -1 -1 -2 -2 -1 -1 -1 0]
[ 0 1 0 0 -1 1 -1 1 1 0 0 0 1 0]
[ 0 0 1 -1 0 1 -1 1 0 -1 0 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? y*z + x + y + z + x-1*y*z + 2*x-1*y + z-1 + y-1 + 2*x-1 + x-2*y + 2*x-1*z-1 + x-1*y-1*z-1 + x-2*z-1
67 ? y*z + x + y + z + x-1*y*z + 2*x-1*y + z-1 + y-1 + 3*x-1 + x-2*y + 2*x-1*z-1 + x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1896
Image of polytope 1896 PALP id: 1896
grdb id: 672736
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 1 0 0 -2 -1 -1 0 0]
[ 0 0 1 -1 0 1 0 1 -1 1 0 1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y + y-1*z + x-1*z + z-1 + y-1 + 2*x-1 + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 1897
Image of polytope 1897 PALP id: 1897
grdb id: 672700
Integer points: [ 1 0 0 1 -1 0 -1 1 -1 1 0 0 0 -1]
[ 0 1 0 -1 1 0 0 -1 0 -2 -1 -1 0 0]
[ 0 0 1 0 0 -1 1 -1 -1 -1 0 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*y-1 + x-1*y + x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1898
Image of polytope 1898 PALP id: 1898
grdb id: 672887
Integer points: [ 1 0 0 1 -1 0 1 0 -1 -2 0 -1 -1 0]
[ 0 1 0 -1 1 0 -1 -1 -1 0 -1 0 0 0]
[ 0 0 1 0 0 -1 -1 1 1 1 0 0 1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*y-1 + x-1*y + y-1*z + 2*x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1899
Image of polytope 1899 PALP id: 1899
grdb id: 672867
Integer points: [ 1 0 0 1 0 -1 -1 0 -1 -1 -1 -1 0 0]
[ 0 1 0 0 0 0 1 -1 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 -1 1 0 -1 1 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + x*z-1 + x-1*y + x-1*z + z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Polytope 1900
Image of polytope 1900 PALP id: 1900
grdb id: 672881
Integer points: [ 1 0 0 1 0 -1 -1 0 -1 -1 0 -1 -1 0]
[ 0 1 0 0 0 0 1 -1 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 -1 1 0 1 0 1 0 0 1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*z-1 + x-1*y + y-1*z + x-1*z + z-1 + 2*y-1 + 2*x-1 + 2*x-1*y-1*z + x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1901
Image of polytope 1901 PALP id: 1901
grdb id: 672795
Integer points: [ 1 0 1 -1 0 -1 -1 -2 -1 -2 -2 -1 0 0]
[ 0 1 -1 1 0 0 -1 1 -1 -1 0 0 -1 0]
[ 0 0 0 0 1 -1 0 -1 -1 -1 -1 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + x*y-1 + x-1*y + 2*y-1 + 2*x-1 + x-1*z-1 + x-2*y*z-1 + x-1*y-1 + x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1*z-1
88 ? x + y + z + x*y-1 + x-1*y + 2*y-1 + 3*x-1 + x-1*z-1 + x-2*y*z-1 + x-1*y-1 + x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1902
Image of polytope 1902 PALP id: 1902
grdb id: 672679
Integer points: [ 1 0 1 -1 0 -1 1 -2 0 -2 -1 -1 0 0]
[ 0 1 -1 1 0 -1 -1 0 -1 -1 -1 0 -1 0]
[ 0 0 0 0 1 -1 1 -1 1 -1 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
88 ? x + y + x*y-1*z + z + x*y-1 + x-1*y + y-1*z + 3*y-1 + 2*x-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-1
67 ? x + y + x*y-1*z + z + x*y-1 + x-1*y + y-1*z + 2*y-1 + 2*x-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-1
81 ? x + y + x*y-1*z + z + x*y-1 + x-1*y + y-1*z + 3*y-1 + 3*x-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-1
88 ? x + y + x*y-1*z + z + x*y-1 + x-1*y + y-1*z + 2*y-1 + 3*x-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 23 2 Lattice Minkowski decompositions of facet 23
Polytope 1903
Image of polytope 1903 PALP id: 1903
grdb id: 672908
Integer points: [ 1 0 1 -1 0 -1 1 -1 0 -1 -1 0 0 0]
[ 0 1 -1 1 0 1 -2 0 -2 -1 0 -1 -1 0]
[ 0 0 0 0 1 1 -1 -1 -1 -1 0 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + x-1*y*z + x*y-1 + x-1*y + 2*y-1 + 2*x-1 + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1 + y-2*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1904
Image of polytope 1904 PALP id: 1904
grdb id: 672916
Integer points: [ 1 0 1 -1 0 0 -1 -1 -2 -2 -1 0 -1 0]
[ 0 1 -1 1 0 -1 0 -1 0 -1 0 -1 -1 0]
[ 0 0 0 0 1 -1 -1 0 -1 -1 0 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x*y-1 + x-1*y + 2*y-1 + x-1 + y-1*z-1 + x-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1905
Image of polytope 1905 PALP id: 1905
grdb id: 672892
Integer points: [ 1 0 1 0 0 -1 -1 -1 -2 -2 -1 0 -1 0]
[ 0 1 -1 0 0 1 1 -1 1 0 0 0 0 -1]
[ 0 0 0 1 -1 0 -1 0 -1 -1 0 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x*y-1 + x-1*y + z-1 + x-1*y*z-1 + 2*y-1 + x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1906
Image of polytope 1906 PALP id: 1906
grdb id: 672909
Integer points: [ 1 0 1 0 0 -1 1 0 -1 -2 0 -1 0 -1]
[ 0 1 -1 0 0 1 -1 -1 -1 0 -1 0 0 0]
[ 0 0 0 1 -1 0 -1 -1 0 1 0 0 0 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + x*y-1 + x-1*y + 2*x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + x-1 + x-2*z + y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1907
Image of polytope 1907 PALP id: 1907
grdb id: 672880
Integer points: [ 1 0 1 0 0 0 -1 0 -2 -2 -1 -1 0 -1]
[ 0 1 -1 0 -1 0 1 -1 1 1 0 1 0 0]
[ 0 0 0 1 0 -1 0 1 -1 -2 0 -1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + x*y-1 + x-1*y + y-1*z + z-1 + 2*x-1*y*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1908
Image of polytope 1908 PALP id: 1908
grdb id: 672614
Integer points: [ 1 0 1 0 0 0 0 -1 -1 -2 0 -1 0 -1]
[ 0 1 -1 0 0 -1 -1 0 0 1 -1 0 0 1]
[ 0 0 0 1 -1 -1 1 1 -1 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
94 ? x + y + z + x*y-1 + 2*x-1*y + y-1*z + x-1*z + z-1 + 2*y-1 + 3*x-1 + x-2*y + y-1*z-1 + x-1*z-1
146 ? x + y + z + x*y-1 + 2*x-1*y + y-1*z + x-1*z + z-1 + 2*y-1 + 2*x-1 + x-2*y + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1909
Image of polytope 1909 PALP id: 1909
grdb id: 671849
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 1 1 0 -1 -1 -1 0 0 0]
[ 0 0 0 1 1 0 -1 1 -1 1 0 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y + y-1*z + x-1*z + x-1*y*z-1 + y-1 + 3*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1910
Image of polytope 1910 PALP id: 1910
grdb id: 672420
Integer points: [ 1 0 0 0 0 -1 -1 -1 0 -1 -1 0 0 0]
[ 0 1 0 1 -1 1 0 1 -1 0 0 -1 0 0]
[ 0 0 1 -1 1 0 1 -1 -1 -1 0 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + y*z-1 + x-1*y + y-1*z + x-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1911
Image of polytope 1911 PALP id: 1911
grdb id: 672298
Integer points: [ 1 0 0 0 0 -1 -1 0 -1 -1 0 -1 -1 0]
[ 0 1 0 0 -1 1 1 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 1 0 -1 -1 0 -1 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*y + y-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + 2*x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1912
Image of polytope 1912 PALP id: 1912
grdb id: 672425
Integer points: [ 1 0 0 1 -1 0 -1 0 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 1 0 1 -1 -1 -1 0 0 -1 0]
[ 0 0 1 0 0 -1 -1 -1 0 -1 -1 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
85 rank 3, number 8 x + y + z + x*y-1 + x-1*y + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + 2*x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1913
Image of polytope 1913 PALP id: 1913
grdb id: 672076
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -2 -2 -2 -1 -1 0]
[ 0 1 -1 0 -1 1 1 -1 -1 1 0 0 0 0]
[ 0 0 0 1 0 0 -1 -1 -1 -1 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + x-1*y + x-1*y*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1*z-1
122 ? x + y + z + x-1*y + x-1*y*z-1 + y-1 + 3*x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1914
Image of polytope 1914 PALP id: 1914
grdb id: 671908
Integer points: [ 1 0 0 0 -1 -1 0 -1 -2 -2 -1 -2 -1 0]
[ 0 1 -1 0 0 1 -1 -1 1 -1 -1 0 0 0]
[ 0 0 0 1 -1 0 1 -1 -1 -1 0 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + x-1*y + y-1*z + y-1 + 3*x-1 + x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 1915
Image of polytope 1915 PALP id: 1915
grdb id: 671859
Integer points: [ 1 0 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 1 0 -1 1 0 -2 -1 -1 0 0]
[ 0 0 0 1 -1 -1 1 0 1 1 0 1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + x-1*y + y-1*z + x-1*z + x-1*y*z-1 + y-1 + 3*x-1 + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 1916
Image of polytope 1916 PALP id: 1916
grdb id: 672378
Integer points: [ 1 0 0 0 0 -1 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 0 -1 0 -1 -1 -1 -1 0 0]
[ 0 0 1 -1 0 1 -1 -1 1 -2 0 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*z + z-1 + y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 1917
Image of polytope 1917 PALP id: 1917
grdb id: 672302
Integer points: [ 1 0 0 0 0 0 -1 -1 -2 -2 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 0 0 -1 -1 0 -1 -1 0]
[ 0 0 1 -1 0 1 -1 1 0 1 0 0 1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + y-1*z + x-1*z + z-1 + y-1 + x-1 + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-2*y-1*z + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1918
Image of polytope 1918 PALP id: 1918
grdb id: 672371
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 0 -1 0 0 -2 -2 -1 -1 0 -1]
[ 0 0 1 -1 -1 1 0 1 1 0 0 1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + y*z-1 + y-1*z + x-1*z + z-1 + 2*y-1 + x-1 + 2*x-1*y-1*z + 2*x-1*y-1 + x-1*y-2*z + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1919
Image of polytope 1919 PALP id: 1919
grdb id: 671936
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -3 -2 -1 -2 0]
[ 0 1 -1 0 -1 1 0 1 -1 1 1 0 0 0]
[ 0 0 0 1 1 -1 -1 0 0 -2 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + x-1*y + y-1*z + x-1*y*z-1 + y-1 + 3*x-1 + x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1 + 2*x-2*z-1 + x-3*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 1920
Image of polytope 1920 PALP id: 1920
grdb id: 670988
Integer points: [ 1 0 0 0 0 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 0 -1 0 -1 -1 -1 0 -1 0]
[ 0 0 1 -1 -1 -1 1 1 -1 1 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + y-1*z + x-1*z + z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1921
Image of polytope 1921 PALP id: 1921
grdb id: 670863
Integer points: [ 1 0 0 0 0 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 1 -1 -1 0 1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 1 0 -1 -1 1 -1 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + y*z-1 + y-1*z + z-1 + x-1*y*z-1 + y-1 + 2*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 1922
Image of polytope 1922 PALP id: 1922
grdb id: 61366
Integer points: [ 1 0 0 0 0 1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 -1 1 0 0 -1 -1 0 -1 0]
[ 0 0 1 -1 0 -1 0 1 -1 0 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
60 rank 2, number 18 x + y + z + x-1*y + x-1*z + x*y-1*z-1 + z-1 + y-1 + x-1 + 2*y-1*z-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 3 5 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1923
Image of polytope 1923 PALP id: 1923
grdb id: 61815
Integer points: [ 1 0 0 1 0 0 -1 0 1 1 -1 -1 0 0]
[ 0 1 0 -1 1 -1 1 0 1 0 -1 0 -1 0]
[ 0 0 1 0 -1 1 0 -1 -1 -1 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x*y*z-1 + x + y + z + x*z-1 + y*z-1 + x*y-1 + x-1*y + y-1*z + z-1 + 2*y-1 + 2*x-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 5 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 1924
Image of polytope 1924 PALP id: 1924
grdb id: 61810
Integer points: [ 1 0 1 -1 0 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 1 0 1 -1 0 -1 0 -1 0 -1 0]
[ 0 0 0 0 1 -1 1 -1 0 1 1 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
85 rank 3, number 8 x + y + z + x*y-1 + x-1*y + y-1*z + x-1*z + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
36 rank 3, number 7 x + y + z + x*y-1 + x-1*y + y-1*z + x-1*z + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Polytope 1925
Image of polytope 1925 PALP id: 1925
grdb id: 61813
Integer points: [ 1 0 1 0 -1 0 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 1 0 1 0 1 0 -1 0 -1 0]
[ 0 0 0 1 0 -1 -1 1 -1 -1 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + y*z-1 + x*y-1 + x-1*y + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1926
Image of polytope 1926 PALP id: 1926
grdb id: 61811
Integer points: [ 1 0 1 0 0 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 0 1 -1 0 0 -1 -1 0 -1 0]
[ 0 0 0 1 -1 0 1 -1 1 0 1 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x*y-1 + x-1*y + y-1*z + x-1*z + z-1 + 2*y-1 + x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1927
Image of polytope 1927 PALP id: 1927
grdb id: 61752
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 1 0 0 -1 -1 -1 0 0]
[ 0 0 1 -1 0 1 0 -1 1 -1 1 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y + y-1*z + x-1*z + z-1 + y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
67 ? x + y + z + x-1*y + y-1*z + x-1*z + z-1 + y-1 + 3*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 1928
Image of polytope 1928 PALP id: 1928
grdb id: 61779
Integer points: [ 1 0 0 1 -1 0 0 -1 1 0 -1 0 -1 0]
[ 0 1 0 -1 1 0 -1 0 -1 -1 0 -1 0 0]
[ 0 0 1 0 0 -1 1 1 -1 -1 -1 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*y-1 + x-1*y + y-1*z + x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 5 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1929
Image of polytope 1929 PALP id: 1929
grdb id: 61780
Integer points: [ 1 0 0 1 0 -1 -1 0 -1 0 -1 0 -1 0]
[ 0 1 0 0 0 0 1 -1 -1 -1 -1 -1 0 0]
[ 0 0 1 -1 -1 1 0 1 1 -1 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*z-1 + x-1*y + y-1*z + x-1*z + z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Polytope 1930
Image of polytope 1930 PALP id: 1930
grdb id: 61802
Integer points: [ 1 0 0 1 1 -1 0 -1 0 -1 -1 0 -1 0]
[ 0 1 0 0 -1 1 0 0 -1 -1 -1 -1 0 0]
[ 0 0 1 -1 0 0 -1 1 1 1 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + x*z-1 + x*y-1 + x-1*y + y-1*z + x-1*z + z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 1931
Image of polytope 1931 PALP id: 1931
grdb id: 61766
Integer points: [ 1 0 0 1 1 0 -1 -1 0 -1 -1 -1 0 0]
[ 0 1 0 0 -1 -1 1 0 -1 1 0 0 0 0]
[ 0 0 1 -1 0 0 0 1 1 1 -1 0 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y*z + x*z-1 + x*y-1 + x-1*y + y-1*z + x-1*z + 2*z-1 + y-1 + 2*x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Polytope 1932
Image of polytope 1932 PALP id: 1932
grdb id: 61797
Integer points: [ 1 0 1 -1 0 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 1 0 -1 1 0 -1 0 -1 0 -1 0]
[ 0 0 0 0 1 -1 1 -1 0 1 -1 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*y*z + x*y-1 + x-1*y + x-1*z + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
85 rank 3, number 8 x + y + z + x-1*y*z + x*y-1 + x-1*y + x-1*z + 2*y-1 + 3*x-1 + y-1*z-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Polytope 1933
Image of polytope 1933 PALP id: 1933
grdb id: 61769
Integer points: [ 1 0 0 0 0 -1 -1 0 -2 -1 -2 -1 -1 0]
[ 0 1 0 0 -1 0 0 -1 -1 -2 -2 -1 -1 0]
[ 0 0 1 -1 0 0 -1 -1 -1 -1 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + z-1 + y-1 + x-1 + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2*z-1 + x-2*y-1*z-1 + x-2*y-2*z-1
50 ? x + y + z + z-1 + y-1 + x-1 + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1 + x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Polytope 1934
Image of polytope 1934 PALP id: 1934
grdb id: 61770
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -2 -2 -1 -1 0]
[ 0 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 0 1 -1 0 -1 1 -1 1 0 1 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + x-1*z + z-1 + y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + 3*x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + x-2*y-1
8 ? x + y + z + x-1*z + z-1 + y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + 2*x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Polytope 1935
Image of polytope 1935 PALP id: 1935
grdb id: 61793
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -2 -2 -1 -1 0]
[ 0 1 0 0 -1 -1 1 0 0 1 1 0 1 0]
[ 0 0 1 -1 0 -1 1 1 -1 0 1 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y*z + 2*x-1*y + x-1*z + x-2*y*z + z-1 + y-1 + 2*x-1 + x-2*y + y-1*z-1 + x-1*z-1
67 ? x + y + z + x-1*y*z + 2*x-1*y + x-1*z + x-2*y*z + z-1 + y-1 + 3*x-1 + x-2*y + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Polytope 1936
Image of polytope 1936 PALP id: 1936
grdb id: 61803
Integer points: [ 1 0 1 0 0 0 0 0 -1 -1 -2 -1 -1 0]
[ 0 1 -1 0 1 -1 -1 0 1 0 1 0 1 0]
[ 0 0 0 1 -1 1 0 -1 0 -1 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + y*z-1 + x*y-1 + x-1*y + y-1*z + z-1 + 2*x-1*y*z-1 + y-1 + 2*x-1 + x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Polytope 1937
Image of polytope 1937 PALP id: 1937
grdb id: 61725
Integer points: [ 1 0 0 -1 1 -1 1 0 0 -1 -1 -1 0 0]
[ 0 1 0 1 -1 1 -1 0 -1 0 -1 0 -1 0]
[ 0 0 1 1 0 0 -1 -1 -1 1 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + x-1*y*z + x*y-1 + x-1*y + x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Polytope 1938
Image of polytope 1938 PALP id: 1938
grdb id: 61687
Integer points: [ 1 0 0 0 0 0 0 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 1 -1 -1 0 0 -1 0 -1 -1 0 0]
[ 0 0 1 -1 1 0 -1 1 1 -1 -1 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + y*z-1 + y-1*z + x-1*z + z-1 + y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1939
Image of polytope 1939 PALP id: 1939
grdb id: 12641
Integer points: [ 1 0 0 -1 1 -1 0 -1 1 0 1 -1 0 0]
[ 0 1 0 1 0 0 -1 0 -1 0 -1 -1 -1 0]
[ 0 0 1 1 -1 1 0 0 -1 -1 -2 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + x-1*y*z + x*z-1 + x-1*z + x*y-1*z-1 + z-1 + y-1 + x-1 + x*y-1*z-2 + 2*y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 7 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1940
Image of polytope 1940 PALP id: 1940
grdb id: 12636
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 0 -1 0 -1 1 1 0 0]
[ 0 0 1 -1 0 1 -1 0 1 -1 0 1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? y*z + x + y + z + x-1*y*z + x-1*y + x-1*z + z-1 + y-1 + 2*x-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
67 ? y*z + x + y + z + x-1*y*z + x-1*y + x-1*z + z-1 + y-1 + 3*x-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 3 5 Lattice Minkowski decompositions of facet 3
Polytope 1941
Image of polytope 1941 PALP id: 1941
grdb id: 12639
Integer points: [ 1 0 1 0 0 0 0 -1 0 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 1 0 1 -1 0 1 0 0 0]
[ 0 0 0 1 1 -1 -1 0 0 1 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + y*z-1 + x*y-1 + x-1*y + y-1*z + x-1*z + z-1 + x-1*y*z-1 + y-1 + 2*x-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 6 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 1942
Image of polytope 1942 PALP id: 1942
grdb id: 125
Integer points: [ 1 0 0 -1 1 1 -1 -1 -1 1 0 0 0 0]
[ 0 1 0 1 0 -1 1 0 0 -1 0 -1 -1 0]
[ 0 0 1 1 -1 0 0 1 0 -1 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y*z + x*z-1 + x*y-1 + x-1*y + x-1*z + x*y-1*z-1 + z-1 + y-1 + x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 9 Lattice Minkowski decompositions of facet 3
Polytope 1943
Image of polytope 1943 PALP id: 1943
grdb id: 547470
Integer points: [ 1 1 1 -5 -2 0 -3 -1 1 -2 0 1 -2 0 1]
[ 0 2 0 -2 -1 0 -1 0 1 0 1 0 -1 0 1]
[ 0 0 2 -2 0 1 -1 0 1 -1 0 1 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 3 Lattice Minkowski decompositions of facet 16
Image of facet 118 1 none
Polytope 1944
Image of polytope 1944 PALP id: 1944
grdb id: 547472
Integer points: [ 1 0 0 -6 -5 -4 -3 -2 -1 -3 -2 -1 0 -1 0]
[ 0 1 1 -5 -4 -3 -2 -1 0 -2 -1 0 1 -1 0]
[ 0 0 2 -4 -3 -2 -1 0 1 -2 -1 0 1 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 4 1 none
Image of facet 53 1 irreducible and admissible
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Polytope 1945
Image of polytope 1945 PALP id: 1945
grdb id: 547460
Integer points: [ 1 0 0 -2 -1 -1 0 -1 0 0 -1 0 0 0 0]
[ 0 1 1 -3 -1 -1 1 -1 1 1 -2 0 0 0 -1]
[ 0 0 4 -6 -1 -2 3 -3 2 1 -4 1 0 -1 -2]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 13 1 irreducible and admissible
Image of facet 14 2 none
Polytope 1946
Image of polytope 1946 PALP id: 1946
grdb id: 547476
Integer points: [ 1 0 1 -7 -1 -3 -5 0 -2 -4 -1 1 -1 -3 0]
[ 0 1 0 -4 -1 -2 -3 0 -1 -2 0 0 -1 -2 0]
[ 0 0 2 -2 1 0 -1 1 0 -1 0 1 0 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 2 irreducible and admissible
Image of facet 120 1 none
Polytope 1947
Image of polytope 1947 PALP id: 1947
grdb id: 547471
Integer points: [ 1 0 1 -8 -5 -2 -6 -3 0 -4 -1 -2 -2 1 0]
[ 0 1 0 -3 -2 -1 -2 -1 0 -1 0 0 -1 0 0]
[ 0 0 2 -4 -2 0 -3 -1 1 -2 0 -1 -1 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 14 1 none
Image of facet 121 1 none
Polytope 1948
Image of polytope 1948 PALP id: 1948
grdb id: 547475
Integer points: [ 1 1 0 -9 -6 -3 -5 -2 -4 -1 0 -4 -1 0 1]
[ 0 2 0 -6 -4 -2 -3 -1 -2 0 1 -3 -1 0 1]
[ 0 0 1 -2 -1 0 -1 0 -1 0 0 -1 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 122 1 none
Image of facet 14 1 none
Polytope 1949
Image of polytope 1949 PALP id: 1949
grdb id: 547474
Integer points: [ 1 0 0 -12 -9 -6 -3 -8 -5 -2 -4 -1 -4 -1 0]
[ 0 1 0 -8 -6 -4 -2 -5 -3 -1 -2 0 -3 -1 0]
[ 0 0 1 -3 -2 -1 0 -2 -1 0 -1 0 -1 0 0]
Degree: 48
Hilbert function: 1 + 27 t + 125 t2 + 343 t3 + 729 t4 + 1331 t5 + 2197 t6 + 3375 t7 + 4913 t8 + 6859 t9 + 9261 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 123 1 none
Image of facet 121 1 none
Polytope 1950
Image of polytope 1950 PALP id: 1950
grdb id: 545979
Integer points: [ 1 0 0 -3 -3 -3 -3 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 0 0 -3 -2 -1 -2 -1 0 -1 0 -1 0 0]
[ 0 0 1 -2 1 0 -1 1 0 -1 1 0 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 124 1 none
Image of facet 14 1 none
Image of facet 9 1 irreducible and admissible
Polytope 1951
Image of polytope 1951 PALP id: 1951
grdb id: 545977
Integer points: [ 1 0 0 -3 0 -1 -2 0 -1 -2 0 -1 0 -1 0]
[ 0 1 0 0 -3 -2 -1 -2 -1 0 -1 0 -1 0 0]
[ 0 0 1 -2 -2 -2 -2 -1 -1 -1 0 0 -1 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 95 1 none
Polytope 1952
Image of polytope 1952 PALP id: 1952
grdb id: 546018
Integer points: [ 1 0 0 -3 -3 -3 -2 -2 -2 -1 -1 -1 0 -1 0]
[ 0 1 1 -2 -2 -2 -1 -1 -1 0 0 0 1 -1 0]
[ 0 0 2 -1 -3 -2 0 -1 -2 1 0 -1 1 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 4 1 none
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Image of facet 9 2 irreducible and admissible
Polytope 1953
Image of polytope 1953 PALP id: 1953
grdb id: 546004
Integer points: [ 1 0 0 -2 0 0 0 0 -1 -1 -1 0 0 0 -1]
[ 0 1 1 -1 -3 0 -1 -2 0 -1 -2 1 0 -1 0]
[ 0 0 2 -2 -2 1 0 -1 0 -1 -2 1 0 -1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 y*z2 + 2*y*z + x + y + 4*z + 6*y-1 + 2*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + 4*y-2*z-1 + 4*x-1*y-1*z-1 + y-3*z-2 + 2*x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 1954
Image of polytope 1954 PALP id: 1954
grdb id: 546017
Integer points: [ 1 0 1 -3 -3 -2 -1 -1 0 -3 -2 -1 0 1 -1]
[ 0 1 0 -2 -2 -1 0 -1 0 -2 -1 -1 0 0 -1]
[ 0 0 2 -2 0 0 0 1 1 -1 -1 0 0 1 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 14 2 none
Polytope 1955
Image of polytope 1955 PALP id: 1955
grdb id: 546015
Integer points: [ 1 0 1 -3 -3 -1 -2 0 -3 -1 -2 -1 1 0 -1]
[ 0 1 0 0 -2 -1 -1 0 -1 0 0 -1 0 0 0]
[ 0 0 2 -2 0 1 0 1 -1 0 -1 0 1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 126 1 none
Polytope 1956
Image of polytope 1956 PALP id: 1956
grdb id: 545981
Integer points: [ 1 0 0 0 -3 -1 -2 0 -1 -2 0 -1 0 -1 0]
[ 0 1 0 -3 3 -1 1 -2 0 2 -1 1 -1 1 0]
[ 0 0 1 -2 1 -1 0 -1 0 1 0 1 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Image of facet 14 1 none
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Polytope 1957
Image of polytope 1957 PALP id: 1957
grdb id: 546003
Integer points: [ 1 0 0 -2 -4 -3 -2 -1 -3 -2 -1 0 -1 -1 0]
[ 0 1 1 -1 -3 -2 -1 0 -2 -1 0 1 0 -1 0]
[ 0 0 2 -2 -2 -1 0 1 -2 -1 0 1 -1 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 4 1 none
Image of facet 13 1 irreducible and admissible
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 1958
Image of polytope 1958 PALP id: 1958
grdb id: 546001
Integer points: [ 1 1 0 -2 -2 -1 -1 -2 -1 -2 -2 0 0 0 1]
[ 0 2 0 0 -4 -2 -1 -3 0 -2 -1 -1 0 1 1]
[ 0 0 1 -1 -1 0 0 -1 0 -1 -1 0 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 4 2 none
Polytope 1959
Image of polytope 1959 PALP id: 1959
grdb id: 546096
Integer points: [ 1 1 -3 0 1 1 0 0 -1 -1 -2 1 1 0 -1]
[ 0 2 -2 0 4 3 1 2 0 1 -1 1 2 0 -1]
[ 0 0 0 1 -2 -1 0 -1 0 -1 0 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 128 1 none
Polytope 1960
Image of polytope 1960 PALP id: 1960
grdb id: 546100
Integer points: [ 1 0 0 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -4 -3 -2 -1 0 -2 -1 0 1 -1 0]
[ 0 0 1 -2 3 2 1 0 -1 2 1 0 -1 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 43 1 irreducible and admissible
Image of facet 4 1 none
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Polytope 1961
Image of polytope 1961 PALP id: 1961
grdb id: 546012
Integer points: [ 1 0 -3 1 -5 -1 -4 -2 0 -3 -1 -1 1 -2 0]
[ 0 1 -2 0 -2 -1 -2 -1 0 -1 0 -1 0 -1 0]
[ 0 0 0 2 -2 1 -1 0 1 -1 0 0 1 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 130 1 none
Polytope 1962
Image of polytope 1962 PALP id: 1962
grdb id: 546010
Integer points: [ 1 0 1 -3 -5 -2 -3 0 -4 -1 -2 -2 1 0 -1]
[ 0 1 0 0 -2 -1 -1 0 -1 0 0 -1 0 0 0]
[ 0 0 2 -2 -2 0 -1 1 -2 0 -1 -1 1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 131 1 none
Polytope 1963
Image of polytope 1963 PALP id: 1963
grdb id: 546005
Integer points: [ 1 1 0 -3 -5 -2 -1 0 -4 -3 -2 -1 0 1 -2]
[ 0 2 0 -2 -4 -1 0 1 -3 -2 -1 -1 0 1 -2]
[ 0 0 1 0 -2 0 0 0 -1 -1 -1 0 0 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
24 ? x*y2 + 2*x*y + x + 4*y + z + 6*x-1 + 2*x-1*y-1 + 4*x-2*y-1 + 2*x-2*y-1*z-1 + 2*x-2*y-2*z-1 + x-3*y-2 + 4*x-3*y-2*z-1 + 2*x-4*y-3*z-1 + x-5*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 1964
Image of polytope 1964 PALP id: 1964
grdb id: 545978
Integer points: [ 1 0 0 -3 -6 -4 -5 -2 -3 -4 -1 -2 -1 -2 0]
[ 0 1 0 -2 -5 -3 -4 -1 -2 -3 0 -1 -1 -2 0]
[ 0 0 1 0 -3 -1 -2 0 -1 -2 0 -1 0 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Image of facet 42 1 none
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Polytope 1965
Image of polytope 1965 PALP id: 1965
grdb id: 545980
Integer points: [ 1 0 0 -3 -6 -4 -5 -2 -3 -4 -1 -2 -1 -2 0]
[ 0 1 0 -2 -2 -2 -2 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 1 0 -3 -1 -2 0 -1 -2 0 -1 0 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 132 1 Lattice Minkowski decompositions of facet 132
Image of facet 14 1 none
Image of facet 9 1 irreducible and admissible
Polytope 1966
Image of polytope 1966 PALP id: 1966
grdb id: 546002
Integer points: [ 1 1 0 -2 -6 -3 -5 -2 -4 -1 -3 0 -1 0 1]
[ 0 2 0 0 -4 -2 -3 -1 -2 0 -1 1 -1 0 1]
[ 0 0 1 -1 -1 0 -1 0 -1 0 -1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 4 1 none
Image of facet 13 1 irreducible and admissible
Image of facet 133 1 Lattice Minkowski decompositions of facet 133
Polytope 1967
Image of polytope 1967 PALP id: 1967
grdb id: 545976
Integer points: [ 1 0 0 -3 -9 -5 -2 -7 -4 -1 -6 -3 -1 -3 0]
[ 0 1 0 -2 -5 -3 -1 -4 -2 0 -3 -1 -1 -2 0]
[ 0 0 1 0 -3 -1 0 -2 -1 0 -2 -1 0 -1 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 124 1 none
Image of facet 14 1 none
Image of facet 9 1 irreducible and admissible
Polytope 1968
Image of polytope 1968 PALP id: 1968
grdb id: 545881
Integer points: [ 1 -1 1 1 -1 0 1 0 1 0 1 0 -1 0 0]
[ 0 0 2 0 -2 -1 0 -1 1 0 1 0 -1 0 1]
[ 0 0 0 2 -2 -1 1 0 0 -1 1 0 -1 1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
26 rank 2, number 8 x*y2 + 2*x*y*z + x*z2 + 2*x*y + 2*x*z + x + 2*y + 2*z + 2*z-1 + 2*y-1 + x-1 + 2*y-1*z-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 6 Lattice Minkowski decompositions of facet 16
Polytope 1969
Image of polytope 1969 PALP id: 1969
grdb id: 545848
Integer points: [ 1 0 0 -3 -3 -2 -1 -3 -2 -1 -3 -2 -1 0 -1]
[ 0 1 0 0 -3 0 0 -1 -1 -1 -2 -2 0 0 -1]
[ 0 0 1 -2 -2 -1 0 -2 -1 0 -2 -1 -1 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 14 1 none
Image of facet 9 2 irreducible and admissible
Polytope 1970
Image of polytope 1970 PALP id: 1970
grdb id: 545842
Integer points: [ 1 0 0 0 -3 0 0 -1 -1 -1 -2 -2 0 0 -1]
[ 0 1 0 -3 0 -2 -1 -2 -1 0 -1 0 -1 0 0]
[ 0 0 1 -2 1 -1 0 -1 0 1 0 1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 14 1 none
Image of facet 9 2 irreducible and admissible
Polytope 1971
Image of polytope 1971 PALP id: 1971
grdb id: 545864
Integer points: [ 1 0 0 -2 0 0 0 0 -1 -1 -1 0 0 0 -1]
[ 0 1 1 1 -3 0 -1 -2 1 0 -1 1 0 -1 1]
[ 0 0 2 0 -2 1 0 -1 1 0 -1 1 0 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 y*z2 + 2*y*z + x + y + 4*z + 2*x-1*y*z + 2*x-1*y + 6*y-1 + 4*x-1 + x-2*y + 2*y-1*z-1 + 4*y-2*z-1 + 2*x-1*y-1*z-1 + y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 1972
Image of polytope 1972 PALP id: 1972
grdb id: 545866
Integer points: [ 1 0 1 -3 -3 0 -1 -2 -1 -2 -3 1 0 -1 -1]
[ 0 1 0 0 -2 0 0 0 -1 -1 -1 0 0 0 -1]
[ 0 0 2 -2 -2 1 0 -1 0 -1 -2 1 0 -1 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
101 ? x*z2 + 2*x*z + x + y + 4*z + 6*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 4*x-2*z-1 + 4*x-2*y-1*z-1 + x-3*z-2 + 2*x-3*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 1973
Image of polytope 1973 PALP id: 1973
grdb id: 545859
Integer points: [ 1 0 1 -3 -1 0 -1 -2 0 -1 -2 1 0 -1 0]
[ 0 1 0 0 -2 0 0 0 -1 -1 -1 0 0 0 -1]
[ 0 0 2 -2 0 1 0 -1 1 0 -1 1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
75 ? x*z2 + 2*x*z + x + y + 4*z + 2*y-1*z + 2*y-1 + 6*x-1 + 2*x-1*z-1 + 4*x-1*y-1 + 4*x-2*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 1974
Image of polytope 1974 PALP id: 1974
grdb id: 545880
Integer points: [ 1 1 -1 0 -3 -2 -1 -1 0 -2 -1 -1 0 1 0]
[ 0 2 -2 0 0 0 0 1 1 -1 -1 0 0 1 -1]
[ 0 0 0 1 -2 -1 0 -1 0 -1 0 -1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 14 2 none
Polytope 1975
Image of polytope 1975 PALP id: 1975
grdb id: 545862
Integer points: [ 1 0 0 0 -4 -1 -2 -3 0 -1 -2 0 -1 -2 0]
[ 0 1 -1 1 1 1 1 1 0 0 0 1 1 1 0]
[ 0 0 0 2 -2 1 0 -1 1 0 -1 1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
32 ? y*z2 + 2*y*z + x + y + 2*z + 4*x-1*y*z + 4*x-1*y + y-1 + 4*x-1 + 6*x-2*y + 2*x-2*y*z-1 + 2*x-2*z-1 + 4*x-3*y*z-1 + x-4*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 2 Lattice Minkowski decompositions of facet 32
Image of facet 1 4 irreducible and admissible
Polytope 1976
Image of polytope 1976 PALP id: 1976
grdb id: 534862
Integer points: [ 1 0 0 -1 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -2 2 -1 0 1 -1 0 1 0 1 -1 0]
[ 0 0 1 -2 1 -2 -1 0 -1 0 1 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 56 1 Lattice Minkowski decompositions of facet 56
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1977
Image of polytope 1977 PALP id: 1977
grdb id: 534863
Integer points: [ 1 0 1 -1 0 -2 0 -1 0 -1 0 1 0 -1 0]
[ 0 1 0 -2 1 -1 -1 -1 0 0 -1 0 0 0 1]
[ 0 0 2 -2 2 -2 0 -1 1 0 -1 1 0 -1 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 83 1 none
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1978
Image of polytope 1978 PALP id: 1978
grdb id: 534865
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 1 1 -3 2 -2 1 0 -1 0 -1 -2 1 0 -1]
[ 0 0 2 -2 2 -2 1 0 -1 1 0 -1 1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 5 2 none
Image of facet 134 1 Lattice Minkowski decompositions of facet 134
Image of facet 13 2 irreducible and admissible
Polytope 1979
Image of polytope 1979 PALP id: 1979
grdb id: 534858
Integer points: [ 1 0 0 1 -3 -3 -2 -1 -1 0 -2 -1 -1 0 1]
[ 0 1 0 -2 1 0 0 0 -1 -1 1 1 0 0 -1]
[ 0 0 1 2 -3 -2 -1 0 0 1 -2 -1 -1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 14 1 none
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 1980
Image of polytope 1980 PALP id: 1980
grdb id: 534860
Integer points: [ 1 0 0 -2 -1 -4 -3 -2 -3 -2 -1 -2 -1 -1 0]
[ 0 1 0 -2 1 -2 -1 0 -2 -1 0 -1 0 -1 0]
[ 0 0 1 -1 1 1 1 1 0 0 0 1 1 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 56 1 Lattice Minkowski decompositions of facet 56
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 14 1 none
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 1981
Image of polytope 1981 PALP id: 1981
grdb id: 534864
Integer points: [ 1 1 0 -2 0 -2 -1 0 -1 -2 -1 0 0 0 1]
[ 0 2 0 -4 2 -2 0 1 -1 -3 -2 1 0 -1 1]
[ 0 0 1 -1 1 -1 0 1 0 -1 0 0 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 4 2 none
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 1982
Image of polytope 1982 PALP id: 1982
grdb id: 534861
Integer points: [ 1 1 0 0 -2 -2 -1 -1 -2 -1 -2 0 0 0 1]
[ 0 2 0 1 -1 -4 0 -1 -2 -2 -3 1 0 -1 1]
[ 0 0 1 1 -1 -1 0 0 -1 0 -1 0 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 4 2 none
Polytope 1983
Image of polytope 1983 PALP id: 1983
grdb id: 534610
Integer points: [ 1 0 0 -1 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 1 -2 -1 1 0 1 0 -1 1 0 1 0 -1]
[ 0 0 2 -2 -2 0 -1 1 0 -1 0 -1 1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 37 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 1984
Image of polytope 1984 PALP id: 1984
grdb id: 534592
Integer points: [ 1 0 0 0 -2 -2 0 -1 -1 -1 -2 -2 0 -1 -1]
[ 0 1 0 -2 0 -3 -1 0 -1 -2 -1 -2 0 0 -1]
[ 0 0 1 -1 1 -2 0 1 0 -1 0 -1 0 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Polytope 1985
Image of polytope 1985 PALP id: 1985
grdb id: 534316
Integer points: [ 1 0 0 -3 -2 -3 -3 -2 -1 -3 -2 -1 -1 -1 0]
[ 0 1 0 -2 -1 -2 -2 -1 0 -2 -1 0 -1 -1 0]
[ 0 0 1 -1 2 2 1 1 1 0 0 0 1 0 0]
Degree: 48
Hilbert function: 1 + 27 t + 125 t2 + 343 t3 + 729 t4 + 1331 t5 + 2197 t6 + 3375 t7 + 4913 t8 + 6859 t9 + 9261 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Image of facet 104 1 none
Polytope 1986
Image of polytope 1986 PALP id: 1986
grdb id: 534504
Integer points: [ 1 0 0 -2 -3 -1 -1 0 -2 -1 -2 -1 0 0 -1]
[ 0 1 1 -1 -2 0 0 1 -1 0 -1 0 0 0 -1]
[ 0 0 2 -2 -2 2 1 1 0 0 -1 -1 1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
3 ? y*z2 + 2*y*z + x + y + 2*z + x-1*z2 + 4*x-1*z + 6*x-1 + 2*x-1*z-1 + 2*x-1*y-1*z-1 + 2*x-2*y-1 + 4*x-2*y-1*z-1 + x-2*y-1*z-2 + x-3*y-2*z-2
60 rank 2, number 18 y*z2 + 2*y*z + x + y + 2*z + x-1*z2 + 2*x-1*z + 3*x-1 + 2*x-1*z-1 + 2*x-1*y-1*z-1 + 2*x-2*y-1 + 2*x-2*y-1*z-1 + x-2*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 4 irreducible and admissible
Image of facet 135 1 Lattice Minkowski decompositions of facet 135
Polytope 1987
Image of polytope 1987 PALP id: 1987
grdb id: 534289
Integer points: [ 1 0 0 -1 -3 -3 -2 -2 -2 -1 -1 -1 -1 0 0]
[ 0 1 0 2 -2 -3 0 -1 -2 1 0 -1 -1 1 0]
[ 0 0 1 -2 0 1 -1 0 1 -1 0 1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 136 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Polytope 1988
Image of polytope 1988 PALP id: 1988
grdb id: 534498
Integer points: [ 1 0 1 -3 -3 1 -2 -2 -1 -1 0 0 -1 0 1]
[ 0 1 0 0 -1 -1 -1 0 -1 0 -1 0 0 0 0]
[ 0 0 2 -2 -1 3 0 -1 1 0 2 1 -1 0 1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
134 ? x*z2 + x*y-1*z3 + 2*x*z + x + y + 2*z + 4*y-1*z2 + 3*x-1 + 6*x-1*y-1*z + 2*x-1*z-1 + 3*x-2*z-1 + 4*x-2*y-1 + x-3*z-2 + x-3*y-1*z-1
135 ? x*z2 + x*y-1*z3 + 2*x*z + x + y + 5*z + 4*y-1*z2 + 6*x-1 + 6*x-1*y-1*z + 2*x-1*z-1 + 4*x-2*z-1 + 4*x-2*y-1 + x-3*z-2 + x-3*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 137 1 Lattice Minkowski decompositions of facet 137
Polytope 1989
Image of polytope 1989 PALP id: 1989
grdb id: 534367
Integer points: [ 1 0 0 -2 -4 -1 -2 -3 -1 -2 -3 -1 0 -1 0]
[ 0 1 0 0 -2 -2 -2 -2 -1 -1 -1 0 -1 -1 0]
[ 0 0 1 -1 -1 2 1 0 1 0 -1 0 1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 138 1 Lattice Minkowski decompositions of facet 138
Image of facet 14 1 none
Polytope 1990
Image of polytope 1990 PALP id: 1990
grdb id: 534507
Integer points: [ 1 0 1 -3 -4 0 -1 0 -2 -1 -3 -2 1 0 -1]
[ 0 1 0 0 -1 -1 -1 0 -1 0 -1 0 0 0 0]
[ 0 0 2 -2 -2 2 1 1 0 0 -1 -1 1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
71 ? x*z2 + 2*x*z + x + y + 4*z + y-1*z2 + 7*x-1 + 4*x-1*y-1*z + 2*x-1*z-1 + 4*x-2*z-1 + 6*x-2*y-1 + x-3*z-2 + 4*x-3*y-1*z-1 + x-4*y-1*z-2
3 ? x*z2 + 2*x*z + x + y + 2*z + y-1*z2 + 2*x-1 + 4*x-1*y-1*z + 2*x-1*z-1 + 2*x-2*z-1 + 6*x-2*y-1 + x-3*z-2 + 4*x-3*y-1*z-1 + x-4*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 139 1 Lattice Minkowski decompositions of facet 139
Image of facet 13 1 irreducible and admissible
Polytope 1991
Image of polytope 1991 PALP id: 1991
grdb id: 534618
Integer points: [ 1 0 1 0 -3 -4 0 -1 -2 -1 -2 -3 1 0 -1]
[ 0 1 0 -1 0 -1 0 0 0 -1 -1 -1 0 0 0]
[ 0 0 2 1 -2 -3 1 0 -1 0 -1 -2 1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 13 2 irreducible and admissible
Image of facet 6 1 none
Image of facet 134 1 Lattice Minkowski decompositions of facet 134
Polytope 1992
Image of polytope 1992 PALP id: 1992
grdb id: 534424
Integer points: [ 1 0 1 0 0 -4 -2 -1 0 -3 -2 -1 -1 0 1]
[ 0 1 -2 0 -2 2 1 0 -1 1 0 -1 1 0 -1]
[ 0 0 0 1 -1 -1 0 0 0 -1 -1 -1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 4 1 none
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Polytope 1993
Image of polytope 1993 PALP id: 1993
grdb id: 534503
Integer points: [ 1 1 0 -2 -4 -2 -1 -3 -2 -1 0 -3 -1 0 1]
[ 0 2 0 0 -2 -2 -1 -2 -1 0 1 -1 -1 0 1]
[ 0 0 1 -1 -1 1 1 0 0 0 0 -1 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 140 1 Lattice Minkowski decompositions of facet 140
Image of facet 4 1 none
Polytope 1994
Image of polytope 1994 PALP id: 1994
grdb id: 534344
Integer points: [ 1 0 0 0 -2 -5 -1 -3 -2 -1 -4 -3 -1 0 -2]
[ 0 1 0 -1 -2 -2 -1 -2 -1 0 -2 -1 -1 0 -1]
[ 0 0 1 1 1 -2 1 0 0 0 -1 -1 0 0 -1]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 102 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 1995
Image of polytope 1995 PALP id: 1995
grdb id: 534453
Integer points: [ 1 1 0 -2 -1 -5 -3 -2 -1 0 -4 -3 -1 0 1]
[ 0 2 0 0 -1 -3 -2 -1 0 1 -2 -1 -1 0 1]
[ 0 0 1 -1 1 -1 0 0 0 0 -1 -1 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 4 1 none
Image of facet 141 1 Lattice Minkowski decompositions of facet 141
Image of facet 9 1 irreducible and admissible
Polytope 1996
Image of polytope 1996 PALP id: 1996
grdb id: 534323
Integer points: [ 1 0 0 -1 -6 -7 -5 -3 -4 -2 -3 -1 -3 -1 0]
[ 0 1 0 -1 -3 -4 -3 -2 -2 -1 -1 0 -2 -1 0]
[ 0 0 1 1 -2 -2 -1 0 -1 0 -1 0 -1 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 136 1 none
Image of facet 14 1 none
Polytope 1997
Image of polytope 1997 PALP id: 1997
grdb id: 533769
Integer points: [ 1 0 0 0 -2 -2 -2 -1 -1 -1 0 -1 -1 0 0]
[ 0 1 -1 1 -1 1 0 1 0 -1 0 1 0 1 0]
[ 0 0 0 2 -2 0 -1 1 0 -1 1 0 -1 1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 y*z2 + 2*y*z + x + y + 2*z + 2*x-1*y*z + 2*x-1*y + y-1 + 4*x-1 + x-2*y + 2*x-1*z-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 4 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Polytope 1998
Image of polytope 1998 PALP id: 1998
grdb id: 533766
Integer points: [ 1 0 0 -2 0 -2 -1 0 -1 -2 -1 0 -1 0 -1]
[ 0 1 -1 -1 1 -3 0 0 -1 -2 -2 1 0 0 -1]
[ 0 0 0 0 2 -2 1 1 0 -1 -1 1 0 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
60 rank 2, number 18 y*z2 + 2*y*z + x + y + 2*z + 2*x-1*z + y-1 + 2*x-1 + 4*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + 2*x-1*y-2*z-1 + 2*x-2*y-2*z-1 + x-2*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 4 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Polytope 1999
Image of polytope 1999 PALP id: 1999
grdb id: 534228
Integer points: [ 1 0 0 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 0 0]
[ 0 1 0 -2 2 -3 1 0 -1 -2 1 0 -1 0 -1]
[ 0 0 1 0 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
100 ? x + y + z + 2*x-1*y + x-2*y2*z-1 + 2*y-1 + 5*x-1 + 5*x-2*y*z-1 + 4*x-1*y-1 + 10*x-2*z-1 + x-1*y-2 + 10*x-2*y-1*z-1 + 5*x-2*y-2*z-1 + x-2*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 43 1 irreducible and admissible
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Polytope 2000
Image of polytope 2000 PALP id: 2000
grdb id: 533771
Integer points: [ 1 0 1 -3 -3 1 0 -1 -2 0 -1 -2 1 0 -1]
[ 0 1 0 0 -1 -1 0 0 0 -1 -1 -1 0 0 0]
[ 0 0 2 -2 -2 2 1 0 -1 1 0 -1 1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
101 ? x*z2 + 2*x*z + x*y-1*z2 + x + y + 4*z + 4*y-1*z + 6*x-1 + 2*x-1*z-1 + 6*x-1*y-1 + 4*x-2*z-1 + 4*x-2*y-1*z-1 + x-3*z-2 + x-3*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 13 2 irreducible and admissible
Image of facet 134 1 Lattice Minkowski decompositions of facet 134
Polytope 2001
Image of polytope 2001 PALP id: 2001
grdb id: 534247
Integer points: [ 1 0 -1 0 -2 -2 -2 -2 -2 -2 -1 -1 -1 0 0]
[ 0 1 1 0 1 -4 -3 -2 -1 0 -2 -1 0 -1 0]
[ 0 0 0 1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 43 1 irreducible and admissible
Image of facet 4 1 none
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Polytope 2002
Image of polytope 2002 PALP id: 2002
grdb id: 533765
Integer points: [ 1 1 -1 -1 0 -3 -2 -1 -2 0 -1 0 -1 0 1]
[ 0 2 0 -2 0 -4 -3 -1 -2 -1 -2 0 -1 1 1]
[ 0 0 0 0 1 -2 -1 0 -1 0 -1 0 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x*y2 + 2*x*y + x + 2*y + z + 2*y-1 + x-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 2*x-2*y-2*z-1 + 2*x-2*y-3*z-1 + x-3*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 3 Lattice Minkowski decompositions of facet 16
Image of facet 1 3 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 2003
Image of polytope 2003 PALP id: 2003
grdb id: 533664
Integer points: [ 1 0 0 -2 -4 -6 -2 -4 -1 -3 -1 -3 -5 0 -2]
[ 0 1 0 -2 -3 -3 -1 -2 0 -1 -1 -2 -3 0 -1]
[ 0 0 1 -1 -2 -2 0 -1 0 -1 0 -1 -2 0 -1]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 14 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2004
Image of polytope 2004 PALP id: 2004
grdb id: 532845
Integer points: [ 1 0 0 0 0 -2 0 -1 0 -1 0 0 -1 -1 0]
[ 0 1 1 -1 -1 1 0 0 -1 1 0 1 0 1 0]
[ 0 0 2 -2 0 0 -1 -1 -1 0 0 1 0 1 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? y*z2 + 2*y*z + x + y + 2*z + 2*x-1*y*z + 2*x-1*y + 2*z-1 + y-1 + 2*x-1 + x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 4 Lattice Minkowski decompositions of facet 16
Image of facet 1 4 irreducible and admissible
Polytope 2005
Image of polytope 2005 PALP id: 2005
grdb id: 492024
Integer points: [ 1 0 0 0 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 2 0 1 0 1 -1 0 1 0]
[ 0 0 1 -1 0 -2 1 -1 0 -1 0 -1 0 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 95 1 none
Polytope 2006
Image of polytope 2006 PALP id: 2006
grdb id: 492043
Integer points: [ 1 0 0 0 0 -1 -1 0 0 -1 -1 -1 0 0 0]
[ 0 1 0 -2 1 -2 2 0 -1 1 0 -1 1 0 -1]
[ 0 0 1 1 -2 2 -2 -1 0 -1 0 1 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 5 2 none
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Polytope 2007
Image of polytope 2007 PALP id: 2007
grdb id: 492044
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 1 -1 -1 -2 2 -1 0 1 0 -1 0 1 0]
[ 0 0 2 -2 0 -2 2 -1 0 1 1 -1 0 1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 59 2 Lattice Minkowski decompositions of facet 59
Image of facet 5 2 none
Polytope 2008
Image of polytope 2008 PALP id: 2008
grdb id: 492025
Integer points: [ 1 0 0 1 -1 -2 -2 -2 -1 0 -1 0 -1 -1 0]
[ 0 1 0 -1 1 1 -1 0 0 0 -1 -1 1 0 0]
[ 0 0 1 -1 -1 0 2 1 0 -1 1 0 0 1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
23 ? x + y + z + 2*x-1*y + 2*x-1*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 3*y-1 + 4*x-1 + x-2*y + 3*x-1*y-1*z + 2*x-2*z + x-2*y-1*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2009
Image of polytope 2009 PALP id: 2009
grdb id: 492045
Integer points: [ 1 0 1 -1 0 -2 0 -1 -1 0 -1 0 0 1 0]
[ 0 1 0 0 -1 -1 1 0 -1 0 0 1 0 0 0]
[ 0 0 2 -2 0 -2 2 0 -1 1 -1 1 0 1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x*z2 + y*z2 + 2*x*z + 2*y*z + x + y + 2*z + 2*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2010
Image of polytope 2010 PALP id: 2010
grdb id: 492017
Integer points: [ 1 0 1 0 0 -2 -2 -2 -1 -1 -1 0 -1 0 1]
[ 0 1 -2 0 -2 0 2 1 -1 0 1 -1 1 0 -1]
[ 0 0 0 1 -1 -1 1 0 -1 0 1 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 4 1 none
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Polytope 2011
Image of polytope 2011 PALP id: 2011
grdb id: 492028
Integer points: [ 1 1 -1 0 1 0 -2 -1 0 -1 0 -1 0 1 0]
[ 0 2 -2 0 2 1 -1 0 1 0 1 -1 0 1 -1]
[ 0 0 0 1 -1 1 -1 0 0 -1 -1 0 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 1 none
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2012
Image of polytope 2012 PALP id: 2012
grdb id: 492026
Integer points: [ 1 0 1 0 -1 0 -3 -2 -1 -2 0 -1 -1 0 1]
[ 0 1 -2 0 1 -2 1 1 0 0 -1 -1 1 0 -1]
[ 0 0 0 1 1 -1 -1 0 0 -1 0 -1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 4 1 none
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Polytope 2013
Image of polytope 2013 PALP id: 2013
grdb id: 492042
Integer points: [ 1 1 -1 -1 0 -2 2 0 -1 0 1 -1 0 1 0]
[ 0 2 -2 0 0 -3 1 -1 -2 -1 0 -1 0 1 1]
[ 0 0 0 0 1 -1 -1 0 -1 -1 -1 0 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 59 2 Lattice Minkowski decompositions of facet 59
Image of facet 6 2 none
Polytope 2014
Image of polytope 2014 PALP id: 2014
grdb id: 492030
Integer points: [ 1 0 0 -1 -1 -3 -4 -3 -2 -2 -1 -2 -1 -1 0]
[ 0 1 0 -1 1 -2 -2 -1 0 -1 0 -1 0 -1 0]
[ 0 0 1 -1 1 0 1 1 1 0 0 1 1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Image of facet 14 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2015
Image of polytope 2015 PALP id: 2015
grdb id: 492031
Integer points: [ 1 0 0 -1 0 -3 -4 -3 -2 -2 -1 -2 -1 -1 0]
[ 0 1 0 0 -1 -2 -3 -2 -1 -1 0 -2 -1 -1 0]
[ 0 0 1 -1 -1 0 -1 -1 -1 0 0 -1 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 9 1 irreducible and admissible
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 14 1 none
Polytope 2016
Image of polytope 2016 PALP id: 2016
grdb id: 492033
Integer points: [ 1 0 0 0 -1 -3 -4 -3 -2 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 1 0 1 1 1 0 0 1 1 0 0]
[ 0 0 0 1 1 -2 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Image of facet 14 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2017
Image of polytope 2017 PALP id: 2017
grdb id: 492047
Integer points: [ 1 0 0 -3 0 2 2 2 1 1 1 0 -1 -1 -2]
[ 0 1 0 3 -1 -3 -1 -2 -1 -2 -1 0 1 1 2]
[ 0 0 1 1 -1 -1 -1 -1 -1 -1 0 0 0 1 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 8 2 none
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2018
Image of polytope 2018 PALP id: 2018
grdb id: 491967
Integer points: [ 1 1 0 -3 -3 -1 -5 -4 -3 -2 -1 0 -1 0 1]
[ 0 2 0 -2 -1 -1 -3 -2 -2 -1 0 1 -1 0 1]
[ 0 0 1 -1 -1 1 -1 -1 0 0 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 8 1 none
Image of facet 113 1 none
Polytope 2019
Image of polytope 2019 PALP id: 2019
grdb id: 491633
Integer points: [ 1 0 0 -2 0 -1 -2 -2 -1 -1 0 -1 -1 0 0]
[ 0 1 0 1 -2 -2 -1 0 -1 0 -1 0 1 -1 0]
[ 0 0 1 0 -1 -2 -2 -1 -1 0 0 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
60 rank 2, number 18 x + y + z + 2*x-1*y + 2*y-1 + x-1 + x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + y-2*z-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 71 1 Lattice Minkowski decompositions of facet 71
Polytope 2020
Image of polytope 2020 PALP id: 2020
grdb id: 491237
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 -2 -1 -2 0 -1 0 -1 -2 0 -1 -1]
[ 0 0 1 1 0 1 -2 0 -1 1 0 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*y*z + 2*x-1*z + 2*y-1 + 3*x-1 + x-1*y-1*z + 2*y-1*z-1 + 4*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2021
Image of polytope 2021 PALP id: 2021
grdb id: 491512
Integer points: [ 1 0 1 0 -2 0 -2 -1 -1 0 -2 -1 0 -1 0]
[ 0 1 -1 0 0 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 0 0 1 -1 1 1 1 1 1 0 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 37 1 none
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 2022
Image of polytope 2022 PALP id: 2022
grdb id: 491583
Integer points: [ 1 0 0 -1 -1 -2 -2 -2 -2 -1 -1 -1 0 0 0]
[ 0 1 0 2 -2 -2 1 0 -1 1 0 -1 1 0 -1]
[ 0 0 1 -2 2 1 -2 -1 0 -1 0 1 -1 0 1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
71 ? x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 4*x-1*y*z-1 + 7*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + x-2*y*z-2 + 3*x-2*z-1 + 3*x-2*y-1 + x-2*y-2*z
3 ? x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 2*x-1*y*z-1 + 2*x-1 + 2*x-1*y-1*z + x-1*y-2*z2 + x-2*y*z-2 + 3*x-2*z-1 + 3*x-2*y-1 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 142 1 Lattice Minkowski decompositions of facet 142
Image of facet 9 1 irreducible and admissible
Polytope 2023
Image of polytope 2023 PALP id: 2023
grdb id: 491381
Integer points: [ 1 0 0 -1 0 -1 1 0 -1 0 -1 0 1 0 0]
[ 0 1 0 1 1 -2 0 -1 -1 0 0 -1 0 0 1]
[ 0 0 1 -1 -2 2 -2 0 1 -1 0 1 -1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + 2*x*z-1 + 2*y*z-1 + 2*y-1*z + x*z-2 + y*z-2 + 3*z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + 3*x-1*y-1*z + x-1*y-2*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2024
Image of polytope 2024 PALP id: 2024
grdb id: 491317
Integer points: [ 1 0 0 0 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 1 -1 -1 -1 -1 0 0 0 -1 -1 0]
[ 0 0 0 1 -1 -1 2 1 0 1 0 -1 1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Polytope 2025
Image of polytope 2025 PALP id: 2025
grdb id: 490522
Integer points: [ 1 0 1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 2 0 -2 -1 0 1 -1 0 1 -1 0]
[ 0 0 0 1 -1 1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Polytope 2026
Image of polytope 2026 PALP id: 2026
grdb id: 490442
Integer points: [ 1 0 -2 1 0 1 -3 0 -1 0 -1 -2 1 0 -1]
[ 0 1 1 -2 0 -3 1 -1 0 -2 -1 0 -1 0 1]
[ 0 0 0 0 1 -1 -1 0 0 -1 -1 -1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
75 ? x + y + z + 2*x*y-1 + 2*x-1*y + x*y-2 + 4*y-1 + 4*x-1 + x-2*y + x*y-3*z-1 + 4*y-2*z-1 + 6*x-1*y-1*z-1 + 4*x-2*z-1 + x-3*y*z-1
24 ? x + y + z + 2*x*y-1 + 2*x-1*y + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + x*y-3*z-1 + 4*y-2*z-1 + 6*x-1*y-1*z-1 + 4*x-2*z-1 + x-3*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 93 1 Lattice Minkowski decompositions of facet 93
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Polytope 2027
Image of polytope 2027 PALP id: 2027
grdb id: 491264
Integer points: [ 1 0 -1 0 -1 0 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 1 1 0 0 -3 -3 -2 -1 -2 -1 -1 0 -1 0]
[ 0 0 0 1 1 -2 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 14 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2028
Image of polytope 2028 PALP id: 2028
grdb id: 491258
Integer points: [ 1 0 -1 0 0 -2 -3 -1 -2 -1 -2 0 -1 0 -1]
[ 0 1 1 0 -2 -3 -3 -1 -2 0 -1 -1 -2 0 -1]
[ 0 0 0 1 -1 -2 -2 0 -1 0 -1 0 -1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2029
Image of polytope 2029 PALP id: 2029
grdb id: 491204
Integer points: [ 1 0 0 -1 -2 -3 -3 -2 -1 -3 -2 -1 -1 0 -1]
[ 0 1 0 -1 -1 -2 -2 -1 0 -2 -1 0 -1 0 -1]
[ 0 0 1 1 -2 0 -2 0 0 -1 -1 -1 0 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + 3*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*y-1 + 4*x-2*y-1*z-1 + x-2*y-1*z-2 + x-3*y-2 + 2*x-3*y-2*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 2030
Image of polytope 2030 PALP id: 2030
grdb id: 490916
Integer points: [ 1 0 0 -1 -2 -3 -3 -3 -2 -2 -1 -1 -1 -1 0]
[ 0 1 0 1 -2 0 -2 -1 -1 0 -1 0 -1 0 0]
[ 0 0 1 -1 1 -2 0 -1 0 -1 1 0 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + x-1*y*z-1 + 3*x-1 + 2*x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + 3*x-2*z-1 + 4*x-2*y-1 + x-2*y-2*z + x-3*z-2 + 2*x-3*y-1*z-1 + x-3*y-2
50 ? x + y + z + x-1*y*z-1 + 3*x-1 + 2*x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-2*z-1 + 3*x-2*y-1 + x-2*y-2*z + x-3*z-2 + 2*x-3*y-1*z-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 143 1 Lattice Minkowski decompositions of facet 143
Polytope 2031
Image of polytope 2031 PALP id: 2031
grdb id: 491364
Integer points: [ 1 0 0 -1 -1 -3 -3 -2 -3 -2 -1 -2 -1 -1 0]
[ 0 1 0 0 1 -1 -3 0 -2 -1 0 -2 -1 -1 0]
[ 0 0 1 -1 0 -2 -2 -1 -2 -1 0 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Image of facet 9 1 irreducible and admissible
Polytope 2032
Image of polytope 2032 PALP id: 2032
grdb id: 491189
Integer points: [ 1 0 0 0 -3 -3 -2 -3 -2 -2 -1 -1 -1 -1 0]
[ 0 1 0 1 -2 0 1 -1 0 -1 1 0 0 -1 0]
[ 0 0 1 -1 0 -2 -2 -1 -1 0 -1 0 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 105 1 none
Polytope 2033
Image of polytope 2033 PALP id: 2033
grdb id: 491391
Integer points: [ 1 0 0 0 -1 -2 -3 -2 -1 -1 -2 -1 -1 0 0]
[ 0 1 0 -1 -2 1 0 0 0 1 -1 -1 0 0 -1]
[ 0 0 1 1 0 -2 -2 -1 0 -1 -1 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + y-1*z + 2*x-1*y*z-1 + 2*y-1 + 3*x-1 + 2*x-1*z-1 + 3*x-1*y-1 + x-2*y*z-2 + 3*x-2*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2034
Image of polytope 2034 PALP id: 2034
grdb id: 490433
Integer points: [ 1 0 0 0 -1 -2 -3 -1 -1 -2 -1 -2 0 -1 0]
[ 0 1 0 1 -2 1 0 1 0 0 -1 -1 0 0 -1]
[ 0 0 1 1 0 -1 -2 0 0 -1 0 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 106 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2035
Image of polytope 2035 PALP id: 2035
grdb id: 491257
Integer points: [ 1 0 0 1 -2 1 0 0 0 1 -1 -1 0 0 -1]
[ 0 1 0 0 -1 -2 -3 -2 -1 -1 -2 -1 -1 0 0]
[ 0 0 1 -1 0 -2 -2 -1 0 -1 -1 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 14 1 none
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2036
Image of polytope 2036 PALP id: 2036
grdb id: 491363
Integer points: [ 1 0 0 1 0 -1 -3 0 -1 -2 -1 -2 0 0 -1]
[ 0 1 0 -1 -2 -2 0 -1 -1 -1 0 0 -1 0 0]
[ 0 0 1 0 -1 -2 -2 0 -1 -2 0 -1 -1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x*y-1 + 2*y-1 + 3*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + y-2*z-1 + 4*x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2*z-2 + 2*x-2*y-1*z-2 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2037
Image of polytope 2037 PALP id: 2037
grdb id: 491259
Integer points: [ 1 0 0 0 -2 -1 -2 -2 -2 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 0 2 3 2 1 2 1 1 0 1 0]
[ 0 0 0 1 -1 2 2 1 0 1 0 1 0 1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 66 1 none
Image of facet 14 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2038
Image of polytope 2038 PALP id: 2038
grdb id: 491281
Integer points: [ 1 0 0 0 -1 -2 -2 -1 -1 -1 -2 -2 0 -1 -1]
[ 0 1 -1 0 -1 0 3 0 1 2 1 2 0 0 1]
[ 0 0 0 1 1 1 -2 1 0 -1 0 -1 0 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + 2*x-1*y2*z-1 + 4*x-1*y + 2*x-1*z + x-2*y3*z-2 + 2*x-1*y*z-1 + 3*x-2*y2*z-1 + y-1 + 3*x-1 + 3*x-2*y + x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2039
Image of polytope 2039 PALP id: 2039
grdb id: 491084
Integer points: [ 1 0 0 -2 -3 -2 -3 -3 -2 -2 -1 -1 -1 -1 0]
[ 0 1 0 -1 -2 -1 -2 -2 -1 -1 0 0 -1 -1 0]
[ 0 0 1 -1 0 2 2 1 0 1 0 1 0 1 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 105 1 none
Polytope 2040
Image of polytope 2040 PALP id: 2040
grdb id: 491586
Integer points: [ 1 0 0 -2 -2 -3 1 0 -1 -1 -1 -2 1 0 -1]
[ 0 1 1 -1 -1 -2 2 1 0 0 0 -1 1 0 -1]
[ 0 0 2 -2 0 -2 2 1 1 0 -1 -1 1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
3 ? x*y2*z2 + 2*x*y*z + y*z2 + 2*y*z + x + y + 2*x-1*z + 2*x-1 + 2*x-1*z-1 + 2*x-1*y-1*z-1 + x-2*y-1 + 2*x-2*y-1*z-1 + x-2*y-1*z-2 + x-3*y-2*z-2
71 ? x*y2*z2 + 2*x*y*z + y*z2 + 4*y*z + x + y + 2*x-1*z + 7*x-1 + 2*x-1*z-1 + 2*x-1*y-1*z-1 + x-2*y-1 + 4*x-2*y-1*z-1 + x-2*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 144 1 Lattice Minkowski decompositions of facet 144
Image of facet 1 6 irreducible and admissible
Polytope 2041
Image of polytope 2041 PALP id: 2041
grdb id: 491247
Integer points: [ 1 0 0 -1 -3 -2 -3 -2 -1 -3 -2 -1 -1 0 -1]
[ 0 1 0 -1 -2 -1 -2 -1 0 -2 -1 0 -1 0 -1]
[ 0 0 1 -1 0 2 2 0 0 1 1 1 0 0 1]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
69 ? x + y + z + 2*x-1*z + 3*x-1 + 2*x-1*y-1*z + x-2*y-1*z2 + 2*x-1*y-1 + 4*x-2*y-1*z + x-1*y-1*z-1 + 3*x-2*y-1 + x-3*y-2*z2 + 2*x-3*y-2*z + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2042
Image of polytope 2042 PALP id: 2042
grdb id: 491423
Integer points: [ 1 0 0 -1 -3 -2 -3 -1 -2 -1 -3 -2 -1 0 -1]
[ 0 1 0 -1 0 2 2 1 1 0 1 0 1 0 0]
[ 0 0 1 0 -2 -1 -2 0 -1 0 -2 -1 -1 0 -1]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
79 ? x + y + z + 2*x-1*y + 2*x-1*y*z-1 + x-2*y2*z-1 + x-1 + 2*x-1*z-1 + 3*x-2*y*z-1 + x-1*y-1 + x-3*y2*z-2 + 2*x-2*z-1 + 2*x-3*y*z-2 + x-3*z-2
160 ? x + y + z + 2*x-1*y + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*x-1 + 2*x-1*z-1 + 3*x-2*y*z-1 + x-1*y-1 + x-3*y2*z-2 + x-2*z-1 + 2*x-3*y*z-2 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 112 1 Lattice Minkowski decompositions of facet 112
Polytope 2043
Image of polytope 2043 PALP id: 2043
grdb id: 491361
Integer points: [ 1 0 0 -1 -2 2 2 1 0 1 0 -1 1 0 -1]
[ 0 1 0 0 1 -2 -3 -2 -1 -1 -1 0 -1 0 1]
[ 0 0 1 1 0 -1 -2 -1 0 0 -1 0 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 14 1 none
Polytope 2044
Image of polytope 2044 PALP id: 2044
grdb id: 491126
Integer points: [ 1 0 0 -1 -1 -2 -2 -2 -1 -2 -1 -1 0 0 0]
[ 0 1 0 2 -2 -1 2 0 -1 1 0 1 -1 0 1]
[ 0 0 1 -2 2 0 -3 -1 1 -2 0 -1 1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
135 ? x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 5*x-1*y*z-1 + 6*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + x-2*y2*z-3 + 3*x-2*y*z-2 + 3*x-2*z-1 + x-2*y-1
134 ? x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 2*x-1*y*z-1 + 3*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + x-2*y2*z-3 + 3*x-2*y*z-2 + 3*x-2*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 145 1 Lattice Minkowski decompositions of facet 145
Polytope 2045
Image of polytope 2045 PALP id: 2045
grdb id: 491603
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 2 -2 -3 1 0 -1 -1 -2 1 0 -1]
[ 0 0 1 -1 -2 2 2 -1 0 1 0 1 -1 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 6 1 none
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 9 1 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Polytope 2046
Image of polytope 2046 PALP id: 2046
grdb id: 491602
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -2 2 -3 -1 0 -2 -1 0 1 -1 0]
[ 0 0 1 0 0 -1 -1 0 0 -1 -1 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 146 1 Lattice Minkowski decompositions of facet 146
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 6 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 43 1 irreducible and admissible
Polytope 2047
Image of polytope 2047 PALP id: 2047
grdb id: 491549
Integer points: [ 1 0 0 0 -2 -3 -3 -1 -2 -1 0 -2 -1 -1 0]
[ 0 1 0 -2 2 2 1 1 1 0 -1 0 -1 1 0]
[ 0 0 1 1 -1 -2 -2 0 -1 0 1 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + 2*x-1*y + 2*y-1*z + 2*x-1*y*z-1 + x-2*y2*z-1 + 5*x-1 + y-2*z + 4*x-2*y*z-1 + 3*x-1*y-1 + x-3*y2*z-2 + 3*x-2*z-1 + x-3*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 9 1 irreducible and admissible
Polytope 2048
Image of polytope 2048 PALP id: 2048
grdb id: 491706
Integer points: [ 1 0 0 0 2 -3 -2 -1 -1 -2 1 0 0 -1 1]
[ 0 1 -1 0 -1 0 -1 -1 0 0 -1 -1 0 0 0]
[ 0 0 0 1 -2 1 0 0 1 1 -1 -1 0 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + 2*x*z-1 + 3*x-1*z + x2*y-1*z-2 + 2*x*y-1*z-1 + y-1 + 2*x-1 + 3*x-2*z + 2*y-1*z-1 + 2*x-1*y-1 + x-3*z + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2049
Image of polytope 2049 PALP id: 2049
grdb id: 491606
Integer points: [ 1 0 0 1 -2 -2 -3 0 -1 -2 -1 -1 1 0 -1]
[ 0 1 0 2 -2 -1 -2 1 0 -1 -1 0 1 0 -1]
[ 0 0 1 2 -1 -2 -2 1 0 -1 0 -1 1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 59 2 Lattice Minkowski decompositions of facet 59
Image of facet 6 1 none
Polytope 2050
Image of polytope 2050 PALP id: 2050
grdb id: 491684
Integer points: [ 1 0 0 1 -2 1 -3 -1 0 -2 -1 0 -1 0 1]
[ 0 1 0 -2 1 -2 2 0 -1 1 0 -1 1 0 -1]
[ 0 0 1 0 0 -1 -1 0 0 -1 -1 -1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 6 1 none
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 9 1 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Polytope 2051
Image of polytope 2051 PALP id: 2051
grdb id: 491147
Integer points: [ 1 1 0 -3 -3 -1 2 1 0 -1 -2 -2 1 0 -1]
[ 0 2 0 -2 -1 1 2 1 1 0 0 -1 1 0 -1]
[ 0 0 1 0 -1 -1 1 1 0 0 -1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
134 ? x2*y2*z + x*y2 + 2*x*y*z + 2*x*y + x + 2*y + z + x-1*y*z-1 + 3*x-1 + 2*x-1*y-1 + 2*x-2*z-1 + 3*x-2*y-1 + x-3*y-1*z-1 + x-3*y-2
135 ? x2*y2*z + x*y2 + 2*x*y*z + 2*x*y + x + 5*y + z + x-1*y*z-1 + 6*x-1 + 2*x-1*y-1 + 2*x-2*z-1 + 4*x-2*y-1 + x-3*y-1*z-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 6 irreducible and admissible
Image of facet 147 1 Lattice Minkowski decompositions of facet 147
Polytope 2052
Image of polytope 2052 PALP id: 2052
grdb id: 490177
Integer points: [ 1 0 -1 0 -2 0 -3 -2 -1 -2 -1 -1 -1 0 0]
[ 0 1 1 0 -1 -1 -4 -3 -2 -2 -1 0 -2 -1 0]
[ 0 0 0 1 -1 1 -2 -1 0 -1 0 0 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Image of facet 111 1 none
Polytope 2053
Image of polytope 2053 PALP id: 2053
grdb id: 491690
Integer points: [ 1 0 0 -2 -2 -2 -4 -1 -3 -2 -1 -3 -1 0 -1]
[ 0 1 0 0 -1 -2 -2 0 -1 -1 -1 -2 0 0 -1]
[ 0 0 1 -1 -2 -1 -3 0 -2 -1 0 -2 -1 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 8 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2054
Image of polytope 2054 PALP id: 2054
grdb id: 491389
Integer points: [ 1 0 0 -2 -1 -2 -4 -2 -3 -1 -1 -2 -3 0 -1]
[ 0 1 0 -1 0 -2 -3 -1 -2 -1 0 -1 -2 0 -1]
[ 0 0 1 -1 1 1 1 1 1 1 0 0 0 0 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 8 1 none
Image of facet 56 1 Lattice Minkowski decompositions of facet 56
Polytope 2055
Image of polytope 2055 PALP id: 2055
grdb id: 491513
Integer points: [ 1 0 0 -1 -2 -2 -4 -3 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 -1 -2 0 -2 -1 -1 0 -2 -1 0 -1 0]
[ 0 0 1 -1 -1 1 1 1 1 1 0 0 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
69 ? x + y + z + 2*x-1*z + 3*x-1 + x-2*z + 2*x-1*y-1 + 2*x-2*y-1*z + x-1*y-1*z-1 + 3*x-2*y-1 + 2*x-3*y-1*z + x-2*y-2*z-1 + 2*x-3*y-2 + x-4*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2056
Image of polytope 2056 PALP id: 2056
grdb id: 491371
Integer points: [ 1 0 0 -1 0 -2 -4 -1 -3 -2 -1 -3 -2 -1 0]
[ 0 1 0 0 1 -1 -3 0 -2 -1 0 -2 -1 -1 0]
[ 0 0 1 -1 1 1 -1 1 0 0 0 -1 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 8 1 none
Image of facet 9 1 irreducible and admissible
Polytope 2057
Image of polytope 2057 PALP id: 2057
grdb id: 491392
Integer points: [ 1 0 0 0 -1 -3 -4 -3 -2 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 0 -2 -3 -2 -1 -2 -1 -1 0 -1 0]
[ 0 0 0 1 1 -2 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 42 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2058
Image of polytope 2058 PALP id: 2058
grdb id: 491282
Integer points: [ 1 0 0 0 -1 -3 -4 -3 -2 -2 -1 -2 -1 -1 0]
[ 0 1 0 -1 0 -3 -3 -2 -1 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 1 -2 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 8 1 none
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 14 1 none
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2059
Image of polytope 2059 PALP id: 2059
grdb id: 490567
Integer points: [ 1 0 0 0 -1 -2 -4 -3 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 -1 1 1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 0 1 1 0 -1 -3 -2 -1 0 -2 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 8 1 none
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 13 1 irreducible and admissible
Polytope 2060
Image of polytope 2060 PALP id: 2060
grdb id: 491205
Integer points: [ 1 0 -1 0 -1 -3 -3 -2 -1 -3 -2 -1 -2 -1 0]
[ 0 1 -1 0 2 1 3 2 1 2 1 0 0 1 0]
[ 0 0 0 1 -1 -2 -2 -1 0 -2 -1 0 -1 -1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Image of facet 8 1 none
Polytope 2061
Image of polytope 2061 PALP id: 2061
grdb id: 491277
Integer points: [ 1 0 0 -2 -3 -3 -5 -3 -4 -1 -2 -1 -2 0 -1]
[ 0 1 0 -1 -2 -3 -4 -2 -3 -1 -2 0 -1 0 -1]
[ 0 0 1 0 -2 -2 -3 -1 -2 0 -1 0 -1 0 -1]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? x + y + z + 2*x-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + 3*x-2*y-1*z-1 + 3*x-2*y-2*z-1 + 3*x-3*y-2*z-1 + x-3*y-2*z-2 + x-3*y-3*z-2 + 3*x-4*y-3*z-2 + x-5*y-4*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2062
Image of polytope 2062 PALP id: 2062
grdb id: 490178
Integer points: [ 1 0 0 -2 -1 -2 -5 -3 -4 -2 -3 -1 -1 -2 0]
[ 0 1 0 -1 0 -1 -4 -2 -3 -1 -2 0 -1 -2 0]
[ 0 0 1 -1 1 1 -2 0 -1 0 -1 0 0 -1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 111 1 none
Polytope 2063
Image of polytope 2063 PALP id: 2063
grdb id: 491122
Integer points: [ 1 0 0 -1 -3 -4 -5 -4 -3 -2 -2 -1 -2 -1 0]
[ 0 1 0 -1 -2 -1 -2 -2 -1 -1 0 0 -1 -1 0]
[ 0 0 1 1 0 -2 -2 -1 -1 0 -1 0 -1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
69 ? x + y + z + 3*x-1 + x-1*y-1*z + 2*x-1*y-1 + 2*x-2*z-1 + 3*x-2*y-1 + 2*x-2*y-1*z-1 + 4*x-3*y-1*z-1 + x-3*y-2 + x-4*y-1*z-2 + 2*x-4*y-2*z-1 + x-5*y-2*z-2
37 rank 3, number 17 x + y + z + 2*x-1 + x-1*y-1*z + 2*x-1*y-1 + 2*x-2*z-1 + 3*x-2*y-1 + 2*x-2*y-1*z-1 + 3*x-3*y-1*z-1 + x-3*y-2 + x-4*y-1*z-2 + 2*x-4*y-2*z-1 + x-5*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 143 1 Lattice Minkowski decompositions of facet 143
Polytope 2064
Image of polytope 2064 PALP id: 2064
grdb id: 490480
Integer points: [ 1 0 -1 0 -3 -2 -4 -1 -2 -3 -1 -1 -2 0 -1]
[ 0 1 -1 0 2 3 4 1 2 3 2 0 1 0 1]
[ 0 0 0 1 -2 -2 -3 0 -1 -2 -1 0 -1 0 -1]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 64 1 none
Polytope 2065
Image of polytope 2065 PALP id: 2065
grdb id: 488560
Integer points: [ 1 0 -1 0 -2 0 -2 -1 0 -1 -2 -1 -2 0 0]
[ 0 1 1 0 1 -2 -2 -2 -1 -1 -1 0 0 -1 0]
[ 0 0 0 1 -1 1 -1 0 1 0 -1 0 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 4 1 none
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 9 1 irreducible and admissible
Polytope 2066
Image of polytope 2066 PALP id: 2066
grdb id: 486941
Integer points: [ 1 0 0 -1 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 0 -1 1 -2 2 1 0 -1 1 0 -1 0 0]
[ 0 0 1 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + 2*x-1*y + x-1*y*z-1 + x-2*y2*z-1 + 4*x-1 + 2*x-1*z-1 + 4*x-2*y*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + 6*x-2*z-1 + 4*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 2067
Image of polytope 2067 PALP id: 2067
grdb id: 489544
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -2 1 -2 2 1 0 -1 0 -1 1 0 -1]
[ 0 0 1 1 -2 2 -2 -1 0 1 -1 0 -1 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
101 ? x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 4*x-1*y*z-1 + 6*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + x-1*y*z-2 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 9 1 irreducible and admissible
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Polytope 2068
Image of polytope 2068 PALP id: 2068
grdb id: 488671
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 -1 -2 -2 -2 -1 0 -1 0 -1 -1 0]
[ 0 0 1 -1 -1 0 2 1 0 -1 1 0 0 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + 2*y-1*z + x-1*y*z-1 + 2*y-1 + 3*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2069
Image of polytope 2069 PALP id: 2069
grdb id: 489480
Integer points: [ 1 0 0 -1 0 -1 -1 -1 0 -1 -1 0 0 0 0]
[ 0 1 -1 0 1 -2 0 -1 0 -1 0 -1 0 1 0]
[ 0 0 0 0 2 -2 -2 -1 1 -2 -1 -1 0 1 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 y*z2 + 2*y*z + x + y + 2*z + 2*z-1 + y-1 + x-1 + 2*y-1*z-1 + 2*x-1*z-1 + x-1*z-2 + 2*x-1*y-1*z-1 + 2*x-1*y-1*z-2 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 4 irreducible and admissible
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2070
Image of polytope 2070 PALP id: 2070
grdb id: 488832
Integer points: [ 1 0 0 0 -2 -1 -2 -1 0 -1 -2 -1 -2 0 0]
[ 0 1 0 -2 2 -2 -1 1 -1 0 1 -1 0 0 -1]
[ 0 0 1 1 -1 0 -1 0 1 0 -1 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
100 ? x + y + z + 2*x-1*y + 2*y-1*z + x-2*y2*z-1 + 2*y-1 + 5*x-1 + y-2*z + 3*x-2*y*z-1 + 4*x-1*y-1 + 3*x-2*z-1 + x-1*y-2 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 9 1 irreducible and admissible
Polytope 2071
Image of polytope 2071 PALP id: 2071
grdb id: 486898
Integer points: [ 1 0 0 0 -1 -2 -2 -1 -1 -1 -2 -2 -2 0 0]
[ 0 1 0 -1 -2 2 -2 1 0 -1 1 0 -1 0 -1]
[ 0 0 1 1 0 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
100 ? x + y + z + 2*x-1*y + y-1*z + x-2*y2*z-1 + 2*y-1 + 5*x-1 + 4*x-2*y*z-1 + 4*x-1*y-1 + 6*x-2*z-1 + x-1*y-2 + 4*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 13 1 irreducible and admissible
Polytope 2072
Image of polytope 2072 PALP id: 2072
grdb id: 488745
Integer points: [ 1 0 0 0 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 -1 -1 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 1 -1 -1 2 1 0 1 0 1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Polytope 2073
Image of polytope 2073 PALP id: 2073
grdb id: 486793
Integer points: [ 1 0 -1 0 -2 0 -2 -1 -1 -1 -2 -2 -2 0 0]
[ 0 1 1 0 1 -1 -3 -2 -1 0 -2 -1 0 -1 0]
[ 0 0 0 1 -1 1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 4 1 none
Image of facet 13 1 irreducible and admissible
Polytope 2074
Image of polytope 2074 PALP id: 2074
grdb id: 488600
Integer points: [ 1 0 0 0 -2 -3 -3 -1 -2 -1 -2 -3 0 -1 -1]
[ 0 1 -1 0 2 0 2 0 0 1 1 1 0 0 1]
[ 0 0 0 1 -1 -2 -2 0 -1 0 -1 -2 0 -1 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? x + y + z + 2*x-1*y + 2*x-1*y*z-1 + x-2*y2*z-1 + y-1 + 3*x-1 + 2*x-1*z-1 + 4*x-2*y*z-1 + x-3*y2*z-2 + 3*x-2*z-1 + 2*x-3*y*z-2 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2075
Image of polytope 2075 PALP id: 2075
grdb id: 489543
Integer points: [ 1 0 1 -2 -1 -3 1 0 -1 -2 0 -1 1 0 -1]
[ 0 1 1 -1 -1 -2 2 1 0 -1 0 0 1 0 -1]
[ 0 0 2 -2 0 -2 2 1 0 -1 1 -1 1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
101 ? x*y2*z2 + x*y*z2 + 2*x*y*z + 4*y*z + x + y + 2*z + 6*x-1 + 2*x-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + 4*x-2*y-1*z-1 + x-2*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 6 irreducible and admissible
Image of facet 59 2 Lattice Minkowski decompositions of facet 59
Polytope 2076
Image of polytope 2076 PALP id: 2076
grdb id: 388983
Integer points: [ 1 0 0 -1 -1 -2 2 1 -1 0 1 -1 0 0 1]
[ 0 1 0 1 -1 0 -1 0 0 0 0 0 0 -1 -1]
[ 0 0 1 1 1 1 -2 -2 1 0 -1 0 -1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 5 2 none
Polytope 2077
Image of polytope 2077 PALP id: 2077
grdb id: 388986
Integer points: [ 1 0 0 -1 1 0 0 -1 1 0 0 0 0 0 -1]
[ 0 1 1 2 -2 -1 -1 0 -1 0 -1 0 1 0 1]
[ 0 0 2 2 -2 -2 0 0 -1 1 -1 0 1 -1 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 5 2 none
Image of facet 15 4 Lattice Minkowski decompositions of facet 15
Polytope 2078
Image of polytope 2078 PALP id: 2078
grdb id: 388982
Integer points: [ 1 0 0 0 -2 2 -2 1 1 0 -1 1 0 -1 -1]
[ 0 1 0 0 2 -2 1 -2 -1 -1 0 -1 0 1 1]
[ 0 0 1 -1 1 -1 0 0 -1 0 0 0 0 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 5 2 none
Polytope 2079
Image of polytope 2079 PALP id: 2079
grdb id: 388985
Integer points: [ 1 1 -1 -1 0 0 1 1 1 1 1 0 0 0 -1]
[ 0 2 -2 0 0 1 2 -1 1 0 1 -1 0 1 -1]
[ 0 0 0 0 1 1 -1 -1 0 -1 -1 0 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 6 2 none
Polytope 2080
Image of polytope 2080 PALP id: 2080
grdb id: 388984
Integer points: [ 1 1 -1 -1 0 1 0 1 1 1 0 0 0 0 -1]
[ 0 2 -2 0 0 -1 2 1 1 0 -1 1 0 1 -1]
[ 0 0 0 0 1 -1 1 -1 0 -1 0 1 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 6 2 none
Image of facet 15 4 Lattice Minkowski decompositions of facet 15
Polytope 2081
Image of polytope 2081 PALP id: 2081
grdb id: 388954
Integer points: [ 1 0 0 -1 0 -2 1 0 -1 -1 0 -1 0 0 1]
[ 0 1 0 1 0 0 -2 -2 0 -1 -1 0 0 -1 -1]
[ 0 0 1 1 -1 1 -2 -1 0 0 -1 1 0 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + x-1*y*z + 2*x-1*z + 2*x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + x-2*z + 2*y-1*z-1 + 2*x-1*y-1 + x*y-2*z-2 + y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2082
Image of polytope 2082 PALP id: 2082
grdb id: 388949
Integer points: [ 1 0 0 -1 0 0 -2 -2 -1 -2 -1 0 -1 -1 0]
[ 0 1 0 1 -1 -1 1 1 0 1 0 -1 0 1 0]
[ 0 0 1 1 -1 1 1 -1 1 0 0 0 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 8 1 none
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 2083
Image of polytope 2083 PALP id: 2083
grdb id: 388956
Integer points: [ 1 0 0 -1 1 1 -2 -2 -1 0 -1 0 -1 0 1]
[ 0 1 0 1 -2 -2 1 1 0 -1 0 -1 1 0 -1]
[ 0 0 1 1 0 -1 0 -1 0 0 -1 -1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 6 1 none
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2084
Image of polytope 2084 PALP id: 2084
grdb id: 388931
Integer points: [ 1 0 0 0 -1 -2 -1 -2 -2 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 1 1 -2 -1 0 0 -1 1 0 0 -1]
[ 0 0 0 1 1 0 -2 -2 -1 0 -1 0 -1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
60 rank 2, number 18 x + y + z + x-1*y*z + 2*x-1*y + y-1 + 2*x-1 + x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
36 rank 3, number 7 x + y + z + x-1*y*z + 2*x-1*y + y-1 + 4*x-1 + x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1*z-1 + 2*x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2085
Image of polytope 2085 PALP id: 2085
grdb id: 388942
Integer points: [ 1 0 0 0 -1 -2 0 1 -1 0 -1 0 -1 1 0]
[ 0 1 0 0 1 0 -2 -2 -1 -1 0 -1 0 -1 0]
[ 0 0 1 -1 0 1 -1 -2 0 0 1 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 46 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2086
Image of polytope 2086 PALP id: 2086
grdb id: 388962
Integer points: [ 1 0 0 0 -1 -1 -2 -2 -2 -1 -1 -1 0 -1 0]
[ 0 1 0 -2 1 -1 0 -2 -1 0 0 -1 0 -2 -1]
[ 0 0 1 -1 1 -1 1 -1 0 0 1 0 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
32 ? x + y + z + x-1*y*z + 2*x-1*z + 2*y-1 + 3*x-1 + x-2*z + 4*x-1*y-1 + y-2*z-1 + x-1*y-1*z-1 + 2*x-2*y-1 + 2*x-1*y-2*z-1 + x-2*y-2*z-1
8 ? x + y + z + x-1*y*z + 2*x-1*z + 2*y-1 + 2*x-1 + x-2*z + 4*x-1*y-1 + y-2*z-1 + x-1*y-1*z-1 + 2*x-2*y-1 + 2*x-1*y-2*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2087
Image of polytope 2087 PALP id: 2087
grdb id: 388967
Integer points: [ 1 0 0 0 -1 -1 -2 -2 -1 -2 -1 -1 0 -1 0]
[ 0 1 0 -1 -1 0 -1 -1 0 -1 0 -1 0 -1 0]
[ 0 0 1 0 1 -2 0 -2 0 -1 -1 0 0 -1 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
25 ? x + y + z + 2*z-1 + y-1 + 2*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-2*y-1 + 2*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2088
Image of polytope 2088 PALP id: 2088
grdb id: 388953
Integer points: [ 1 0 0 0 1 -2 0 -2 -1 -1 0 -1 0 -1 0]
[ 0 1 0 0 -1 1 -2 0 -1 0 -1 0 -1 1 0]
[ 0 0 1 -1 -1 0 -1 -1 -1 0 0 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + 2*x-1*y + x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2089
Image of polytope 2089 PALP id: 2089
grdb id: 388874
Integer points: [ 1 0 1 0 -2 0 -1 -2 -1 -2 -1 0 -1 0 1]
[ 0 1 -2 0 1 -1 1 1 0 1 0 -1 1 0 -1]
[ 0 0 0 1 -1 1 1 1 1 0 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 37 1 none
Image of facet 8 1 none
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 2090
Image of polytope 2090 PALP id: 2090
grdb id: 388932
Integer points: [ 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 -2 2 2 1 -1 0 1 0 -1 0 1]
[ 0 0 1 0 -2 1 2 2 -1 0 1 1 -1 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? y2*z + x-1*y2*z2 + y*z + x-1*y*z2 + x + y + z + 4*x-1*y*z + 2*x-1*z + 6*x-1 + 2*y-1*z-1 + x-1*y-1 + 4*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2091
Image of polytope 2091 PALP id: 2091
grdb id: 388966
Integer points: [ 1 0 0 0 -2 1 0 -2 -1 -1 -1 -1 0 0 1]
[ 0 1 -1 0 -1 2 2 0 1 0 0 -1 1 0 1]
[ 0 0 0 1 -2 2 1 -1 0 -1 0 -1 1 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x*y2*z2 + 2*x*y*z + y2*z + 2*y*z + x + y + z + 2*x-1*y + y-1 + 2*x-1 + 2*x-1*z-1 + 2*x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2092
Image of polytope 2092 PALP id: 2092
grdb id: 388964
Integer points: [ 1 0 0 0 0 -1 -1 1 0 -1 0 1 0 0 0]
[ 0 1 1 -1 -1 0 0 -2 -1 0 0 -1 0 0 1]
[ 0 0 2 -2 0 1 -1 -2 -1 0 1 -1 0 -1 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 y*z2 + 2*y*z + x + y + 2*z + x-1*z + 2*x*y-1*z-1 + 2*z-1 + y-1 + 2*x-1 + 3*y-1*z-1 + x-1*z-1 + x*y-2*z-2 + y-1*z-2
20 rank 1, V16 y*z2 + 2*y*z + x + y + 2*z + x-1*z + 2*x*y-1*z-1 + 2*z-1 + y-1 + 2*x-1 + 2*y-1*z-1 + x-1*z-1 + x*y-2*z-2 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 15 3 Lattice Minkowski decompositions of facet 15
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2093
Image of polytope 2093 PALP id: 2093
grdb id: 388975
Integer points: [ 1 0 0 0 0 1 -1 -1 0 -1 -1 0 0 0 0]
[ 0 1 1 -1 -1 0 1 -2 0 -1 0 -1 0 1 0]
[ 0 0 2 -2 0 -1 1 -2 -1 -1 0 -1 0 1 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 y*z2 + 2*y*z + x + y + 2*z + x-1*y*z + x*z-1 + 2*z-1 + y-1 + 3*x-1 + y-1*z-1 + y-1*z-2 + 3*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Polytope 2094
Image of polytope 2094 PALP id: 2094
grdb id: 388959
Integer points: [ 1 0 0 0 1 0 -1 -1 0 -1 -1 -1 0 0 0]
[ 0 1 0 0 -1 -2 2 -2 -1 1 0 -1 1 0 -1]
[ 0 0 1 -1 0 1 -2 2 0 -1 0 1 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + 2*y*z-1 + x*y-1 + y-1*z + x-1*y2*z-2 + z-1 + 4*x-1*y*z-1 + 2*y-1 + 6*x-1 + y-2*z + 4*x-1*y-1*z + x-1*y-2*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2095
Image of polytope 2095 PALP id: 2095
grdb id: 388952
Integer points: [ 1 0 1 0 1 -1 -2 -2 0 -1 0 -1 1 0 -1]
[ 0 1 -2 0 -2 0 2 1 -1 0 -1 1 -1 0 1]
[ 0 0 0 1 -1 -1 1 0 0 0 -1 1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 6 1 none
Polytope 2096
Image of polytope 2096 PALP id: 2096
grdb id: 388971
Integer points: [ 1 0 1 1 -2 -1 1 0 0 0 -1 0 1 -1 0]
[ 0 1 0 -1 0 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 0 2 0 -1 -2 -1 -2 -1 -1 -1 0 1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 1 none
Image of facet 1 1 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 9 1 irreducible and admissible
Polytope 2097
Image of polytope 2097 PALP id: 2097
grdb id: 388876
Integer points: [ 1 0 1 -2 0 -1 1 -2 0 0 -1 -1 1 0 -1]
[ 0 1 -2 1 0 1 -3 0 -1 -2 0 -1 -1 0 1]
[ 0 0 0 0 1 1 -1 -1 0 -1 0 -1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
24 ? x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + x*y-3*z-1 + 3*y-2*z-1 + 3*x-1*y-1*z-1 + x-2*z-1
75 ? x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + x*y-2 + 4*y-1 + 4*x-1 + x-2*y + x*y-3*z-1 + 3*y-2*z-1 + 3*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Polytope 2098
Image of polytope 2098 PALP id: 2098
grdb id: 388879
Integer points: [ 1 0 -1 0 1 -3 -2 0 -1 0 -1 -2 1 0 -1]
[ 0 1 -1 0 2 -2 0 2 1 1 0 -1 1 0 -1]
[ 0 0 0 1 2 -2 -1 1 0 1 0 -1 1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x*y2*z2 + 2*x*y*z + y2*z + y*z + x + y + z + 2*x-1*y + x-1 + x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + 2*x-2*y-1*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 114 1 Lattice Minkowski decompositions of facet 114
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 2099
Image of polytope 2099 PALP id: 2099
grdb id: 388738
Integer points: [ 1 0 0 1 -3 -2 1 0 -1 0 -1 -2 1 0 -1]
[ 0 1 0 2 -2 0 1 2 1 1 0 -1 1 0 -1]
[ 0 0 1 2 -2 -1 2 1 0 1 0 -1 1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
100 ? x*y2*z2 + x*y*z2 + 2*x*y*z + y2*z + y*z + x + y + z + 2*x-1*y + 3*x-1 + 2*x-1*y-1*z-1 + x-2*z-1 + 3*x-2*y-1*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 116 1 Lattice Minkowski decompositions of facet 116
Polytope 2100
Image of polytope 2100 PALP id: 2100
grdb id: 388847
Integer points: [ 1 0 0 1 -1 0 -1 -3 -2 -1 0 -2 -1 0 1]
[ 0 1 0 -2 0 -1 0 2 1 0 -1 1 1 0 -1]
[ 0 0 1 0 -1 1 1 -1 0 0 0 -1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 8 1 none
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Polytope 2101
Image of polytope 2101 PALP id: 2101
grdb id: 388943
Integer points: [ 1 0 1 -2 0 1 -2 -1 -1 -1 0 0 -1 0 1]
[ 0 1 -2 1 0 -3 2 -1 0 1 -2 -1 1 0 -1]
[ 0 0 0 0 1 -1 1 -1 0 1 -1 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
24 ? x + y + z + 2*x-1*y*z + x-2*y2*z + 2*x*y-1 + 2*x-1*y + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + x*y-3*z-1 + 2*y-2*z-1 + x-1*y-1*z-1
75 ? x + y + z + 2*x-1*y*z + x-2*y2*z + 2*x*y-1 + 2*x-1*y + x*y-2 + 4*y-1 + 4*x-1 + x-2*y + x*y-3*z-1 + 2*y-2*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 96 1 Lattice Minkowski decompositions of facet 96
Image of facet 1 4 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 2102
Image of polytope 2102 PALP id: 2102
grdb id: 388950
Integer points: [ 1 0 0 0 -1 -2 -2 -4 -2 -3 -1 -3 -1 -2 0]
[ 0 1 -1 0 1 0 2 2 1 1 0 2 1 1 0]
[ 0 0 0 1 -1 -1 -1 -1 0 -1 0 -1 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
76 ? x + y + z + 2*x-1*y + x-1*y*z-1 + x-2*y2*z-1 + y-1 + 2*x-1 + 2*x-2*y + 2*x-2*y*z-1 + 2*x-3*y2*z-1 + x-2*z-1 + 2*x-3*y*z-1 + x-4*y2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 22 3 Lattice Minkowski decompositions of facet 22
Polytope 2103
Image of polytope 2103 PALP id: 2103
grdb id: 388295
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 0 -2 -1 -2 -2 -1 -1 0 -1 -1 0]
[ 0 0 1 -1 1 0 1 -2 -1 0 -1 0 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
55 rank 2, number 19 x + y + z + x-1*z + 2*y-1 + 2*x-1 + x-1*y-1*z + 2*y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 71 1 Lattice Minkowski decompositions of facet 71
Polytope 2104
Image of polytope 2104 PALP id: 2104
grdb id: 387010
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 1 -1 -2 -1 0 1 0 -1 0 0 -1]
[ 0 0 1 -1 1 -1 0 1 1 0 0 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
85 rank 3, number 8 x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + x-1*y*z-1 + 2*y-1 + 4*x-1 + x-1*y-1*z + 2*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
134 ? x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + x-1*y*z-1 + 2*y-1 + 5*x-1 + x-1*y-1*z + 2*x-1*z-1 + 4*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Polytope 2105
Image of polytope 2105 PALP id: 2105
grdb id: 388129
Integer points: [ 1 0 0 -1 0 -1 -2 -2 -2 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -1 -2 0 -2 -1 -1 0 -1 0 -1 0]
[ 0 0 1 0 -1 0 1 1 1 0 0 1 1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + x-1*y + 2*x-1*z + 2*y-1 + 2*x-1 + 2*x-1*y-1*z + x-2*z + y-1*z-1 + x-1*y-1 + 2*x-2*y-1*z + x-1*y-2 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 47 1 Lattice Minkowski decompositions of facet 47
Polytope 2106
Image of polytope 2106 PALP id: 2106
grdb id: 388443
Integer points: [ 1 0 0 -1 1 0 -2 -2 -1 -1 0 -1 0 -1 0]
[ 0 1 0 1 -1 -2 -1 -2 -2 -1 -1 -1 -1 0 0]
[ 0 0 1 0 -1 -1 -1 -1 -1 0 0 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2107
Image of polytope 2107 PALP id: 2107
grdb id: 387279
Integer points: [ 1 0 0 -1 1 1 0 -2 0 -1 0 -1 0 -1 0]
[ 0 1 0 1 -1 0 -2 0 -1 0 0 -1 -1 0 0]
[ 0 0 1 0 0 -1 1 -1 1 0 0 0 0 -1 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*z-1 + x*y-1 + x-1*y + 2*y-1*z + 3*z-1 + 3*y-1 + 2*x-1 + y-2*z + 3*x-1*z-1 + 2*x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 2108
Image of polytope 2108 PALP id: 2108
grdb id: 388579
Integer points: [ 1 0 0 0 -1 -2 -1 -2 -2 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 0 -2 -2 -1 0 -1 0 -1 0 -1]
[ 0 0 1 -1 0 1 0 1 1 0 0 1 1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
55 rank 2, number 19 x + y + z + x-1*y + 2*x-1*z + z-1 + 2*y-1 + x-1 + 2*x-1*y-1*z + x-2*z + x-1*y-1 + 2*x-2*y-1*z + x-1*y-2 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 48 1 Lattice Minkowski decompositions of facet 48
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2109
Image of polytope 2109 PALP id: 2109
grdb id: 387399
Integer points: [ 1 0 0 0 -1 -1 -2 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 -1 -1 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 0 1 1 1 1 -2 0 -1 0 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + x-1*z + y-1 + 3*x-1 + x-1*y-1*z + 2*x-1*z-1 + 3*x-1*y-1 + x-2*y-1*z + 2*x-1*y-1*z-1 + 3*x-2*y-1 + 3*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Polytope 2110
Image of polytope 2110 PALP id: 2110
grdb id: 387994
Integer points: [ 1 0 0 0 -1 -1 -2 -2 -2 -1 -1 -1 -1 0 0]
[ 0 1 0 1 1 -2 0 -2 -1 0 -1 0 -1 0 -1]
[ 0 0 1 -1 0 0 1 1 1 0 0 1 1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
60 rank 2, number 18 x + y + z + y*z-1 + x-1*y + 2*x-1*z + 2*y-1 + x-1 + 2*x-1*y-1*z + x-2*z + 2*x-1*y-1 + 2*x-2*y-1*z + x-1*y-2 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 47 1 Lattice Minkowski decompositions of facet 47
Polytope 2111
Image of polytope 2111 PALP id: 2111
grdb id: 387274
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 0 0 -1 -1]
[ 0 1 0 -1 1 -1 -2 -2 0 -1 -2 0 -1 0 -1]
[ 0 0 1 1 -1 1 1 -1 0 0 0 0 0 -1 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2112
Image of polytope 2112 PALP id: 2112
grdb id: 387295
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 1 1 -2 0 0 -1 0 -1 0 -1 0]
[ 0 0 1 1 0 -1 0 -2 0 0 -1 -1 0 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 y*z + x + y + z + x-1*y + 2*z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2113
Image of polytope 2113 PALP id: 2113
grdb id: 388555
Integer points: [ 1 0 0 0 -1 -1 0 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 -1 1 -1 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 1 1 1 -2 -1 0 0 1 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y*z + y-1*z + 2*x-1*z + 2*z-1 + 3*y-1 + 2*x-1 + x-1*y-1*z + 3*y-1*z-1 + 2*x-1*y-1 + y-1*z-2 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2114
Image of polytope 2114 PALP id: 2114
grdb id: 388599
Integer points: [ 1 0 0 0 -1 0 -2 -2 -1 -1 0 -1 -1 0 0]
[ 0 1 0 0 1 -2 1 0 -1 0 -1 0 1 -1 0]
[ 0 0 1 -1 -1 1 0 1 1 0 0 1 0 1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + 2*x-1*y + 2*y-1*z + 2*x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-2*y + y-2*z + 2*x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2115
Image of polytope 2115 PALP id: 2115
grdb id: 388505
Integer points: [ 1 0 0 0 1 -2 1 0 -1 0 1 -1 0 -1 0]
[ 0 1 0 -1 -1 1 -1 -1 0 -1 -1 0 0 1 0]
[ 0 0 1 0 1 0 -1 -2 0 -1 0 -1 0 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + x*y-1*z + z + 2*x*y-1 + 2*x-1*y + x*y-1*z-1 + 2*z-1 + y-1 + 2*x-1 + x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2116
Image of polytope 2116 PALP id: 2116
grdb id: 387282
Integer points: [ 1 0 1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 1 1 0 -2 1 0 -1 0 -1 0 -1]
[ 0 0 0 1 -1 1 1 -1 0 0 0 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 8 1 none
Polytope 2117
Image of polytope 2117 PALP id: 2117
grdb id: 387523
Integer points: [ 1 0 1 0 -1 0 -2 -2 -1 -2 -1 0 -1 -1 0]
[ 0 1 -1 0 -1 -2 0 -2 -2 -1 -1 -1 0 0 0]
[ 0 0 0 1 -1 -1 1 -1 -1 0 0 0 1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Polytope 2118
Image of polytope 2118 PALP id: 2118
grdb id: 387296
Integer points: [ 1 0 1 0 0 -1 -2 -2 -1 0 -2 -1 -1 0 -1]
[ 0 1 -1 0 -1 0 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 0 1 -1 1 0 -2 0 0 -1 -1 0 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x*y-1 + x-1*z + 3*y-1 + 2*x-1 + y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + x-2*y-1 + 2*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 2119
Image of polytope 2119 PALP id: 2119
grdb id: 388519
Integer points: [ 1 0 0 -1 -2 1 1 -2 -1 0 -1 0 -1 0 1]
[ 0 1 0 1 1 -2 -2 1 0 -1 0 -1 1 0 -1]
[ 0 0 1 0 -1 1 2 -2 0 1 -1 0 -1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + 2*x*y-1*z + z + x*y-2*z2 + x-1*y + x*y-2*z + 3*y-1*z + 2*x-1*y*z-1 + 3*y-1 + 3*x-1 + 3*x-1*z-1 + x-2*y*z-1 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2120
Image of polytope 2120 PALP id: 2120
grdb id: 387405
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 -1 -2 2 -1 0 1 0 1 -1 0]
[ 0 0 1 1 1 -1 0 -1 0 0 0 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y2*z-1 + 2*x-1*y + x-1*z + 3*x-1*y*z-1 + 2*y-1 + 4*x-1 + x-1*y-1*z + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 9 1 irreducible and admissible
Polytope 2121
Image of polytope 2121 PALP id: 2121
grdb id: 387412
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 2 -2 -1 0 1 -1 0 1 -1 0]
[ 0 0 1 -1 0 -1 2 2 1 0 1 0 -1 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y2*z-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + 2*x-1*y*z-1 + 4*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Polytope 2122
Image of polytope 2122 PALP id: 2122
grdb id: 388247
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 0 -2 -1 -2 0 -1 -1 -2 0 -1 -1]
[ 0 0 1 -1 1 0 2 2 0 1 0 1 0 1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
29 rank 2, number 23 x + y + z + 2*y-1*z + x-1*z + x-1*y-1*z2 + 2*y-1 + 2*x-1 + 2*x-1*y-1*z + x-1*y-2*z2 + x-1*z-1 + x-1*y-1 + 2*x-1*y-2*z + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 71 1 Lattice Minkowski decompositions of facet 71
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2123
Image of polytope 2123 PALP id: 2123
grdb id: 388446
Integer points: [ 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 2 1 -2 -1 -2 -1 0 0 1 -1 -1 0]
[ 0 0 1 -1 0 1 -1 0 0 0 -1 -1 1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 6 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2124
Image of polytope 2124 PALP id: 2124
grdb id: 387335
Integer points: [ 1 0 0 -1 0 -2 -1 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 1 -1 2 2 0 1 0 1 0 1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + y-1*z + 2*x-1*z + x-1*y-1*z2 + 3*x-1 + 3*x-1*y-1*z + x-2*y-1*z2 + x-1*z-1 + 2*x-1*y-1 + 3*x-2*y-1*z + 3*x-2*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Polytope 2125
Image of polytope 2125 PALP id: 2125
grdb id: 387330
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 -2 -1 2 1 0 1 0 -1 0 -1]
[ 0 0 1 -1 1 0 1 1 1 1 0 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
143 ? y*z + x-1*y2*z + x + y + z + 3*x-1*y*z + 2*x-1*y + 3*x-1*z + 2*y-1 + 3*x-1 + x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 56 1 Lattice Minkowski decompositions of facet 56
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2126
Image of polytope 2126 PALP id: 2126
grdb id: 387374
Integer points: [ 1 0 0 0 -2 0 -1 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 0 1 -1 1 2 2 1 0 1 0 1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 66 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Polytope 2127
Image of polytope 2127 PALP id: 2127
grdb id: 388474
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 -1 0 0 2 -2 2 -1 0 1 1 -1 0 1]
[ 0 0 0 1 -1 1 -2 2 -1 0 1 0 -1 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
109 ? x-1*y2*z2 + 2*y*z + x-1*y2*z + x + y + z + 4*x-1*y*z + 2*x-1*y + y-1 + 6*x-1 + 2*y-1*z-1 + x-1*z-1 + 4*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Polytope 2128
Image of polytope 2128 PALP id: 2128
grdb id: 388559
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 1 2 -2 -2 0 -1 1 0 -1 0 -1]
[ 0 0 1 1 0 -1 0 -1 0 0 -1 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 6 1 none
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 13 1 irreducible and admissible
Polytope 2129
Image of polytope 2129 PALP id: 2129
grdb id: 388581
Integer points: [ 1 0 0 1 -2 2 0 -1 0 1 1 -1 0 0 -1]
[ 0 1 0 -1 1 -2 -2 -1 -1 -2 -1 0 -1 0 1]
[ 0 0 1 -1 0 -1 -1 -1 0 -1 0 0 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 8 1 none
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2130
Image of polytope 2130 PALP id: 2130
grdb id: 388625
Integer points: [ 1 1 -1 -1 0 0 1 -1 -1 0 0 0 0 0 1]
[ 0 2 -2 0 0 2 0 -2 -1 1 -1 0 1 -1 1]
[ 0 0 0 0 1 1 -1 -1 0 0 -1 0 1 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 x*y2 + y2*z + 2*x*y + 2*y*z + x + 2*y + z + x*z-1 + 2*y-1 + x-1 + 2*y-1*z-1 + 2*x-1*y-1 + x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 15 4 Lattice Minkowski decompositions of facet 15
Polytope 2131
Image of polytope 2131 PALP id: 2131
grdb id: 386440
Integer points: [ 1 0 -1 0 -2 -1 0 -3 -2 -1 -2 -1 0 -1 0]
[ 0 1 1 0 0 -2 -1 -2 -2 -1 -1 0 -1 -1 0]
[ 0 0 0 1 -1 0 1 -2 -1 0 -1 0 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
32 ? x + y + z + x-1*y + y-1*z + 2*y-1 + 3*x-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + 2*x-2*y-2*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 117 1 Lattice Minkowski decompositions of facet 117
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2132
Image of polytope 2132 PALP id: 2132
grdb id: 387287
Integer points: [ 1 0 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 -1 -1]
[ 0 1 1 0 0 0 -1 -3 -2 -1 0 -1 0 -2 -1]
[ 0 0 0 1 -1 1 1 -1 0 0 0 0 0 -1 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 8 1 none
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Polytope 2133
Image of polytope 2133 PALP id: 2133
grdb id: 387304
Integer points: [ 1 0 -1 0 1 -2 1 0 0 0 -1 -1 -1 0 0]
[ 0 1 1 0 -1 -1 -2 -3 -1 -2 0 -1 -2 0 -1]
[ 0 0 0 1 1 -1 1 1 1 1 0 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 56 1 Lattice Minkowski decompositions of facet 56
Polytope 2134
Image of polytope 2134 PALP id: 2134
grdb id: 387303
Integer points: [ 1 0 0 -2 0 -3 -1 -3 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 0 -1 -1 -2 -3 -2 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 1 -1 1 1 1 1 0 0 0 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 8 1 none
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Polytope 2135
Image of polytope 2135 PALP id: 2135
grdb id: 387302
Integer points: [ 1 0 0 -1 -2 0 -1 -2 -2 -2 -1 -1 -1 0 0]
[ 0 1 0 -1 0 -1 -2 -3 -1 -2 0 -1 -2 0 -1]
[ 0 0 1 -1 -1 1 -1 -1 -1 -1 0 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 8 1 none
Polytope 2136
Image of polytope 2136 PALP id: 2136
grdb id: 386225
Integer points: [ 1 0 0 -1 -1 -2 -3 -3 -2 -3 -1 -2 -1 0 -1]
[ 0 1 0 0 0 -1 -2 -2 -1 -2 0 -1 -1 0 -1]
[ 0 0 1 -1 1 1 0 -2 0 -1 0 -1 0 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + x-1*z + 3*x-1 + x-1*z-1 + 2*x-1*y-1 + x-2*y-1*z + 2*x-1*y-1*z-1 + 2*x-2*y-1 + 2*x-2*y-1*z-1 + x-3*y-2 + 2*x-3*y-2*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 117 1 Lattice Minkowski decompositions of facet 117
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2137
Image of polytope 2137 PALP id: 2137
grdb id: 387531
Integer points: [ 1 0 0 -1 -1 -1 -3 -3 -2 -3 -2 -1 -2 -1 0]
[ 0 1 0 -1 1 1 -1 1 1 0 0 0 -1 0 0]
[ 0 0 1 0 0 -1 -2 -2 -1 -2 -1 0 -1 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 8 1 none
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Polytope 2138
Image of polytope 2138 PALP id: 2138
grdb id: 387402
Integer points: [ 1 0 0 -1 -1 0 -1 -1 -1 -1 0 -1 -1 0 0]
[ 0 1 0 0 0 -2 -2 -3 -2 -1 -1 -1 0 -1 0]
[ 0 0 1 -1 1 -1 -2 -2 -1 0 0 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*z + 2*y-1 + 2*x-1 + 2*y-1*z-1 + x-1*z-1 + 3*x-1*y-1 + y-2*z-1 + 3*x-1*y-1*z-1 + 3*x-1*y-2*z-1 + x-1*y-2*z-2 + x-1*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2139
Image of polytope 2139 PALP id: 2139
grdb id: 388485
Integer points: [ 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 0 -2 -2 -3 0 -1 -1 -2 0 -1 -1]
[ 0 0 1 1 1 -1 -2 -2 0 -1 0 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y*z + x-1*z + 2*y-1 + 3*x-1 + 2*y-1*z-1 + 3*x-1*y-1 + y-2*z-1 + 3*x-1*y-1*z-1 + 3*x-1*y-2*z-1 + x-1*y-2*z-2 + x-1*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2140
Image of polytope 2140 PALP id: 2140
grdb id: 387580
Integer points: [ 1 0 0 -1 0 -2 -1 -3 -1 -2 -1 -2 0 -1 0]
[ 0 1 0 1 -1 1 -2 0 0 0 -1 -1 0 0 -1]
[ 0 0 1 0 1 -1 0 -2 0 -1 0 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
55 rank 2, number 19 x + y + z + x-1*y + y-1*z + 2*y-1 + 2*x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + x-2*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 115 1 Lattice Minkowski decompositions of facet 115
Polytope 2141
Image of polytope 2141 PALP id: 2141
grdb id: 387300
Integer points: [ 1 0 0 0 -1 -2 -1 -3 -2 -1 -2 -1 -1 0 0]
[ 0 1 -1 0 1 1 -2 0 0 0 -1 -1 0 0 -1]
[ 0 0 0 1 0 -1 -2 -2 -1 0 -2 -1 -1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y + y-1 + 3*x-1 + 2*y-1*z-1 + 3*x-1*z-1 + x-2*y*z-1 + 3*x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2*z-2 + 2*x-2*y-1*z-2 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2142
Image of polytope 2142 PALP id: 2142
grdb id: 388437
Integer points: [ 1 0 0 0 -1 -2 -1 -2 -1 -1 -2 0 0 -1 -1]
[ 0 1 -1 0 0 -1 -2 -3 -2 -1 -2 -1 0 -1 0]
[ 0 0 0 1 1 0 -2 -2 -1 0 -1 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + x-1*z + y-1 + 2*x-1 + 2*y-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + 2*x-1*y-2*z-1 + x-1*y-2*z-2 + 2*x-2*y-2*z-1 + x-2*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2143
Image of polytope 2143 PALP id: 2143
grdb id: 388557
Integer points: [ 1 0 0 0 -1 -1 -1 -3 -2 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 -1 1 1 1 0 1 0 1 0 1 0]
[ 0 0 0 1 -1 -1 1 -1 -1 0 0 -1 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + x-1*y*z + 2*x-1*y + x-1*y*z-1 + y-1 + 3*x-1 + 2*x-2*y + 2*x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1*z-1 + 2*x-2*z-1 + x-3*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2144
Image of polytope 2144 PALP id: 2144
grdb id: 387394
Integer points: [ 1 0 0 0 -1 0 -2 -3 -1 -2 -1 -1 -2 0 -1]
[ 0 1 -1 0 1 -1 -3 -3 -1 -2 -2 0 -1 0 -1]
[ 0 0 0 1 0 -1 -2 -2 0 -1 -1 0 -1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 14 1 none
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2145
Image of polytope 2145 PALP id: 2145
grdb id: 387411
Integer points: [ 1 0 0 0 0 -2 -2 -3 -1 -2 0 -1 -1 0 -1]
[ 0 1 0 -1 -2 1 1 1 -1 0 -1 0 0 0 1]
[ 0 0 1 -1 -1 0 -1 -1 -1 -1 0 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + 2*x-1*y + 2*y-1 + 3*x-1 + x-2*y + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1 + y-2*z-1 + 3*x-1*y-1*z-1 + 3*x-2*z-1 + x-3*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2146
Image of polytope 2146 PALP id: 2146
grdb id: 388498
Integer points: [ 1 0 0 0 0 -2 -1 -2 -2 -1 -1 -1 0 -1 0]
[ 0 1 0 0 -1 0 -2 -2 -1 -1 0 -1 -1 0 0]
[ 0 0 1 -1 0 -1 -2 -3 -2 -1 0 -2 -1 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + z-1 + y-1 + 2*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1*z-1 + x-2*z-1 + 2*x-1*y-1*z-2 + x-1*y-2*z-2 + 2*x-2*y-1*z-2 + x-2*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2147
Image of polytope 2147 PALP id: 2147
grdb id: 388435
Integer points: [ 1 0 0 1 -1 -1 -3 -3 -2 -1 -2 0 -1 0 -1]
[ 0 1 0 -1 1 -1 0 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 0 -1 0 -2 -2 -1 0 -1 0 -1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x*y-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + 2*x-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*z-1 + 2*x-2*y-1*z-1 + x-3*z-2 + x-3*y-1*z-2
36 rank 3, number 7 x + y + z + x*y-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + 3*x-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*z-1 + 2*x-2*y-1*z-1 + x-3*z-2 + x-3*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2148
Image of polytope 2148 PALP id: 2148
grdb id: 387256
Integer points: [ 1 0 1 -1 0 0 -1 -1 -1 -1 0 0 -1 -1 0]
[ 0 1 -1 1 0 -1 0 -3 -2 -1 -2 -1 -1 0 0]
[ 0 0 0 0 1 -1 1 -2 -1 0 -1 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2149
Image of polytope 2149 PALP id: 2149
grdb id: 388568
Integer points: [ 1 0 1 0 -1 -1 -2 -3 -2 -2 -1 -1 0 -1 0]
[ 0 1 -1 0 1 -1 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 0 1 -1 -1 0 -1 -1 -1 -1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x*y-1 + x-1*y*z-1 + 3*y-1 + 2*x-1 + 2*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1 + 2*x-2*y-1*z-1 + x-3*y-1*z-1
85 rank 3, number 8 x + y + z + x*y-1 + x-1*y*z-1 + 3*y-1 + 3*x-1 + 2*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1 + 2*x-2*y-1*z-1 + x-3*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2150
Image of polytope 2150 PALP id: 2150
grdb id: 387291
Integer points: [ 1 0 1 0 -1 1 -2 0 0 0 -1 -1 0 0 -1]
[ 0 1 -1 0 1 -2 1 -3 -2 -1 -1 0 -1 0 1]
[ 0 0 0 1 1 -1 0 -2 -1 0 -1 0 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + x-1*y*z + x*y-1 + 2*x-1*y + 3*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + 3*y-2*z-1 + 2*x-1*y-1*z-1 + y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2151
Image of polytope 2151 PALP id: 2151
grdb id: 388570
Integer points: [ 1 0 0 0 0 -1 -2 -2 -1 -1 0 0 0 -1 -1]
[ 0 1 -1 0 -2 2 2 3 1 2 -1 0 1 0 1]
[ 0 0 0 1 1 -2 -1 -2 0 -1 1 0 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + 2*y*z-1 + 2*x-1*y2*z-1 + 2*x-1*y + 2*y-1*z + x-1*y2*z-2 + x-2*y3*z-2 + 3*x-1*y*z-1 + x-2*y2*z-1 + y-1 + 2*x-1 + y-2*z
13 rank 2, number 12 x + y + z + 2*y*z-1 + 2*x-1*y2*z-1 + 2*x-1*y + 2*y-1*z + x-1*y2*z-2 + x-2*y3*z-2 + 2*x-1*y*z-1 + x-2*y2*z-1 + y-1 + 2*x-1 + y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2152
Image of polytope 2152 PALP id: 2152
grdb id: 387007
Integer points: [ 1 0 0 0 0 -2 -2 -3 -1 0 -1 -2 -1 0 -1]
[ 0 1 -1 0 -2 2 0 2 1 -1 0 1 -1 0 1]
[ 0 0 0 1 1 -1 -1 -2 0 1 0 -1 0 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
3 ? x + y + z + 2*x-1*y + 2*y-1*z + 2*x-1*y*z-1 + x-2*y2*z-1 + y-1 + 5*x-1 + y-2*z + 4*x-2*y*z-1 + 2*x-1*y-1 + x-3*y2*z-2 + x-2*z-1
36 rank 3, number 7 x + y + z + 2*x-1*y + 2*y-1*z + 2*x-1*y*z-1 + x-2*y2*z-1 + y-1 + 4*x-1 + y-2*z + 3*x-2*y*z-1 + 2*x-1*y-1 + x-3*y2*z-2 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Polytope 2153
Image of polytope 2153 PALP id: 2153
grdb id: 387094
Integer points: [ 1 0 0 -2 -2 0 -4 -2 -1 -3 -2 -1 -3 -1 0]
[ 0 1 0 0 -1 -1 -2 -2 -1 -2 -1 0 -1 -1 0]
[ 0 0 1 -1 -1 1 -1 1 1 0 0 0 -1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
87 ? x + y + z + y-1*z + 3*x-1 + 2*x-1*y-1*z + 3*x-1*y-1 + x-2*z-1 + 4*x-2*y-1 + x-2*y-2*z + x-2*y-1*z-1 + 2*x-3*y-1*z-1 + 2*x-3*y-2 + x-4*y-2*z-1
69 ? x + y + z + y-1*z + 3*x-1 + 2*x-1*y-1*z + 2*x-1*y-1 + x-2*z-1 + 4*x-2*y-1 + x-2*y-2*z + x-2*y-1*z-1 + 2*x-3*y-1*z-1 + 2*x-3*y-2 + x-4*y-2*z-1
131 ? x + y + z + y-1*z + 4*x-1 + 2*x-1*y-1*z + 3*x-1*y-1 + x-2*z-1 + 5*x-2*y-1 + x-2*y-2*z + x-2*y-1*z-1 + 2*x-3*y-1*z-1 + 2*x-3*y-2 + x-4*y-2*z-1
43 ? x + y + z + y-1*z + 4*x-1 + 2*x-1*y-1*z + 2*x-1*y-1 + x-2*z-1 + 5*x-2*y-1 + x-2*y-2*z + x-2*y-1*z-1 + 2*x-3*y-1*z-1 + 2*x-3*y-2 + x-4*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Polytope 2154
Image of polytope 2154 PALP id: 2154
grdb id: 387777
Integer points: [ 1 0 0 -1 -1 -3 -2 -4 -2 -3 -1 -2 -1 0 -1]
[ 0 1 0 -1 1 0 1 1 1 1 0 0 1 0 0]
[ 0 0 1 0 0 -2 -2 -3 -1 -2 0 -1 -1 0 -1]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
160 ? x + y + z + x-1*y + 2*x-1*y*z-1 + 2*x-1 + 2*x-1*z-1 + 3*x-2*y*z-1 + x-1*y-1 + x-2*y*z-2 + 2*x-2*z-1 + 3*x-3*y*z-2 + x-3*z-2 + x-4*y*z-3
87 ? x + y + z + x-1*y + 2*x-1*y*z-1 + 3*x-1 + 2*x-1*z-1 + 3*x-2*y*z-1 + x-1*y-1 + x-2*y*z-2 + 4*x-2*z-1 + 3*x-3*y*z-2 + x-3*z-2 + x-4*y*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Polytope 2155
Image of polytope 2155 PALP id: 2155
grdb id: 387543
Integer points: [ 1 0 0 -1 -1 -2 -3 -4 -3 -2 -1 -2 -1 -1 0]
[ 0 1 0 0 0 -2 -2 -3 -2 -1 -1 -1 0 -1 0]
[ 0 0 1 -1 1 -1 -2 -2 -1 0 0 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 66 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2156
Image of polytope 2156 PALP id: 2156
grdb id: 388153
Integer points: [ 1 0 0 -1 0 -2 -3 -4 -1 -2 -3 -2 -1 0 -1]
[ 0 1 -1 0 0 -3 -2 -4 -1 -2 -3 -1 -2 0 -1]
[ 0 0 0 0 1 -2 -2 -3 0 -1 -2 -1 -1 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
28 rank 2, number 25 x + y + z + y-1 + x-1 + 4*x-1*y-1 + x-1*y-1*z-1 + 2*x-1*y-2*z-1 + 2*x-2*y-1*z-1 + 6*x-2*y-2*z-1 + x-2*y-3*z-2 + x-3*y-2*z-2 + 4*x-3*y-3*z-2 + x-4*y-4*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 59 2 Lattice Minkowski decompositions of facet 59
Polytope 2157
Image of polytope 2157 PALP id: 2157
grdb id: 387964
Integer points: [ 1 0 0 0 -1 -2 -3 -4 -3 -1 -2 -1 -2 0 -1]
[ 0 1 -1 0 -1 1 0 1 1 0 0 1 1 0 0]
[ 0 0 0 1 -1 0 -2 -2 -1 0 -1 0 -1 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? x + y + z + 2*x-1*y + y-1 + 3*x-1 + x-2*y + 2*x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1*z-1 + 4*x-2*z-1 + 2*x-3*y*z-1 + x-3*z-2 + x-4*y*z-2
50 ? x + y + z + 2*x-1*y + y-1 + 2*x-1 + x-2*y + 2*x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1*z-1 + 2*x-2*z-1 + 2*x-3*y*z-1 + x-3*z-2 + x-4*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2158
Image of polytope 2158 PALP id: 2158
grdb id: 388450
Integer points: [ 1 0 0 0 -1 -2 -3 -4 -3 -1 -2 -1 -2 0 -1]
[ 0 1 -1 0 0 -1 -2 -3 -2 -1 -2 0 -1 0 -1]
[ 0 0 0 1 -1 0 -2 -2 -1 0 -1 0 -1 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + y-1 + 2*x-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + 3*x-2*y-1*z-1 + 2*x-2*y-2*z-1 + 2*x-3*y-2*z-1 + x-3*y-2*z-2 + x-4*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2159
Image of polytope 2159 PALP id: 2159
grdb id: 388451
Integer points: [ 1 0 0 0 -1 -2 -3 -4 -1 -2 -2 -3 0 -1 -1]
[ 0 1 -1 0 1 1 0 1 0 0 1 1 0 0 1]
[ 0 0 0 1 0 -2 -2 -3 0 -1 -1 -2 0 -1 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
29 rank 2, number 23 x + y + z + x-1*y + 2*x-1*y*z-1 + y-1 + 3*x-1 + x-1*z-1 + 3*x-2*y*z-1 + x-2*y*z-2 + 3*x-2*z-1 + 3*x-3*y*z-2 + x-3*z-2 + x-4*y*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2160
Image of polytope 2160 PALP id: 2160
grdb id: 387220
Integer points: [ 1 0 0 0 -1 -2 -3 -4 -2 -3 -1 -2 -1 0 -1]
[ 0 1 0 -1 -1 -1 0 -1 -1 -1 0 0 -1 0 0]
[ 0 0 1 1 1 -1 -2 -2 0 -1 0 -1 0 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? x + y + z + y-1*z + 4*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + 3*x-2*z-1 + 3*x-2*y-1 + x-2*y-1*z-1 + x-3*z-2 + 3*x-3*y-1*z-1 + x-4*y-1*z-2
66 rank 2, number 24 x + y + z + y-1*z + 2*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-2*z-1 + 3*x-2*y-1 + x-2*y-1*z-1 + x-3*z-2 + 3*x-3*y-1*z-1 + x-4*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Polytope 2161
Image of polytope 2161 PALP id: 2161
grdb id: 387280
Integer points: [ 1 0 0 0 -1 0 -1 -4 -2 -3 -1 -2 -1 -2 0]
[ 0 1 -1 0 1 1 1 1 1 1 1 1 0 0 0]
[ 0 0 0 1 -1 1 1 -2 0 -1 0 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 66 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2162
Image of polytope 2162 PALP id: 2162
grdb id: 387298
Integer points: [ 1 0 0 0 -1 -1 -3 -4 -2 -3 -1 -2 -2 0 -1]
[ 0 1 -1 0 0 -1 2 2 0 1 0 1 1 0 1]
[ 0 0 0 1 -1 -1 -1 -1 -1 -1 0 0 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2163
Image of polytope 2163 PALP id: 2163
grdb id: 385181
Integer points: [ 1 0 0 -1 0 0 -2 -2 -1 -2 -1 -1 0 -1 0]
[ 0 1 0 1 -1 -1 1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 0 -1 1 -1 -1 0 -1 0 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y + y-1*z + 2*y-1 + 3*x-1 + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 2164
Image of polytope 2164 PALP id: 2164
grdb id: 385229
Integer points: [ 1 0 0 0 -1 -2 0 -2 -1 -2 -1 -1 0 -1 0]
[ 0 1 0 -1 0 0 -2 -2 -1 -1 0 -2 -1 -1 0]
[ 0 0 1 -1 -1 -1 -1 -1 0 -1 0 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + y-2*z-1 + 3*x-1*y-1*z-1 + x-2*z-1 + 2*x-1*y-2*z-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 2165
Image of polytope 2165 PALP id: 2165
grdb id: 382978
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 1 1 0 -2 0 -1 0 -1 0 -1 0]
[ 0 0 1 1 0 -1 -2 0 0 0 -1 -1 0 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + x-1*y + y-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2166
Image of polytope 2166 PALP id: 2166
grdb id: 385006
Integer points: [ 1 0 0 0 -1 -1 0 -1 -1 0 0 -1 -1 0 0]
[ 0 1 0 -1 1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 1 1 0 0 -2 -2 -1 0 -1 0 -1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + x-1*y + y-1*z + 2*z-1 + 3*y-1 + 2*x-1 + 3*y-1*z-1 + 2*x-1*z-1 + x-1*y-1 + y-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2167
Image of polytope 2167 PALP id: 2167
grdb id: 384995
Integer points: [ 1 0 0 0 -1 0 -2 -2 -1 -2 -1 -1 0 0 -1]
[ 0 1 0 -1 0 -1 -1 -1 -1 -1 0 -1 0 -1 -1]
[ 0 0 1 -1 1 1 -1 1 1 0 0 0 0 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 8 1 none
Polytope 2168
Image of polytope 2168 PALP id: 2168
grdb id: 385207
Integer points: [ 1 0 0 0 0 -2 -1 -2 -2 -1 -1 -1 0 -1 0]
[ 0 1 0 0 -1 0 -2 -2 -1 -1 0 -1 -1 0 0]
[ 0 0 1 -1 -1 1 0 1 1 0 0 1 0 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + 2*x-1*z + z-1 + 2*y-1 + 2*x-1 + 2*x-1*y-1*z + x-2*z + y-1*z-1 + 3*x-1*y-1 + 2*x-2*y-1*z + x-1*y-2 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2169
Image of polytope 2169 PALP id: 2169
grdb id: 385054
Integer points: [ 1 0 1 -1 0 0 -2 -2 -1 -2 -1 -1 0 -1 0]
[ 0 1 -1 1 0 -2 0 -2 -1 -1 0 -2 -1 -1 0]
[ 0 0 0 0 1 -1 -1 -1 0 -1 0 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + x*y-1 + x-1*y + 2*y-1 + 2*x-1 + 2*x-1*y-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-2*z-1 + 2*x-1*y-2*z-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Polytope 2170
Image of polytope 2170 PALP id: 2170
grdb id: 385085
Integer points: [ 1 0 1 0 0 -2 0 -2 0 -1 -1 0 0 -1 -1]
[ 0 1 -1 0 0 1 -2 0 -1 -1 0 -1 0 0 1]
[ 0 0 0 1 -1 0 -1 -1 0 -1 0 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + x*y-1 + 2*x-1*y + z-1 + 2*y-1 + 2*x-1 + x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2171
Image of polytope 2171 PALP id: 2171
grdb id: 382866
Integer points: [ 1 0 0 -1 -1 -2 -1 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 -1 -1 2 2 0 1 0 1 0 1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + 2*x-1*z + x-1*y-1*z2 + 3*x-1 + 3*x-1*y-1*z + x-2*y-1*z2 + x-1*z-1 + 3*x-1*y-1 + 3*x-2*y-1*z + x-1*y-1*z-1 + 3*x-2*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2172
Image of polytope 2172 PALP id: 2172
grdb id: 382503
Integer points: [ 1 0 0 0 -1 -1 -2 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 0 -1 0 2 -1 2 1 0 1 0 -1 1 0]
[ 0 0 1 1 -1 -1 -1 -1 -1 -1 0 0 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
55 rank 2, number 19 x + y + z + x-1*y2*z-1 + 2*x-1*y + y-1*z + 2*x-1*y*z-1 + x-2*y2*z-1 + 4*x-1 + x-1*z-1 + 3*x-2*y*z-1 + 2*x-1*y-1 + 3*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Polytope 2173
Image of polytope 2173 PALP id: 2173
grdb id: 382516
Integer points: [ 1 0 0 -1 -1 -1 0 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 0 -2 -2 -3 -1 -2 0 -1 -1 0 -1]
[ 0 0 1 -1 1 0 1 1 1 1 0 0 1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? x + y + z + 2*y-1*z + x-1*z + 2*y-1 + 2*x-1 + y-2*z + 3*x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-2*z + x-1*y-2 + x-1*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2174
Image of polytope 2174 PALP id: 2174
grdb id: 384994
Integer points: [ 1 0 0 -1 0 -1 -1 -3 -2 -2 -1 -2 -1 -1 0]
[ 0 1 0 0 -1 0 -2 -2 -1 -1 0 -2 -1 -1 0]
[ 0 0 1 -1 1 1 1 1 0 1 0 1 0 1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? x + y + z + y-1*z + x-1*z + 2*x-1 + 3*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z + 2*x-2*y-1*z + 2*x-2*y-1 + 2*x-2*y-2*z + x-3*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2175
Image of polytope 2175 PALP id: 2175
grdb id: 385001
Integer points: [ 1 0 0 0 -1 -1 -1 -3 -2 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 0 0 -2 -2 -1 -2 -1 -1 0 -1 0]
[ 0 0 0 1 -1 1 -1 -1 0 -1 0 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + x-1*z + y-1 + 2*x-1 + x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*y-1 + x-1*y-2*z-1 + 2*x-2*y-1*z-1 + 2*x-2*y-2*z-1 + x-3*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2176
Image of polytope 2176 PALP id: 2176
grdb id: 382868
Integer points: [ 1 0 0 0 -1 0 -2 -3 -2 -1 -2 -1 -1 -1 0]
[ 0 1 -1 0 -1 -1 0 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 0 1 -1 1 1 1 1 1 0 0 1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 8 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2177
Image of polytope 2177 PALP id: 2177
grdb id: 382876
Integer points: [ 1 0 0 0 -1 0 -2 -3 -2 -1 -2 -1 -1 -1 0]
[ 0 1 -1 0 1 -1 -1 -1 -1 -1 0 0 -1 0 0]
[ 0 0 0 1 0 1 -2 -2 -1 0 -1 0 -1 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y + y-1*z + y-1 + 3*x-1 + 2*x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + 3*x-2*y-1*z-1 + x-2*y-1*z-2 + x-3*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2178
Image of polytope 2178 PALP id: 2178
grdb id: 383090
Integer points: [ 1 0 0 0 -1 0 -1 -4 -2 -3 -1 -2 -1 -2 0]
[ 0 1 -1 0 0 -1 -1 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 0 1 -1 1 1 -2 0 -1 0 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? x + y + z + y-1*z + y-1 + 3*x-1 + x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + 2*x-2*z-1 + 3*x-2*y-1 + 2*x-2*y-1*z-1 + 3*x-3*y-1*z-1 + x-4*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Polytope 2179
Image of polytope 2179 PALP id: 2179
grdb id: 223165
Integer points: [ 1 1 -1 0 -1 0 -1 0 -1 -1 0 -1 0 1 0]
[ 0 2 -2 0 -1 1 0 1 0 0 1 -1 0 1 -1]
[ 0 0 0 1 1 -1 -1 1 1 0 0 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 1 none
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2180
Image of polytope 2180 PALP id: 2180
grdb id: 223147
Integer points: [ 1 0 0 -1 0 -2 1 -2 0 -1 0 -1 1 0 -1]
[ 0 1 0 0 -1 1 -2 0 -2 -1 -1 0 -1 0 1]
[ 0 0 1 -1 -1 0 0 -1 -1 -1 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + 2*x*y-1 + 2*x-1*y + x*y-2 + y-1 + x-1 + x-2*y + y-1*z-1 + x-1*z-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 48 1 Lattice Minkowski decompositions of facet 48
Polytope 2181
Image of polytope 2181 PALP id: 2181
grdb id: 222882
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 1 -1 -2 -2 0 -1 0 -1 0 -1]
[ 0 0 1 -1 1 1 -1 0 1 1 1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y*z + y-1*z + 3*x-1*z + z-1 + 2*y-1 + 2*x-1 + 3*x-1*y-1*z + 3*x-1*y-1 + x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2182
Image of polytope 2182 PALP id: 2182
grdb id: 223087
Integer points: [ 1 0 0 1 -2 -1 0 -1 1 0 -1 1 0 -1 0]
[ 0 1 0 -2 1 0 -1 0 -2 -1 0 -1 0 1 -1]
[ 0 0 1 0 0 -1 1 1 -1 0 0 0 0 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
109 ? x + y + z + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + x*y-2 + 4*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
39 ? x + y + z + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + x*y-2 + 2*y-1 + 2*x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Polytope 2183
Image of polytope 2183 PALP id: 2183
grdb id: 223152
Integer points: [ 1 0 0 1 -1 0 1 -1 -2 0 1 0 -1 0 -1]
[ 0 1 0 -1 1 1 -2 1 1 0 -1 0 1 -1 0]
[ 0 0 1 -1 1 1 0 -1 0 -1 0 0 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 y*z + x + y + z + x-1*y*z + 2*x*y-1 + x-1*y + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2184
Image of polytope 2184 PALP id: 2184
grdb id: 222912
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -1 0 0 -2 2 1 1 0 -1 0 -1]
[ 0 0 1 -1 1 -1 1 0 -1 -1 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
128 ? x + y + z + y*z-1 + x-1*y2*z-1 + 2*x-1*y + x-1*z + 2*x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Polytope 2185
Image of polytope 2185 PALP id: 2185
grdb id: 223128
Integer points: [ 1 0 0 0 -1 -1 0 -1 -1 -1 -1 0 -1 0 0]
[ 0 1 0 0 1 1 -2 -1 -2 -1 0 -1 0 -1 0]
[ 0 0 1 -1 0 -1 1 2 2 1 0 0 1 1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
35 rank 2, number 15 x + y + z + x-1*y + y-1*z + 2*x-1*z + x-1*y-1*z2 + z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + y-2*z + 3*x-1*y-1*z + x-1*y-2*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Polytope 2186
Image of polytope 2186 PALP id: 2186
grdb id: 223100
Integer points: [ 1 0 0 0 -1 1 1 1 -2 -1 0 0 -1 0 1]
[ 0 1 0 0 0 -1 -2 -2 1 0 -1 -1 1 0 -1]
[ 0 0 1 -1 0 0 1 2 -2 -1 0 1 -1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + 2*x*y-1*z + z + x*y-2*z2 + x*y-1 + x*y-2*z + 2*y-1*z + z-1 + 2*x-1*y*z-1 + 3*y-1 + x-1 + 3*x-1*z-1 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2187
Image of polytope 2187 PALP id: 2187
grdb id: 223102
Integer points: [ 1 0 0 0 0 1 -1 -2 -2 0 -1 -1 1 0 -1]
[ 0 1 0 0 -1 -2 0 1 2 -1 0 1 -1 0 1]
[ 0 0 1 -1 1 0 1 0 -1 0 0 -1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + 2*x*y-1 + x-1*y + y-1*z + x-1*z + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2188
Image of polytope 2188 PALP id: 2188
grdb id: 223154
Integer points: [ 1 0 0 0 0 1 -1 -2 -2 -1 0 -1 1 0 -1]
[ 0 1 0 0 1 -2 2 1 2 1 -1 0 -1 0 1]
[ 0 0 1 -1 -1 0 -1 0 -1 -1 0 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + y*z-1 + x-1*y2*z-1 + 2*x*y-1 + x-1*y + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2189
Image of polytope 2189 PALP id: 2189
grdb id: 223123
Integer points: [ 1 0 0 1 0 0 -1 -1 -2 0 -1 0 1 -1 0]
[ 0 1 -1 0 -1 1 -1 1 0 0 0 0 0 0 0]
[ 0 0 0 2 -1 -1 -1 -1 -1 -1 -1 0 1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
161 ? x*z2 + 2*x*z + x + y + 3*z + y*z-1 + 2*z-1 + x-1*y*z-1 + y-1 + 3*x-1 + y-1*z-1 + 3*x-1*z-1 + x-1*y-1*z-1 + x-2*z-1
40 rank 2, number 10 x*z2 + 2*x*z + x + y + 3*z + y*z-1 + 2*z-1 + x-1*y*z-1 + y-1 + 3*x-1 + y-1*z-1 + 2*x-1*z-1 + x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2190
Image of polytope 2190 PALP id: 2190
grdb id: 223112
Integer points: [ 1 0 0 2 1 -2 -2 0 -1 0 1 -1 -1 0 -1]
[ 0 1 0 -1 -1 1 0 -1 -1 -1 -1 0 0 0 1]
[ 0 0 1 -1 -1 0 1 1 1 0 0 0 1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 8 1 none
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2191
Image of polytope 2191 PALP id: 2191
grdb id: 223129
Integer points: [ 1 0 0 0 0 -1 -2 -1 -3 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 -1 0 -1 -2 -2 -2 -1 -1 0 -1 0]
[ 0 0 0 1 -1 -1 0 -1 -1 -1 0 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + y-1 + 2*x-1 + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + x-1*y-2*z-1 + 2*x-2*y-1*z-1 + 2*x-2*y-2*z-1 + x-3*y-2*z-1
77 ? x + y + z + y-1 + 2*x-1 + y-1*z-1 + x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + x-1*y-2*z-1 + 2*x-2*y-1*z-1 + 2*x-2*y-2*z-1 + x-3*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2192
Image of polytope 2192 PALP id: 2192
grdb id: 222883
Integer points: [ 1 0 0 0 0 -1 -2 -1 -3 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 -1 1 1 -2 0 0 0 -1 -1 0 0]
[ 0 0 0 1 -1 1 1 -1 1 1 1 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + x-1*y*z + 3*x-1*z + x-2*y*z + y-1 + 2*x-1 + 3*x-2*z + y-1*z-1 + 3*x-1*y-1 + x-3*z + 2*x-2*y-1 + x-1*y-2*z-1
144 rank 3, number 12 x + y + z + x-1*y*z + 3*x-1*z + x-2*y*z + y-1 + 3*x-1 + 3*x-2*z + y-1*z-1 + 3*x-1*y-1 + x-3*z + 2*x-2*y-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2193
Image of polytope 2193 PALP id: 2193
grdb id: 223127
Integer points: [ 1 0 0 0 0 -1 -2 -1 -3 -2 -1 -2 -1 -1 0]
[ 0 1 0 0 -1 1 1 -1 1 0 0 1 0 1 0]
[ 0 0 1 -1 0 -1 0 -1 -1 -1 0 -1 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + 2*x-1*y + z-1 + x-1*y*z-1 + y-1 + 2*x-1 + x-2*y + 2*x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1*z-1 + 2*x-2*z-1 + x-3*y*z-1
32 ? x + y + z + 2*x-1*y + z-1 + x-1*y*z-1 + y-1 + 3*x-1 + x-2*y + 2*x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1*z-1 + 2*x-2*z-1 + x-3*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2194
Image of polytope 2194 PALP id: 2194
grdb id: 223126
Integer points: [ 1 0 0 0 0 -1 -1 -2 -3 -2 -2 -1 -1 -1 0]
[ 0 1 -1 0 1 0 0 -2 -2 -1 -1 0 -1 -1 0]
[ 0 0 0 1 -1 -1 1 1 1 0 1 0 0 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2195
Image of polytope 2195 PALP id: 2195
grdb id: 223025
Integer points: [ 1 0 0 0 1 -2 1 -1 1 0 0 -1 1 0 -1]
[ 0 1 0 -1 -2 1 -2 -1 -3 -2 -1 0 -1 0 1]
[ 0 0 1 -1 0 0 -1 -1 -1 -1 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + 2*x*y-1 + 2*x-1*y + x*y-2 + y-1 + 2*x-1 + x-2*y + x*y-2*z-1 + y-1*z-1 + x*y-3*z-1 + 2*y-2*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 47 1 Lattice Minkowski decompositions of facet 47
Polytope 2196
Image of polytope 2196 PALP id: 2196
grdb id: 223136
Integer points: [ 1 0 1 -1 0 1 1 -1 -3 0 1 -1 0 -2 -1]
[ 0 1 -1 1 0 1 -1 -1 0 -1 0 0 0 0 0]
[ 0 0 0 0 1 -1 -1 0 1 0 -1 0 0 1 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x*y*z-1 + x + y + z + 2*x*z-1 + x*y-1 + x-1*y + 3*x-1*z + x*y-1*z-1 + 2*y-1 + 3*x-1 + 3*x-2*z + x-1*y-1 + x-3*z
62 rank 2, number 9 x*y*z-1 + x + y + z + 2*x*z-1 + x*y-1 + x-1*y + 3*x-1*z + x*y-1*z-1 + 2*y-1 + 2*x-1 + 3*x-2*z + x-1*y-1 + x-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2197
Image of polytope 2197 PALP id: 2197
grdb id: 222907
Integer points: [ 1 0 1 0 -1 -2 0 -1 -3 -2 -1 0 -1 0 -2]
[ 0 1 -1 0 -1 0 -1 -1 -1 -1 -1 -1 0 0 -1]
[ 0 0 0 1 -1 -1 1 1 -1 0 0 0 0 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
82 ? x + y + z + x*y-1 + y-1*z + 3*y-1 + 3*x-1 + x-1*y-1*z + 3*x-1*y-1 + x-1*y-1*z-1 + x-2*z-1 + 2*x-2*y-1 + 2*x-2*y-1*z-1 + x-3*y-1*z-1
159 ? x + y + z + x*y-1 + y-1*z + 3*y-1 + 2*x-1 + x-1*y-1*z + 3*x-1*y-1 + x-1*y-1*z-1 + x-2*z-1 + 2*x-2*y-1 + 2*x-2*y-1*z-1 + x-3*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Polytope 2198
Image of polytope 2198 PALP id: 2198
grdb id: 222949
Integer points: [ 1 0 1 0 -2 -2 0 -1 -3 -2 -1 0 -1 0 1]
[ 0 1 -2 0 2 1 -1 0 2 1 0 -1 1 0 -1]
[ 0 0 0 1 -1 -1 1 1 -1 0 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 45 1 none
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2199
Image of polytope 2199 PALP id: 2199
grdb id: 223110
Integer points: [ 1 0 1 0 -1 -1 -2 -2 -3 -2 0 -1 1 0 -1]
[ 0 1 -2 0 1 0 1 2 2 1 -1 0 -1 0 1]
[ 0 0 0 1 -1 -1 0 -1 -1 -1 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + 2*x*y-1 + x-1*y + x-1*y*z-1 + x-2*y2*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + x-1*z-1 + 2*x-2*y*z-1 + x-3*y2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2200
Image of polytope 2200 PALP id: 2200
grdb id: 222775
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 -1 1 -1 -1 0 0 0 1 0]
[ 0 0 1 -1 0 -1 -1 1 1 0 -1 0 1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
3 ? x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + z-1 + x-1*y*z-1 + y-1 + 4*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Polytope 2201
Image of polytope 2201 PALP id: 2201
grdb id: 220430
Integer points: [ 1 0 0 -1 0 -1 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -1 0 -1 -1 -1 -1 -1 0 0 -1 0]
[ 0 0 1 0 -1 -1 1 -1 2 0 1 0 1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y + y-1*z + 2*x-1*z + x-1*y-1*z2 + 2*y-1 + 3*x-1 + 3*x-1*y-1*z + y-1*z-1 + x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2202
Image of polytope 2202 PALP id: 2202
grdb id: 222698
Integer points: [ 1 0 0 1 -1 1 -1 -1 -1 0 0 0 0 -1 -1]
[ 0 1 0 -1 1 -1 1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 1 0 0 -1 -1 1 2 0 1 -1 0 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
56 rank 2, number 11 x + y + z + x*y-1 + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2203
Image of polytope 2203 PALP id: 2203
grdb id: 220604
Integer points: [ 1 0 -1 0 -1 -1 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 1 0 -1 1 -2 -1 -2 0 -1 0 -1 0 -1]
[ 0 0 0 1 -1 1 0 1 1 1 1 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
129 ? x + y + z + x-1*y*z + x-1*y + y-1*z + 3*x-1*z + 2*y-1 + 3*x-1 + 3*x-1*y-1*z + 4*x-1*y-1 + x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
122 ? x + y + z + x-1*y*z + x-1*y + y-1*z + 3*x-1*z + 2*y-1 + 2*x-1 + 3*x-1*y-1*z + 2*x-1*y-1 + x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2204
Image of polytope 2204 PALP id: 2204
grdb id: 220597
Integer points: [ 1 0 -1 0 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 1 0 -1 -1 0 -2 -2 -1 -2 -1 0 -1 0]
[ 0 0 0 1 -1 1 1 -1 1 1 0 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Polytope 2205
Image of polytope 2205 PALP id: 2205
grdb id: 221373
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 0 1 -2 -2 -1 0 0 -1 -1 0 -1]
[ 0 0 1 0 -1 1 0 -1 1 1 0 0 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + x-1*y*z + x-1*y + 2*x-1*z + 2*y-1 + 3*x-1 + x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
88 ? x + y + z + x-1*y*z + x-1*y + 2*x-1*z + 2*y-1 + 4*x-1 + x-1*y-1*z + x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 96 1 Lattice Minkowski decompositions of facet 96
Polytope 2206
Image of polytope 2206 PALP id: 2206
grdb id: 220898
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 -1 -1]
[ 0 1 0 1 0 1 -1 -2 -2 -1 0 -1 0 -1 0]
[ 0 0 1 0 1 -1 1 0 -1 0 0 0 0 -1 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
85 rank 3, number 8 x + y + z + x-1*y + x-1*z + x-1*y*z-1 + 2*y-1 + 4*x-1 + x-1*y-1*z + 3*x-1*z-1 + 4*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
36 rank 3, number 7 x + y + z + x-1*y + x-1*z + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + 3*x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2207
Image of polytope 2207 PALP id: 2207
grdb id: 220645
Integer points: [ 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 0 -1 -2 1 -2 0 -1 0 -1 0 -1]
[ 0 0 1 0 -1 1 0 1 1 1 1 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
82 ? x + y + z + x-1*y*z + x-1*y + y-1*z + 3*x-1*z + 2*y-1 + 4*x-1 + 3*x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z + x-1*y-2
144 rank 3, number 12 x + y + z + x-1*y*z + x-1*y + y-1*z + 3*x-1*z + 2*y-1 + 2*x-1 + 3*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2208
Image of polytope 2208 PALP id: 2208
grdb id: 222568
Integer points: [ 1 0 0 -1 0 -1 -1 -2 -2 -1 -2 -1 -1 0 0]
[ 0 1 0 1 -1 -1 -2 0 -2 0 -1 -1 0 0 -1]
[ 0 0 1 -1 1 -1 0 -1 -1 0 -1 0 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + y-1*z + x-1*y*z-1 + 2*y-1 + 2*x-1 + 2*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + x-2*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2209
Image of polytope 2209 PALP id: 2209
grdb id: 220595
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 1 -2 -1 1 0 1 0 -1 0 -1]
[ 0 0 1 -1 1 -1 0 1 1 1 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 y*z + x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Polytope 2210
Image of polytope 2210 PALP id: 2210
grdb id: 222581
Integer points: [ 1 0 0 0 -1 -1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 1 0 0 -2 -2 -1 -1 0 -1 -1 0]
[ 0 0 1 -1 0 -1 1 1 1 0 1 0 0 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*y + 2*y-1*z + x-1*z + z-1 + 2*y-1 + 2*x-1 + y-2*z + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2211
Image of polytope 2211 PALP id: 2211
grdb id: 222629
Integer points: [ 1 0 0 0 -1 -1 0 -2 -2 -1 -1 0 -1 0 0]
[ 0 1 0 0 1 1 -2 1 0 0 -1 -1 0 0 -1]
[ 0 0 1 -1 0 1 -1 1 1 1 0 0 0 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y*z + x-1*y + 2*x-1*z + x-2*y*z + z-1 + 2*y-1 + 3*x-1 + x-2*z + 2*y-1*z-1 + 2*x-1*y-1 + y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2212
Image of polytope 2212 PALP id: 2212
grdb id: 222537
Integer points: [ 1 0 0 0 -1 -1 0 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 1 0 -1 1 0 1 0 0 0 0 -1]
[ 0 0 1 1 1 1 -1 -1 -2 0 0 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y*z + 2*x-1*y + y-1*z + x-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + y-1*z-1 + 3*x-1*z-1 + x-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2213
Image of polytope 2213 PALP id: 2213
grdb id: 222761
Integer points: [ 1 0 0 0 -1 0 -2 -1 -2 -1 -1 0 -1 0 0]
[ 0 1 0 -1 1 -1 1 0 1 0 0 -1 1 0 0]
[ 0 0 1 1 0 -1 -1 -2 -2 0 -1 0 -1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y + y-1*z + 2*z-1 + 2*x-1*y*z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + 3*x-1*z-1 + x-2*y*z-1 + x-1*z-2 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2214
Image of polytope 2214 PALP id: 2214
grdb id: 222458
Integer points: [ 1 0 0 0 0 0 -2 -1 -2 -1 -2 -1 -1 0 -1]
[ 0 1 0 0 -1 -1 0 -2 -2 -1 -1 0 -1 0 0]
[ 0 0 1 -1 0 1 -1 1 1 1 0 0 0 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + y-1*z + z-1 + y-1 + 2*x-1 + 2*x-1*y-1*z + 2*x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z + x-2*z-1 + 2*x-2*y-1 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2215
Image of polytope 2215 PALP id: 2215
grdb id: 222534
Integer points: [ 1 0 0 0 0 0 -1 -2 -2 -1 -2 -1 -1 0 -1]
[ 0 1 0 -1 0 1 1 1 -1 1 0 0 0 0 -1]
[ 0 0 1 0 -1 1 1 0 -2 0 -1 0 -1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? y*z + x + y + z + x-1*y*z + 2*x-1*y + z-1 + y-1 + 3*x-1 + x-2*y + 2*x-1*z-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2216
Image of polytope 2216 PALP id: 2216
grdb id: 222714
Integer points: [ 1 0 0 0 0 0 -1 -2 -2 -1 -1 -1 0 -1 0]
[ 0 1 0 0 -1 -1 1 0 -1 -1 0 -1 -1 0 0]
[ 0 0 1 -1 1 -1 -1 -1 -1 0 0 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + y-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-1
36 rank 3, number 7 x + y + z + y-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + 3*x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2217
Image of polytope 2217 PALP id: 2217
grdb id: 222793
Integer points: [ 1 0 0 0 1 -2 1 -1 1 0 -1 0 1 0 -1]
[ 0 1 0 0 -1 1 -2 0 -2 -1 0 -1 -1 0 1]
[ 0 0 1 -1 -1 0 0 -1 -1 0 0 -1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
109 ? x + y + z + 2*x*y-1 + 2*x-1*y + x*y-1*z-1 + z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2218
Image of polytope 2218 PALP id: 2218
grdb id: 222647
Integer points: [ 1 0 0 0 1 1 -2 -1 -2 0 -1 0 -1 0 -1]
[ 0 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 0 -1 1 -1 0 -1 0 0 0 0 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + x*y-1 + 2*x-1*z + x*y-1*z-1 + z-1 + 3*y-1 + x-1 + x-2*z + 2*y-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Polytope 2219
Image of polytope 2219 PALP id: 2219
grdb id: 222606
Integer points: [ 1 0 0 0 1 1 -2 0 1 -1 0 0 -1 -1 0]
[ 0 1 0 -1 0 -1 -1 -1 -1 -1 -1 0 -1 0 0]
[ 0 0 1 0 -1 -1 0 -2 -2 0 -1 0 -1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x*z-1 + x*y-1*z-1 + 2*z-1 + y-1 + 2*x-1 + x*y-1*z-2 + 3*y-1*z-1 + 2*x-1*y-1 + y-1*z-2 + 2*x-1*y-1*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2220
Image of polytope 2220 PALP id: 2220
grdb id: 222519
Integer points: [ 1 0 0 1 -1 0 -1 -1 -1 -1 -1 0 -1 0 0]
[ 0 1 0 -1 1 1 0 -1 1 1 0 0 0 0 -1]
[ 0 0 1 0 0 -1 1 0 -2 -1 0 0 -1 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + y*z-1 + x*y-1 + x-1*y + x-1*z + 2*z-1 + 2*x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y*z-2 + 2*x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2221
Image of polytope 2221 PALP id: 2221
grdb id: 222798
Integer points: [ 1 0 0 1 0 -1 1 -2 1 0 0 -1 1 0 -1]
[ 0 1 0 0 1 1 -2 1 -1 0 -1 0 -1 0 1]
[ 0 0 1 -1 -1 -1 0 0 -1 -1 0 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? x + y + z + x*z-1 + y*z-1 + 2*x*y-1 + 2*x-1*y + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2222
Image of polytope 2222 PALP id: 2222
grdb id: 222475
Integer points: [ 1 0 0 1 0 0 -1 0 -2 -1 0 -1 0 -1 0]
[ 0 1 0 0 -1 1 1 -1 1 0 -1 0 0 1 0]
[ 0 0 1 -1 1 -1 1 -1 1 0 0 1 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + x*z-1 + y*z-1 + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + 2*z-1 + 2*y-1 + 2*x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 2223
Image of polytope 2223 PALP id: 2223
grdb id: 222803
Integer points: [ 1 0 0 1 1 -1 0 -1 0 0 0 0 0 0 -1]
[ 0 1 0 0 -1 1 -2 -1 1 -1 0 1 -1 0 0]
[ 0 0 1 -1 0 -1 1 1 -2 1 0 -1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? x + y + z + x*z-1 + 2*y*z-1 + x*y-1 + 2*y-1*z + y*z-2 + 3*z-1 + x-1*y*z-1 + 3*y-1 + 2*x-1 + y-2*z + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2224
Image of polytope 2224 PALP id: 2224
grdb id: 222624
Integer points: [ 1 0 0 1 1 0 -1 -2 -2 -1 0 -1 0 -1 0]
[ 0 1 0 0 -1 1 1 -1 0 0 0 -1 -1 0 0]
[ 0 0 1 -1 0 -1 -1 0 -1 -1 -1 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + x*z-1 + y*z-1 + x*y-1 + 3*z-1 + x-1*y*z-1 + 3*y-1 + x-1 + 3*x-1*z-1 + 3*x-1*y-1 + x-2*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2225
Image of polytope 2225 PALP id: 2225
grdb id: 222414
Integer points: [ 1 0 1 -1 0 -2 0 -2 -1 0 -1 -1 0 0 -1]
[ 0 1 -1 1 0 0 -2 -1 -2 -1 0 -1 0 -1 0]
[ 0 0 0 0 1 -1 -1 -2 -2 0 0 -1 0 -1 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x*y-1 + x-1*y + 2*y-1 + 2*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + y-2*z-1 + 3*x-1*y-1*z-1 + x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2226
Image of polytope 2226 PALP id: 2226
grdb id: 222625
Integer points: [ 1 0 1 -1 0 -1 -2 -1 -2 -1 -2 -1 0 -1 0]
[ 0 1 -1 1 0 0 0 -2 -2 -1 -1 0 -1 -1 0]
[ 0 0 0 0 1 -1 -1 -1 -1 0 -1 0 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2227
Image of polytope 2227 PALP id: 2227
grdb id: 222574
Integer points: [ 1 0 1 0 -2 -1 1 0 -2 0 -1 -1 0 0 -1]
[ 0 1 -1 0 1 0 -2 -2 0 -1 -1 0 -1 0 1]
[ 0 0 0 1 0 -1 -1 -1 -1 0 -1 0 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*y-1 + 2*x-1*y + 2*y-1 + 2*x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2228
Image of polytope 2228 PALP id: 2228
grdb id: 222533
Integer points: [ 1 0 1 0 0 -1 -1 -1 -1 0 -1 -1 0 0 -1]
[ 0 1 -1 0 0 1 0 -1 -1 -1 -1 0 -1 0 0]
[ 0 0 0 1 -1 0 1 0 -2 0 -1 0 -1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*y-1 + x-1*y + x-1*z + z-1 + 2*y-1 + 2*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2229
Image of polytope 2229 PALP id: 2229
grdb id: 221494
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 0 1 -2 -1 -2 0 -1 0 -1 -1 0]
[ 0 0 1 -1 -1 0 1 2 2 1 1 0 0 1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + x-1*y*z-1 + 3*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
144 rank 3, number 12 x + y + z + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + x-1*y*z-1 + 4*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 96 1 Lattice Minkowski decompositions of facet 96
Polytope 2230
Image of polytope 2230 PALP id: 2230
grdb id: 222362
Integer points: [ 1 0 0 0 -1 -2 0 -1 -2 -2 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 0 1 -1 0 1 2 2 1 0 1 0 1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
47 ? x + y + z + y-1*z + 2*x-1*z + x-1*y-1*z2 + y-1 + 2*x-1 + 2*x-1*y-1*z + x-2*y-1*z2 + 2*x-1*y-1 + 2*x-2*y-1*z + x-1*y-1*z-1 + x-2*y-1
65 ? x + y + z + y-1*z + 2*x-1*z + x-1*y-1*z2 + y-1 + 2*x-1 + 4*x-1*y-1*z + x-2*y-1*z2 + 3*x-1*y-1 + 2*x-2*y-1*z + x-1*y-1*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2231
Image of polytope 2231 PALP id: 2231
grdb id: 222619
Integer points: [ 1 0 0 0 -1 0 -2 -1 -2 -2 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 1 1 1 1 1 0 0 1 1 0]
[ 0 0 0 1 -1 1 0 2 2 1 0 1 0 1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 y*z + x-1*y*z2 + x + y + z + 3*x-1*y*z + x-2*y*z2 + 2*x-1*y + 2*x-1*z + 2*x-2*y*z + y-1 + 2*x-1 + x-2*y + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2232
Image of polytope 2232 PALP id: 2232
grdb id: 222817
Integer points: [ 1 0 0 0 -1 0 -1 -1 -1 -1 0 -1 0 0 0]
[ 0 1 0 0 0 -2 -1 2 1 1 -1 0 0 1 -1]
[ 0 0 1 -1 0 1 0 -2 -2 -1 1 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + z-1 + 2*x-1*y*z-1 + 2*y-1 + x-1 + y-2*z + x-1*y*z-2 + 2*x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2233
Image of polytope 2233 PALP id: 2233
grdb id: 222548
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 -1 0 2 0 1 -2 2 -1 0 1 -1 0 1]
[ 0 0 0 1 1 -1 1 -2 1 -1 0 0 -1 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? y2*z + 2*y*z + x-1*y2*z + x + y + z + x-1*y*z + 2*x-1*y + y-1 + 3*x-1 + 2*y-1*z-1 + x-1*z-1 + 3*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2234
Image of polytope 2234 PALP id: 2234
grdb id: 222478
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 1 -1 -2 2 0 1 -1 0 -1 0]
[ 0 0 1 -1 -1 0 -1 0 -1 -1 -1 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + y*z-1 + x-1*y2*z-1 + x-1*y + z-1 + 3*x-1*y*z-1 + 2*y-1 + 3*x-1 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2235
Image of polytope 2235 PALP id: 2235
grdb id: 222648
Integer points: [ 1 0 1 0 0 0 0 -2 -2 -1 0 -1 0 -1 -1]
[ 0 1 -1 0 0 -1 -1 2 1 0 -1 1 0 0 1]
[ 0 0 0 1 -1 1 -1 -1 -1 -1 0 -1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*y-1 + 2*x-1*y + y-1*z + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2236
Image of polytope 2236 PALP id: 2236
grdb id: 220607
Integer points: [ 1 0 0 -1 -1 -2 -1 -3 -3 -2 -3 -2 -1 -1 0]
[ 0 1 0 -1 0 -1 -1 -2 -2 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 1 -1 1 -1 1 1 0 0 0 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
69 ? x + y + z + x-1*z + 3*x-1 + x-1*y-1*z + 2*x-1*y-1 + 2*x-2*y-1*z + x-1*y-1*z-1 + 3*x-2*y-1 + x-2*y-1*z-1 + x-3*y-2*z + 2*x-3*y-2 + x-3*y-2*z-1
87 ? x + y + z + x-1*z + 3*x-1 + x-1*y-1*z + 3*x-1*y-1 + 2*x-2*y-1*z + x-1*y-1*z-1 + 3*x-2*y-1 + x-2*y-1*z-1 + x-3*y-2*z + 2*x-3*y-2 + x-3*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2237
Image of polytope 2237 PALP id: 2237
grdb id: 222726
Integer points: [ 1 0 0 -1 -1 -1 0 -1 -1 -1 0 -1 -1 0 0]
[ 0 1 0 1 0 -1 -2 -2 -3 -2 -1 0 -1 0 -1]
[ 0 0 1 0 -1 0 -1 -2 -2 -1 0 0 -1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y + 2*y-1 + 2*x-1 + 2*y-1*z-1 + x-1*z-1 + x-1*y-1 + y-2*z-1 + 3*x-1*y-1*z-1 + 2*x-1*y-2*z-1 + x-1*y-2*z-2 + x-1*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2238
Image of polytope 2238 PALP id: 2238
grdb id: 220641
Integer points: [ 1 0 0 -1 0 -2 -1 -3 -3 -2 -1 -2 -1 -1 0]
[ 0 1 -1 1 0 0 -2 -2 -3 -2 -1 -1 0 -1 0]
[ 0 0 0 0 1 -1 -1 -2 -2 -1 0 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 66 1 none
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Polytope 2239
Image of polytope 2239 PALP id: 2239
grdb id: 220654
Integer points: [ 1 0 0 -1 0 -2 -1 -3 -3 -2 -1 -2 -1 -1 0]
[ 0 1 0 -1 1 -1 1 0 1 1 1 0 0 0 0]
[ 0 0 1 0 1 -1 -1 -2 -2 -1 0 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 y*z + x + y + z + 3*x-1*y + x-1*y*z-1 + 3*x-1 + 2*x-1*z-1 + 3*x-2*y*z-1 + x-1*y-1 + 3*x-2*z-1 + x-3*y*z-2 + x-2*y-1*z-1 + x-3*z-2
147 ? y*z + x + y + z + 3*x-1*y + x-1*y*z-1 + 4*x-1 + 2*x-1*z-1 + 3*x-2*y*z-1 + x-1*y-1 + 4*x-2*z-1 + x-3*y*z-2 + x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Polytope 2240
Image of polytope 2240 PALP id: 2240
grdb id: 221492
Integer points: [ 1 0 0 -1 0 -1 -3 -2 -3 -1 -2 -1 -2 -1 0]
[ 0 1 0 -1 1 0 -2 -1 -2 0 -1 0 -1 -1 0]
[ 0 0 1 -1 1 -1 -1 1 0 1 0 0 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? y*z + x + y + z + 2*x-1*z + 3*x-1 + x-1*z-1 + 2*x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + 3*x-2*y-1 + 2*x-2*y-1*z-1 + x-3*y-2 + x-3*y-2*z-1
122 ? y*z + x + y + z + 2*x-1*z + 4*x-1 + x-1*z-1 + 2*x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + 4*x-2*y-1 + 2*x-2*y-1*z-1 + x-3*y-2 + x-3*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 96 1 Lattice Minkowski decompositions of facet 96
Polytope 2241
Image of polytope 2241 PALP id: 2241
grdb id: 221583
Integer points: [ 1 0 0 0 -1 -1 -2 -3 -3 -1 -2 -1 -2 -1 0]
[ 0 1 -1 0 1 0 -2 -1 -2 -1 -1 0 0 -1 0]
[ 0 0 0 1 0 -1 -1 -2 -2 0 -1 0 -1 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
66 rank 2, number 24 x + y + z + x-1*y + y-1 + x-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1 + x-3*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 71 1 Lattice Minkowski decompositions of facet 71
Polytope 2242
Image of polytope 2242 PALP id: 2242
grdb id: 222640
Integer points: [ 1 0 0 0 0 -1 -1 -2 -3 -2 -2 -1 -1 -1 0]
[ 0 1 -1 0 -1 -1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 0 0 1 -1 -1 1 1 1 0 1 0 0 1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2243
Image of polytope 2243 PALP id: 2243
grdb id: 222610
Integer points: [ 1 0 0 0 0 -1 -1 -2 -3 -2 -1 -2 -1 0 -1]
[ 0 1 -1 0 1 -1 1 1 1 1 0 0 1 0 0]
[ 0 0 0 1 -1 0 0 -2 -2 -1 0 -1 -1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
80 ? x + y + z + y*z-1 + x-1*y + 3*x-1*y*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1 + x-2*y*z-2 + 2*x-2*z-1 + x-3*y*z-2
107 rank 3, number 11 x + y + z + y*z-1 + x-1*y + 2*x-1*y*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1 + x-2*y*z-2 + 2*x-2*z-1 + x-3*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2244
Image of polytope 2244 PALP id: 2244
grdb id: 222612
Integer points: [ 1 0 0 0 0 -1 -1 -2 -3 -2 -2 -1 -1 -1 0]
[ 0 1 0 0 -1 0 0 -2 -2 -1 -1 0 -1 -1 0]
[ 0 0 1 -1 0 -1 1 1 1 0 1 0 0 1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + x-1*z + z-1 + y-1 + 2*x-1 + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + 2*x-2*y-1*z + 2*x-2*y-1 + x-2*y-2*z + x-3*y-2*z
144 rank 3, number 12 x + y + z + x-1*z + z-1 + y-1 + 2*x-1 + 2*x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + 2*x-2*y-1*z + 2*x-2*y-1 + x-2*y-2*z + x-3*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2245
Image of polytope 2245 PALP id: 2245
grdb id: 222575
Integer points: [ 1 0 0 0 0 0 -2 -2 -3 -1 -2 -1 -1 0 -1]
[ 0 1 0 0 -1 -1 0 -1 -1 0 -1 -1 0 0 -1]
[ 0 0 1 -1 0 1 -1 -2 -2 0 -1 0 -1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
55 rank 2, number 19 x + y + z + y-1*z + z-1 + y-1 + 2*x-1 + x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + 3*x-2*y-1*z-1 + x-2*y-1*z-2 + x-3*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Polytope 2246
Image of polytope 2246 PALP id: 2246
grdb id: 222570
Integer points: [ 1 0 0 0 0 0 -2 -2 -3 -2 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 -2 -1 -2 -1 0 -1 0 -1 0]
[ 0 0 1 -1 0 1 -1 -2 -2 -1 0 0 -1 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? y*z + x + y + z + z-1 + y-1 + 3*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*y-1*z-1 + x-2*y-1*z-2 + x-2*y-2*z-1 + x-3*y-2*z-2
36 rank 3, number 7 y*z + x + y + z + z-1 + y-1 + 3*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + 3*x-2*y-1*z-1 + x-2*y-1*z-2 + x-2*y-2*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Polytope 2247
Image of polytope 2247 PALP id: 2247
grdb id: 222531
Integer points: [ 1 0 1 -1 0 -1 0 -1 -3 -2 -1 -2 0 -1 0]
[ 0 1 -1 1 0 1 -1 -1 1 1 0 0 0 0 -1]
[ 0 0 0 0 1 -1 1 0 -2 -1 0 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*y-1 + x-1*y + y-1*z + x-1*y*z-1 + 2*y-1 + 3*x-1 + 2*x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1 + 2*x-2*z-1 + x-3*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2248
Image of polytope 2248 PALP id: 2248
grdb id: 222623
Integer points: [ 1 0 1 0 0 -1 -2 -2 -3 -1 0 -2 -1 -1 0]
[ 0 1 -1 0 -1 1 1 -1 0 -1 -1 0 0 0 0]
[ 0 0 0 1 -1 1 1 0 1 0 0 1 1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y*z + x*y-1 + 3*x-1*z + x-2*y*z + 3*y-1 + x-1 + 3*x-2*z + y-1*z-1 + 3*x-1*y-1 + x-3*z + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2249
Image of polytope 2249 PALP id: 2249
grdb id: 222443
Integer points: [ 1 0 0 0 0 -1 -1 -3 -3 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 -1 0 2 2 3 2 1 1 0 1 0]
[ 0 0 0 1 1 -1 -1 -2 -2 -1 0 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
55 rank 2, number 19 x + y + z + x-1*y2*z-1 + 3*x-1*y + y-1*z + x-1*y*z-1 + 3*x-2*y2*z-1 + y-1 + 3*x-1 + x-3*y3*z-2 + x-1*z-1 + 3*x-2*y*z-1 + x-3*y2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2250
Image of polytope 2250 PALP id: 2250
grdb id: 234668
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 1 -1 1 -1 1 -1 0 0 0 1 0]
[ 0 0 0 1 1 -1 -1 1 1 0 1 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? y*z + x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + x-1*y*z-1 + y-1 + 4*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 2251
Image of polytope 2251 PALP id: 2251
grdb id: 231193
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 1 1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 0 1 1 -1 0 -1 2 0 1 -1 0 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y + y-1*z + 2*x-1*z + x-1*y-1*z2 + x-1*y*z-1 + y-1 + 4*x-1 + 3*x-1*y-1*z + 2*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2252
Image of polytope 2252 PALP id: 2252
grdb id: 234667
Integer points: [ 1 0 0 0 0 -1 0 -1 -1 -1 0 -1 0 -1 0]
[ 0 1 0 1 -1 1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 1 -1 1 0 -1 0 2 1 0 0 -1 1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + y*z-1 + x-1*y + y-1*z + 2*x-1*z + x-1*y-1*z2 + 2*z-1 + 2*y-1 + 2*x-1 + 2*x-1*y-1*z + y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2253
Image of polytope 2253 PALP id: 2253
grdb id: 231089
Integer points: [ 1 0 0 0 -1 -1 -1 -2 -2 -2 -2 -1 -1 -1 0]
[ 0 1 -1 0 1 0 -2 1 -2 -1 0 -1 0 -1 0]
[ 0 0 0 1 0 -1 -1 -1 -1 -1 -1 0 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + x-1*y + y-1 + 3*x-1 + x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2*z-1 + 3*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2254
Image of polytope 2254 PALP id: 2254
grdb id: 231107
Integer points: [ 1 0 0 0 -1 -1 -1 -2 -2 -2 -2 -1 -1 -1 0]
[ 0 1 -1 0 1 1 -1 1 -2 -1 0 -1 0 0 0]
[ 0 0 0 1 0 -1 -1 -1 -1 -1 -1 0 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + x-1*y + x-1*y*z-1 + y-1 + 3*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + 3*x-2*z-1 + 3*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2255
Image of polytope 2255 PALP id: 2255
grdb id: 234481
Integer points: [ 1 0 0 0 -1 -1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 0 0 -1 -1 -1 -1 -1 0 -1 0 0]
[ 0 0 1 0 1 -1 1 -2 -2 0 -1 0 -1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*z + 2*z-1 + y-1 + 2*x-1 + x-1*y-1*z + 2*y-1*z-1 + x-1*z-1 + 3*x-1*y-1 + y-1*z-2 + 3*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2256
Image of polytope 2256 PALP id: 2256
grdb id: 234961
Integer points: [ 1 0 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 -1 1 -2 -2 -1 0 -1 0 -1 0]
[ 0 0 1 -1 0 -1 -1 0 -1 0 0 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
85 rank 3, number 8 x + y + z + x-1*y + z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + y-1*z-1 + 3*x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2257
Image of polytope 2257 PALP id: 2257
grdb id: 234713
Integer points: [ 1 0 0 0 -1 0 0 -2 -2 -1 -1 0 -1 -1 0]
[ 0 1 0 0 1 -1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 0 -1 1 1 1 0 1 0 0 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*y + y-1*z + 2*x-1*z + z-1 + 2*y-1 + 2*x-1 + 2*x-1*y-1*z + x-2*z + y-1*z-1 + 2*x-1*y-1 + x-2*y-1*z
3 ? x + y + z + x-1*y + y-1*z + 2*x-1*z + z-1 + 2*y-1 + 3*x-1 + 2*x-1*y-1*z + x-2*z + y-1*z-1 + 2*x-1*y-1 + x-2*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2258
Image of polytope 2258 PALP id: 2258
grdb id: 231184
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 0 -1 -1]
[ 0 1 -1 0 1 0 1 -2 1 1 0 -1 0 0 -1]
[ 0 0 0 1 1 1 1 -1 -1 0 0 0 0 -1 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 y*z + x + y + z + x-1*y*z + 2*x-1*y + x-1*z + x-1*y*z-1 + y-1 + 4*x-1 + 3*x-1*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Polytope 2259
Image of polytope 2259 PALP id: 2259
grdb id: 234759
Integer points: [ 1 0 0 0 0 0 -2 -1 -2 -1 -2 -1 -1 0 -1]
[ 0 1 0 0 -1 -1 -1 -1 -1 -1 -1 0 -1 0 0]
[ 0 0 1 -1 0 -1 0 -2 -2 0 -1 0 -1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + z-1 + y-1 + 2*x-1 + y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + x-2*y-1 + x-1*y-1*z-2 + 2*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2260
Image of polytope 2260 PALP id: 2260
grdb id: 234737
Integer points: [ 1 0 0 0 0 0 -1 -2 -2 -1 -2 -1 -1 0 -1]
[ 0 1 0 0 -1 -1 -1 -1 -1 0 -1 0 -1 0 -1]
[ 0 0 1 -1 0 1 1 0 -2 0 -1 -1 0 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + y-1*z + z-1 + y-1 + 2*x-1 + x-1*y-1*z + 2*x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + 2*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2261
Image of polytope 2261 PALP id: 2261
grdb id: 234741
Integer points: [ 1 0 0 0 0 0 -1 -2 -2 -1 -2 -1 -1 0 -1]
[ 0 1 0 0 -1 1 1 0 -2 -1 -1 0 -1 0 0]
[ 0 0 1 -1 0 -1 0 1 1 0 1 0 1 0 1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + y*z-1 + x-1*y + 2*x-1*z + z-1 + y-1 + 3*x-1 + 2*x-1*y-1*z + x-2*z + 2*x-1*y-1 + 2*x-2*y-1*z + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2262
Image of polytope 2262 PALP id: 2262
grdb id: 234763
Integer points: [ 1 0 0 1 -1 -1 1 -1 1 0 1 0 0 -1 0]
[ 0 1 0 -1 1 0 0 -1 -1 -1 -1 0 -1 0 0]
[ 0 0 1 0 0 1 -1 0 -2 0 -1 0 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + x*z-1 + x*y-1 + x-1*y + x-1*z + 2*x*y-1*z-1 + 2*z-1 + 2*y-1 + 2*x-1 + x*y-1*z-2 + 2*y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 2263
Image of polytope 2263 PALP id: 2263
grdb id: 234647
Integer points: [ 1 0 1 -1 0 -2 1 0 -2 -1 0 -1 0 -1 0]
[ 0 1 -1 1 0 1 -2 -2 0 -1 -1 0 -1 0 0]
[ 0 0 0 0 1 -1 -1 -1 -1 -1 0 0 -1 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + x*y-1 + x-1*y + 2*y-1 + 2*x-1 + x*y-2*z-1 + 3*y-1*z-1 + 3*x-1*z-1 + x-2*y*z-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2264
Image of polytope 2264 PALP id: 2264
grdb id: 234666
Integer points: [ 1 0 1 -1 0 0 -1 -2 -2 -2 -1 -1 0 -1 0]
[ 0 1 -1 1 0 -1 -1 1 -1 0 0 -1 -1 0 0]
[ 0 0 0 0 1 -1 0 -1 -1 -1 0 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
85 rank 3, number 8 x + y + z + x*y-1 + x-1*y + 2*y-1 + 3*x-1 + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1*z-1
36 rank 3, number 7 x + y + z + x*y-1 + x-1*y + 2*y-1 + 2*x-1 + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2265
Image of polytope 2265 PALP id: 2265
grdb id: 231109
Integer points: [ 1 0 0 0 0 -1 -1 -2 -2 -2 -2 -1 -1 -1 0]
[ 0 1 -1 0 -1 0 1 2 -1 1 0 1 0 -1 0]
[ 0 0 0 1 1 -1 -1 -1 -1 -1 -1 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + 2*x-1*y + y-1*z + x-1*y*z-1 + x-2*y2*z-1 + y-1 + 4*x-1 + x-1*z-1 + 3*x-2*y*z-1 + 2*x-1*y-1 + 3*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Polytope 2266
Image of polytope 2266 PALP id: 2266
grdb id: 234529
Integer points: [ 1 0 0 0 0 -1 -1 -2 -3 -2 -1 -2 -1 0 -1]
[ 0 1 -1 0 -1 1 -1 1 1 1 0 0 1 0 0]
[ 0 0 0 1 1 0 0 -2 -2 -1 0 -1 -1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y + y-1*z + 2*x-1*y*z-1 + y-1 + 3*x-1 + 2*x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1 + x-2*y*z-2 + 2*x-2*z-1 + x-3*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2267
Image of polytope 2267 PALP id: 2267
grdb id: 234442
Integer points: [ 1 0 0 0 0 0 -2 -2 -3 -1 -2 -1 -1 0 -1]
[ 0 1 0 0 -1 1 0 1 1 1 1 1 0 0 0]
[ 0 0 1 -1 0 1 1 0 1 0 1 1 0 0 1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 y*z + x + y + z + 3*x-1*y*z + 2*x-1*y + 2*x-1*z + 3*x-2*y*z + z-1 + y-1 + x-1 + x-2*y + x-2*z + x-3*y*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Polytope 2268
Image of polytope 2268 PALP id: 2268
grdb id: 228178
Integer points: [ 1 0 0 0 0 -1 -1 0 -1 -1 0 -1 -1 0 0]
[ 0 1 0 1 -1 -1 1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 1 -1 1 1 -1 -1 -1 0 0 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + y*z-1 + y-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2269
Image of polytope 2269 PALP id: 2269
grdb id: 662845
Integer points: [ 1 1 -1 -1 0 0 -1 -1 -1 -1 0 -1 0 1 0]
[ 0 2 -2 0 0 1 -2 -1 0 -1 1 -1 0 1 -1]
[ 0 0 0 0 1 1 -1 -1 1 1 0 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? x*y2 + 2*x*y + y*z + x + 2*y + z + x-1*z + 2*y-1 + x-1 + x-1*y-1*z + 3*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
31 rank 3, number 3 x*y2 + 2*x*y + y*z + x + 2*y + z + x-1*z + 2*y-1 + x-1 + x-1*y-1*z + 2*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 1 2 irreducible and admissible
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Polytope 2270
Image of polytope 2270 PALP id: 2270
grdb id: 662848
Integer points: [ 1 1 0 0 -1 -1 0 -1 -1 -1 -1 0 0 0 1]
[ 0 2 0 0 -2 0 -1 -2 -1 -1 -1 -1 0 1 1]
[ 0 0 1 -1 0 0 1 1 1 -1 0 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x*y2 + 2*x*y + x + 2*y + z + y-1*z + z-1 + 2*y-1 + x-1 + x-1*y-1*z + x-1*y-1 + x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 5 Lattice Minkowski decompositions of facet 11
Polytope 2271
Image of polytope 2271 PALP id: 2271
grdb id: 662847
Integer points: [ 1 0 0 -1 -1 0 1 1 0 1 0 0 1 0 1]
[ 0 1 0 1 0 -1 0 -2 -1 -2 0 -1 -1 0 -1]
[ 0 0 1 1 0 0 -1 -2 -2 -3 -1 -1 -2 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
35 rank 2, number 15 x + y + z + x-1*y*z + x*z-1 + 2*x*y-1*z-1 + 2*z-1 + y-1 + x-1 + 2*x*y-1*z-2 + y-1*z-1 + x*y-2*z-2 + y-1*z-2 + x*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2272
Image of polytope 2272 PALP id: 2272
grdb id: 662846
Integer points: [ 1 0 0 -1 1 0 0 -2 -2 -3 -1 -2 -1 -1 0]
[ 0 1 0 1 -1 -1 0 0 1 1 0 1 1 0 0]
[ 0 0 1 1 -1 0 -1 1 0 1 0 1 0 1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + 2*x-2*y*z + x*y-1*z-1 + z-1 + y-1 + 2*x-1 + x-2*y + x-2*z + x-3*y*z
17 rank 1, V22 x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + 2*x-2*y*z + x*y-1*z-1 + z-1 + y-1 + 3*x-1 + x-2*y + x-2*z + x-3*y*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 1 2 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2273
Image of polytope 2273 PALP id: 2273
grdb id: 662772
Integer points: [ 1 0 0 0 -1 -1 1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 1 0 -1 0 -1 -1 -1 0 -1 -1 0]
[ 0 0 1 -1 0 1 -1 -1 1 -1 0 0 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + x-1*y + x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + 2*y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
17 rank 1, V22 x + y + z + x-1*y + x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + 2*y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2274
Image of polytope 2274 PALP id: 2274
grdb id: 662766
Integer points: [ 1 0 1 -1 0 1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 1 -1 1 0 -1 0 -1 -1 -1 -1 0 -1 -1 0]
[ 0 0 0 0 1 -1 1 1 1 -1 0 0 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2275
Image of polytope 2275 PALP id: 2275
grdb id: 662648
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 -1]
[ 0 1 0 1 -1 0 0 -2 -1 -2 -1 0 -1 0 -1]
[ 0 0 1 0 -1 -1 1 0 1 -1 0 0 0 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
143 ? x + y + z + x-1*y + x-1*z + 2*y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
46 ? x + y + z + x-1*y + x-1*z + 2*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Polytope 2276
Image of polytope 2276 PALP id: 2276
grdb id: 662810
Integer points: [ 1 0 0 -1 0 -1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 1 0 -1 -1 -2 -2 -1 -1 0 -1 0]
[ 0 0 1 0 -1 -1 1 -1 0 -1 -1 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + y*z-1 + 2*z-1 + 2*y-1 + x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
38 ? x + y + z + y*z-1 + 2*z-1 + 2*y-1 + x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2277
Image of polytope 2277 PALP id: 2277
grdb id: 662786
Integer points: [ 1 0 0 -1 1 1 -1 -1 0 -1 -1 0 0 0 0]
[ 0 1 0 1 -1 0 1 0 -2 -1 0 0 -1 0 -1]
[ 0 0 1 1 -1 -1 0 -1 -1 -1 0 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y*z + x*z-1 + x-1*y + x*y-1*z-1 + 2*z-1 + 2*y-1 + 2*x-1 + 3*y-1*z-1 + x-1*z-1 + y-2*z-1 + x-1*y-1*z-1
13 rank 2, number 12 x + y + z + x-1*y*z + x*z-1 + x-1*y + x*y-1*z-1 + 2*z-1 + 2*y-1 + 2*x-1 + 2*y-1*z-1 + x-1*z-1 + y-2*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2278
Image of polytope 2278 PALP id: 2278
grdb id: 662796
Integer points: [ 1 0 0 0 -2 0 -1 0 -1 1 0 -1 1 0 -1]
[ 0 1 0 0 1 -1 0 -1 0 -2 -1 0 -1 0 1]
[ 0 0 1 -1 0 -1 -1 1 1 0 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + z-1 + x*y-2 + y-1 + x-1 + x-2*y + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 50 1 Lattice Minkowski decompositions of facet 50
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Polytope 2279
Image of polytope 2279 PALP id: 2279
grdb id: 662688
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 1 1 0 0 -2 -2 -1 0 -1 0 -1]
[ 0 0 0 1 1 0 -1 1 -1 -2 0 0 -1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*y*z + x-1*y + x-1*z + y-1 + 4*x-1 + 2*y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2*z-1 + x-1*y-2*z-2
60 rank 2, number 18 x + y + z + x-1*y*z + x-1*y + x-1*z + y-1 + 2*x-1 + 2*y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Polytope 2280
Image of polytope 2280 PALP id: 2280
grdb id: 662683
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 0 1 -1 -1 -2 0 -1 0 -1 0]
[ 0 0 1 -1 0 1 -1 1 -1 0 -1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
100 ? x + y + z + x-1*y + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + x-1*y-1*z + 2*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
38 ? x + y + z + x-1*y + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Polytope 2281
Image of polytope 2281 PALP id: 2281
grdb id: 662771
Integer points: [ 1 0 0 0 -1 -1 0 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 0 1 -1 -1 -2 -2 -1 0 -1 0 -1]
[ 0 0 1 -1 0 -1 1 -1 0 -1 0 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
60 rank 2, number 18 x + y + z + y-1*z + z-1 + x-1*y*z-1 + y-1 + x-1 + y-1*z-1 + 3*x-1*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2282
Image of polytope 2282 PALP id: 2282
grdb id: 662750
Integer points: [ 1 0 0 0 -1 0 -1 -2 -1 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 1 -1 0 0 -2 -2 -1 -1 0 -1 0]
[ 0 0 0 1 0 -1 -1 -1 -1 -1 0 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
80 ? x + y + z + x-1*y + y-1 + 2*x-1 + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + x-2*z-1 + x-1*y-2*z-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
107 rank 3, number 11 x + y + z + x-1*y + y-1 + 2*x-1 + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + x-1*y-2*z-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2283
Image of polytope 2283 PALP id: 2283
grdb id: 662809
Integer points: [ 1 0 0 0 -1 1 0 -2 -1 -2 -1 0 -1 0 -1]
[ 0 1 0 0 1 -1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 0 -1 -1 1 1 1 0 0 0 0 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + x-1*y + 2*x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + x-2*z + y-1*z-1 + 2*x-1*y-1 + x-2*y-1*z
17 rank 1, V22 x + y + z + x-1*y + 2*x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + x-2*z + y-1*z-1 + 2*x-1*y-1 + x-2*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2284
Image of polytope 2284 PALP id: 2284
grdb id: 662742
Integer points: [ 1 0 0 0 0 -1 -1 -1 -2 -2 -2 -1 -1 0 -1]
[ 0 1 -1 0 -1 0 0 -1 -1 -1 -1 0 -1 0 -1]
[ 0 0 0 1 -1 -1 1 1 -1 1 0 0 0 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + x-1*z + y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 3*x-1*y-1 + x-2*y-1*z + 2*x-1*y-1*z-1 + 2*x-2*y-1 + x-2*y-1*z-1
144 rank 3, number 12 x + y + z + x-1*z + y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 3*x-1*y-1 + x-2*y-1*z + 2*x-1*y-1*z-1 + 2*x-2*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2285
Image of polytope 2285 PALP id: 2285
grdb id: 662754
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 1 -1 1 -1 0 1 0 0 -1 0 0]
[ 0 0 1 0 -1 1 -1 -1 -2 -2 0 -1 0 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + y*z-1 + 2*z-1 + x-1*y*z-1 + y-1 + 2*x-1 + x-1*y-1*z + x-1*y*z-2 + 3*x-1*z-1 + 2*x-1*y-1 + x-1*z-2 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 2286
Image of polytope 2286 PALP id: 2286
grdb id: 662831
Integer points: [ 1 0 0 0 0 1 -1 1 0 -1 0 -1 -1 0 0]
[ 0 1 0 1 -1 -1 0 -1 -1 0 -1 0 0 0 0]
[ 0 0 1 -1 1 1 1 0 -1 -2 0 0 -1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
56 rank 2, number 11 x + y + x*y-1*z + z + y*z-1 + x*y-1 + y-1*z + x-1*z + z-1 + 2*y-1 + 3*x-1 + y-1*z-1 + 3*x-1*z-1 + x-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2287
Image of polytope 2287 PALP id: 2287
grdb id: 662764
Integer points: [ 1 0 0 0 1 0 -1 -1 -2 -2 -1 0 -1 0 -1]
[ 0 1 0 0 -1 -1 1 -1 0 -1 -1 -1 0 0 0]
[ 0 0 1 -1 0 1 -1 1 -1 0 0 0 0 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*y-1 + y-1*z + z-1 + x-1*y*z-1 + 3*y-1 + 2*x-1 + x-1*y-1*z + 2*x-1*z-1 + 3*x-1*y-1 + x-2*z-1 + x-2*y-1
146 ? x + y + z + x*y-1 + y-1*z + z-1 + x-1*y*z-1 + 3*y-1 + 3*x-1 + x-1*y-1*z + 2*x-1*z-1 + 3*x-1*y-1 + x-2*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2288
Image of polytope 2288 PALP id: 2288
grdb id: 662834
Integer points: [ 1 0 0 0 1 1 -2 1 0 -1 0 -1 1 0 -1]
[ 0 1 0 0 1 -1 0 -1 -1 -1 -1 0 0 0 0]
[ 0 0 1 -1 -1 0 1 -1 -1 0 0 0 -1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x*y*z-1 + x + y + z + 2*x*z-1 + x*y-1 + 2*x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + x-2*z + y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 5 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2289
Image of polytope 2289 PALP id: 2289
grdb id: 662706
Integer points: [ 1 0 0 1 -2 0 -1 1 1 0 0 -1 1 0 -1]
[ 0 1 0 -1 1 -1 0 -2 -2 -1 -1 0 -1 0 1]
[ 0 0 1 -1 0 -1 1 0 -1 1 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + x*y-1*z-1 + x*y-2 + y-1 + 2*x-1 + x-2*y + x*y-2*z-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 51 1 Lattice Minkowski decompositions of facet 51
Polytope 2290
Image of polytope 2290 PALP id: 2290
grdb id: 662829
Integer points: [ 1 0 0 1 0 -1 1 0 1 -2 1 0 -1 0 -1]
[ 0 1 0 -1 0 1 0 1 -2 1 -1 0 1 -1 0]
[ 0 0 1 1 -1 -1 1 -1 0 0 0 0 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x*z + x + y + x*y-1*z + z + y*z-1 + 2*x*y-1 + 2*x-1*y + z-1 + x-1*y*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Polytope 2291
Image of polytope 2291 PALP id: 2291
grdb id: 662798
Integer points: [ 1 0 0 1 0 1 0 -2 -1 -2 0 -1 -1 0 -1]
[ 0 1 0 -1 0 -1 -1 1 -1 0 -1 0 0 0 1]
[ 0 0 1 0 -1 -1 1 0 1 1 0 0 1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + x-2*y + x-1*y-1*z + x-2*z
39 ? x + y + z + x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 3*x-1 + x-2*y + x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2292
Image of polytope 2292 PALP id: 2292
grdb id: 662763
Integer points: [ 1 0 1 -1 0 -1 0 -1 0 -1 -1 0 -1 -1 0]
[ 0 1 -1 1 0 0 -1 0 -2 -2 -1 -1 -1 0 0]
[ 0 0 0 0 1 -1 -1 1 -1 -1 0 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x*y-1 + x-1*y + x-1*z + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1
85 rank 3, number 8 x + y + z + x*y-1 + x-1*y + x-1*z + 3*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2293
Image of polytope 2293 PALP id: 2293
grdb id: 662736
Integer points: [ 1 0 1 -1 0 0 1 -1 -1 -1 -1 0 0 -1 0]
[ 0 1 -1 1 0 -1 -2 0 -1 -2 -1 -2 -1 0 0]
[ 0 0 0 0 1 -1 -1 1 -1 -1 0 -1 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2294
Image of polytope 2294 PALP id: 2294
grdb id: 662747
Integer points: [ 1 0 1 0 -1 1 -1 -2 -1 -2 0 -1 0 -1 0]
[ 0 1 -1 0 1 -2 0 1 0 1 -1 0 0 1 -1]
[ 0 0 0 1 1 -1 -1 0 1 1 0 0 0 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y*z + x*y-1 + 2*x-1*y + x-1*z + x-2*y*z + 2*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 2295
Image of polytope 2295 PALP id: 2295
grdb id: 662775
Integer points: [ 1 0 1 0 0 -1 -1 -2 0 -2 0 -1 -1 0 -1]
[ 0 1 -1 0 -1 1 0 1 -1 1 -1 0 0 0 1]
[ 0 0 0 1 -1 1 -1 0 1 1 0 1 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + x-1*y*z + x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + 2*y-1 + 3*x-1 + x-2*y + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 2296
Image of polytope 2296 PALP id: 2296
grdb id: 662762
Integer points: [ 1 0 1 0 0 1 -1 -2 -1 1 0 0 -1 0 -1]
[ 0 1 -1 0 0 -1 0 1 0 -2 -1 -1 0 0 1]
[ 0 0 0 1 -1 -1 1 0 -1 -1 0 -1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*y-1 + 2*x-1*y + x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 2297
Image of polytope 2297 PALP id: 2297
grdb id: 662835
Integer points: [ 1 0 0 -2 2 0 0 -1 0 -1 1 1 0 -1 -1]
[ 0 1 0 1 -1 0 -1 0 1 1 0 -1 0 1 0]
[ 0 0 1 2 -2 -1 0 0 1 2 -1 -1 0 1 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? y*z + x-1*y*z2 + x + y + z + 2*x-1*y*z + x-2*y*z2 + 2*x*z-1 + 2*x-1*z + x2*y-1*z-2 + 2*x*y-1*z-1 + z-1 + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 1 2 irreducible and admissible
Image of facet 11 6 Lattice Minkowski decompositions of facet 11
Polytope 2298
Image of polytope 2298 PALP id: 2298
grdb id: 662833
Integer points: [ 1 0 0 -1 0 0 2 1 -2 2 1 0 -1 1 -1]
[ 0 1 0 1 -1 0 -1 0 1 -2 -1 0 1 -1 0]
[ 0 0 1 1 0 -1 -1 -1 0 -1 0 0 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + z + x-1*y*z + x2*y-1*z-1 + x*z-1 + 2*x*y-1 + 2*x-1*y + x2*y-2*z-1 + 2*x*y-1*z-1 + z-1 + y-1 + 2*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 1 2 irreducible and admissible
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2299
Image of polytope 2299 PALP id: 2299
grdb id: 662797
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 0 -1 0 0]
[ 0 1 -1 0 -2 2 0 1 -1 2 0 -1 1 0 1]
[ 0 0 0 1 1 -1 -1 0 0 -2 0 1 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + 2*y*z-1 + x-1*y2*z-1 + x-1*y + 2*y-1*z + x-1*y2*z-2 + 2*x-1*y*z-1 + y-1 + 2*x-1 + y-2*z + x-1*z-1 + x-1*y-1
52 rank 2, number 52 x + y + z + 2*y*z-1 + x-1*y2*z-1 + x-1*y + 2*y-1*z + x-1*y2*z-2 + 3*x-1*y*z-1 + y-1 + 2*x-1 + y-2*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2300
Image of polytope 2300 PALP id: 2300
grdb id: 662770
Integer points: [ 1 0 0 1 -1 0 -1 -2 -1 -2 -1 0 -1 0 1]
[ 0 1 0 -2 2 -1 1 1 0 2 0 -1 1 0 -1]
[ 0 0 1 0 -1 1 -1 0 1 -1 0 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? x + y + z + x-1*y2*z-1 + 2*x*y-1 + 3*x-1*y + y-1*z + x-1*z + x-1*y*z-1 + x-2*y2*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
31 rank 3, number 3 x + y + z + x-1*y2*z-1 + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + x-1*y*z-1 + x-2*y2*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Polytope 2301
Image of polytope 2301 PALP id: 2301
grdb id: 662832
Integer points: [ 1 0 0 1 -1 0 0 2 -2 2 -1 0 1 -1 1]
[ 0 1 0 -1 1 -1 0 -1 0 -1 0 0 -1 0 0]
[ 0 0 1 0 0 0 -1 -1 1 -2 1 0 -1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x2*y-1*z-1 + 2*x*z-1 + x*y-1 + x-1*y + 2*x-1*z + x2*y-1*z-2 + 2*x*y-1*z-1 + z-1 + y-1 + 2*x-1 + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 5 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2302
Image of polytope 2302 PALP id: 2302
grdb id: 669048
Integer points: [ 1 0 0 -1 0 -1 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -1 1 0 -1 -1 -1 -1 0 0 -1 0]
[ 0 0 1 0 -1 1 -1 1 -1 1 0 0 1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y*z + x-1*y + y-1*z + 2*x-1*z + 2*y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2303
Image of polytope 2303 PALP id: 2303
grdb id: 669376
Integer points: [ 1 0 0 0 0 -1 0 -1 -1 -1 -1 0 0 -1 0]
[ 0 1 0 1 -1 1 -1 0 1 0 0 -1 0 1 0]
[ 0 0 1 -1 1 1 -1 1 -1 -1 0 0 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y*z + y*z-1 + 2*x-1*y + y-1*z + x-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2304
Image of polytope 2304 PALP id: 2304
grdb id: 668736
Integer points: [ 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 0 -1 -1 0 -2 -2 -1 -1 0 -1 0]
[ 0 0 1 0 -1 1 -1 1 0 1 1 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
114 ? x + y + z + x-1*y + y-1*z + x-1*z + 2*y-1 + 3*x-1 + 2*x-1*y-1*z + x-1*z-1 + 4*x-1*y-1 + x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
144 rank 3, number 12 x + y + z + x-1*y + y-1*z + x-1*z + 2*y-1 + 2*x-1 + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Polytope 2305
Image of polytope 2305 PALP id: 2305
grdb id: 668857
Integer points: [ 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 1 -1 0 0 -2 -2 -1 0 -1 0 -1]
[ 0 0 1 -1 0 1 -1 1 0 1 1 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
88 ? x + y + z + x-1*y + y-1*z + x-1*z + x-1*y*z-1 + 2*y-1 + 4*x-1 + 2*x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z + x-1*y-2
46 ? x + y + z + x-1*y + y-1*z + x-1*z + x-1*y*z-1 + 2*y-1 + 2*x-1 + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Polytope 2306
Image of polytope 2306 PALP id: 2306
grdb id: 669080
Integer points: [ 1 0 0 0 -1 0 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 -1 -1 0 -2 -2 -1 0 -1 -1 0]
[ 0 0 1 -1 0 -1 1 1 0 1 0 0 1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y + y-1*z + x-1*z + z-1 + y-1 + 3*x-1 + 2*x-1*y-1*z + y-1*z-1 + 3*x-1*y-1 + x-1*y-2*z + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2307
Image of polytope 2307 PALP id: 2307
grdb id: 668969
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 0 0 -1 -2 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 0 1 -1 -2 -1 -2 0 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*z + z-1 + y-1 + 2*x-1 + 2*y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-1*z-2 + x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 2308
Image of polytope 2308 PALP id: 2308
grdb id: 668938
Integer points: [ 1 0 0 0 0 -1 -1 0 -2 -2 -1 -1 0 -1 0]
[ 0 1 0 0 -1 0 1 -1 1 1 0 0 -1 1 0]
[ 0 0 1 -1 1 1 -1 -1 0 -1 -1 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + 2*x-1*y + y-1*z + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-2*y + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 2309
Image of polytope 2309 PALP id: 2309
grdb id: 667989
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 -1 0 -1 0 1 -1 -1 -1 -1 0 0 0]
[ 0 0 1 0 -1 -1 1 0 1 -2 0 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*y + x-1*z + z-1 + y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2310
Image of polytope 2310 PALP id: 2310
grdb id: 668983
Integer points: [ 1 0 0 1 -1 -1 -1 1 -1 1 0 0 0 0 -1]
[ 0 1 0 0 0 1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 1 0 1 -1 0 -2 -1 0 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + x*z-1 + x-1*y + x-1*z + x*y-1*z-1 + 2*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + x*y-1*z-2 + 2*y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2311
Image of polytope 2311 PALP id: 2311
grdb id: 669393
Integer points: [ 1 0 0 1 -1 0 -1 1 -1 0 0 0 -1 0 0]
[ 0 1 0 -1 1 -1 0 -1 0 -1 -1 -1 0 0 0]
[ 0 0 1 0 0 1 1 -1 -1 -2 0 -1 0 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + x*y-1 + x-1*y + y-1*z + x-1*z + x*y-1*z-1 + 2*z-1 + 3*y-1 + 2*x-1 + 3*y-1*z-1 + x-1*z-1 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2312
Image of polytope 2312 PALP id: 2312
grdb id: 669424
Integer points: [ 1 0 0 1 -1 0 0 -1 -2 -2 -1 -1 0 -1 0]
[ 0 1 0 -1 1 0 1 -1 1 0 0 1 0 0 -1]
[ 0 0 1 0 0 -1 -1 0 -1 -1 0 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + y*z-1 + x*y-1 + x-1*y + z-1 + 2*x-1*y*z-1 + 2*y-1 + x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2313
Image of polytope 2313 PALP id: 2313
grdb id: 669391
Integer points: [ 1 0 0 1 0 -1 1 0 -2 1 0 -1 1 0 -1]
[ 0 1 0 0 0 0 -1 -1 1 -2 -1 0 -1 0 1]
[ 0 0 1 -1 -1 1 -1 1 0 0 0 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? x + y + z + x*z-1 + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + x*y-1*z-1 + z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Polytope 2314
Image of polytope 2314 PALP id: 2314
grdb id: 669245
Integer points: [ 1 0 1 -1 0 -1 -1 -2 -1 -2 -2 -1 0 -1 0]
[ 0 1 -1 1 0 1 -1 1 -1 -1 0 0 -1 0 0]
[ 0 0 0 0 1 -1 0 -1 -1 -1 -1 0 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x*y-1 + x-1*y + x-1*y*z-1 + 2*y-1 + 2*x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1*z-1
85 rank 3, number 8 x + y + z + x*y-1 + x-1*y + x-1*y*z-1 + 2*y-1 + 3*x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2315
Image of polytope 2315 PALP id: 2315
grdb id: 669421
Integer points: [ 1 0 1 0 0 -1 0 -1 -2 -2 -1 0 -1 0 -1]
[ 0 1 -1 0 0 1 -1 -1 0 -1 0 -1 -1 0 0]
[ 0 0 0 1 -1 0 -1 0 -1 -1 0 0 -1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x*y-1 + x-1*y + z-1 + 2*y-1 + x-1 + y-1*z-1 + 2*x-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2316
Image of polytope 2316 PALP id: 2316
grdb id: 668872
Integer points: [ 1 0 0 0 -1 -1 -1 -2 -3 -3 -2 -1 -2 0 -1]
[ 0 1 -1 0 1 -1 1 -1 0 1 1 0 0 0 0]
[ 0 0 0 1 0 0 -1 -1 -2 -2 -1 0 -1 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + x-1*y + x-1*y*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1 + 2*x-2*z-1 + x-3*y*z-2 + x-2*y-1*z-1 + x-3*z-2
122 ? x + y + z + x-1*y + x-1*y*z-1 + y-1 + 3*x-1 + 2*x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1 + 4*x-2*z-1 + x-3*y*z-2 + x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 2317
Image of polytope 2317 PALP id: 2317
grdb id: 669420
Integer points: [ 1 0 0 0 0 0 -1 -1 -2 -2 0 -1 -1 0 -1]
[ 0 1 0 1 -1 0 0 -2 -2 -3 -1 -1 -2 0 -1]
[ 0 0 1 -1 1 -1 0 0 1 1 0 0 1 0 1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + y*z-1 + y-1*z + z-1 + 2*y-1 + x-1 + 2*x-1*y-1*z + 2*x-1*y-1 + 2*x-1*y-2*z + x-1*y-2 + x-2*y-2*z + x-2*y-3*z
36 rank 3, number 7 x + y + z + y*z-1 + y-1*z + z-1 + 2*y-1 + x-1 + 2*x-1*y-1*z + 3*x-1*y-1 + 2*x-1*y-2*z + x-1*y-2 + x-2*y-2*z + x-2*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2318
Image of polytope 2318 PALP id: 2318
grdb id: 669041
Integer points: [ 1 0 1 -1 0 0 -1 -1 -3 -3 -1 -2 -2 0 -1]
[ 0 1 -1 1 -1 0 1 -1 1 0 0 0 1 0 0]
[ 0 0 0 0 0 1 -1 -1 -2 -2 0 -1 -1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x*y-1 + x-1*y + x-1*y*z-1 + y-1 + 3*x-1 + 2*x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1*z-1 + 3*x-2*z-1 + x-3*y*z-2 + x-3*z-2
36 rank 3, number 7 x + y + z + x*y-1 + x-1*y + x-1*y*z-1 + y-1 + 3*x-1 + 3*x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1*z-1 + 3*x-2*z-1 + x-3*y*z-2 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2319
Image of polytope 2319 PALP id: 2319
grdb id: 669046
Integer points: [ 1 0 0 0 0 -1 -1 -1 -2 -3 -2 -2 -1 -1 0]
[ 0 1 -1 0 -1 0 1 0 2 2 1 1 0 1 0]
[ 0 0 0 1 1 -1 -1 1 -1 -1 -1 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + 3*x-1*y + y-1*z + x-1*z + x-1*y*z-1 + x-2*y2*z-1 + y-1 + 3*x-1 + 2*x-2*y + x-1*z-1 + 2*x-2*y*z-1 + x-3*y2*z-1
8 ? x + y + z + 2*x-1*y + y-1*z + x-1*z + x-1*y*z-1 + x-2*y2*z-1 + y-1 + 3*x-1 + 2*x-2*y + x-1*z-1 + 2*x-2*y*z-1 + x-3*y2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2320
Image of polytope 2320 PALP id: 2320
grdb id: 667828
Integer points: [ 1 0 0 0 0 -1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 -1 0 -1 -1 0 -1 -1 0 -1 0 0]
[ 0 0 1 -1 1 1 1 -1 -1 -1 0 0 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + y*z-1 + y-1*z + x-1*z + 2*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2321
Image of polytope 2321 PALP id: 2321
grdb id: 667186
Integer points: [ 1 0 0 0 -1 0 -1 -1 -2 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 0 -1 -1 0 -1 -1 -1 -1 0 -1 0]
[ 0 0 0 1 -1 1 -1 1 -1 1 1 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? x + y + z + y-1*z + x-1*z + y-1 + 3*x-1 + 2*x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + 2*x-2*y-1 + x-2*y-1*z-1
16 ? x + y + z + y-1*z + x-1*z + y-1 + 2*x-1 + 2*x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + 2*x-2*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2322
Image of polytope 2322 PALP id: 2322
grdb id: 667189
Integer points: [ 1 0 0 0 0 -1 -1 -1 -2 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 -1 1 1 -1 1 -1 -1 0 0 0 0]
[ 0 0 0 1 1 -1 0 -1 -1 -1 0 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y + y-1*z + x-1*y*z-1 + y-1 + 3*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2323
Image of polytope 2323 PALP id: 2323
grdb id: 667043
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 0 0 -1 -2 -2 0 -1 -1 0 -1]
[ 0 0 1 -1 1 -1 1 -1 0 1 0 0 1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + y-1*z + x-1*z + z-1 + 2*y-1 + 2*x-1 + 2*x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2324
Image of polytope 2324 PALP id: 2324
grdb id: 667195
Integer points: [ 1 0 0 0 0 -1 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 0 -1 0 -1 -1 -1 -1 0 -1 0]
[ 0 0 1 -1 1 1 -1 -1 1 -2 0 -1 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + y-1*z + x-1*z + z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Polytope 2325
Image of polytope 2325 PALP id: 2325
grdb id: 667896
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 0 -1 1 0 -2 -2 -1 0 -1 -1 0]
[ 0 0 1 -1 -1 1 0 1 1 0 0 0 1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + y*z-1 + x-1*y + y-1*z + x-1*z + z-1 + 2*y-1 + 3*x-1 + 2*x-1*y-1*z + 3*x-1*y-1 + x-1*y-2*z + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2326
Image of polytope 2326 PALP id: 2326
grdb id: 60046
Integer points: [ 1 0 0 1 1 -1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 -1 1 0 1 1 -1 0 0 0 0 -1]
[ 0 0 1 -1 0 0 1 1 1 0 -1 0 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
56 rank 2, number 11 y*z + x + y + z + x-1*y*z + x*z-1 + x*y-1 + x-1*y + x-1*z + 2*z-1 + 2*y-1 + x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2327
Image of polytope 2327 PALP id: 2327
grdb id: 61360
Integer points: [ 1 0 0 1 1 -1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 -1 0 1 1 1 -1 0 0 0 -1 0]
[ 0 0 1 -1 0 1 0 -1 -1 0 -1 0 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + x*z-1 + y*z-1 + x*y-1 + x-1*y + x-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2328
Image of polytope 2328 PALP id: 2328
grdb id: 61317
Integer points: [ 1 0 1 -1 0 0 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 1 0 -1 0 -1 0 -1 -1 -1 0 -1 0]
[ 0 0 0 0 1 -1 -1 1 1 -1 1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
134 ? x + y + z + x*y-1 + x-1*y + y-1*z + x-1*z + 3*y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
85 rank 3, number 8 x + y + z + x*y-1 + x-1*y + y-1*z + x-1*z + 3*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
36 rank 3, number 7 x + y + z + x*y-1 + x-1*y + y-1*z + x-1*z + 2*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
85 rank 3, number 8 x + y + z + x*y-1 + x-1*y + y-1*z + x-1*z + 2*y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 23 2 Lattice Minkowski decompositions of facet 23
Polytope 2329
Image of polytope 2329 PALP id: 2329
grdb id: 61322
Integer points: [ 1 0 1 0 -1 0 -1 -1 0 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 1 0 1 0 -1 -1 -1 0 0 -1 0]
[ 0 0 0 1 0 -1 -1 1 -1 0 -1 -1 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*y-1 + x-1*y + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + 2*x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
146 ? x + y + z + x*y-1 + x-1*y + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + y-1*z-1 + 2*x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2330
Image of polytope 2330 PALP id: 2330
grdb id: 61357
Integer points: [ 1 0 1 0 -1 0 1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 -1 0 1 0 -1 0 0 -1 -1 0 -1 -1 0]
[ 0 0 0 1 0 -1 -1 1 -1 0 -1 0 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + x*y-1 + x-1*y + x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + x-1 + 2*y-1*z-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2331
Image of polytope 2331 PALP id: 2331
grdb id: 61352
Integer points: [ 1 0 1 0 0 -1 -1 0 0 -1 -1 0 -1 0 -1]
[ 0 1 -1 0 0 1 1 -1 -1 0 0 -1 0 0 1]
[ 0 0 0 1 -1 1 -1 1 -1 1 -1 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y*z + x*y-1 + 2*x-1*y + y-1*z + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 3 6 Lattice Minkowski decompositions of facet 3
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2332
Image of polytope 2332 PALP id: 2332
grdb id: 61364
Integer points: [ 1 0 1 0 0 0 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 1 -1 1 0 2 -1 0 1 0 -1 0]
[ 0 0 0 1 -1 1 0 -1 -1 0 -1 -1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + y*z-1 + x-1*y2*z-1 + x*y-1 + x-1*y + y-1*z + z-1 + 2*x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2333
Image of polytope 2333 PALP id: 2333
grdb id: 61316
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -2 -2 -2 -1 -1 0]
[ 0 1 0 0 -1 0 0 -1 -1 -1 -1 -1 0 -1 0]
[ 0 0 1 -1 0 1 -1 -1 1 1 -1 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + x-1*z + z-1 + y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + 2*x-2*y-1 + x-2*y-1*z-1
8 ? x + y + z + x-1*z + z-1 + y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + 2*x-2*y-1 + x-2*y-1*z-1
32 ? x + y + z + x-1*z + z-1 + y-1 + 3*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + 2*x-2*y-1 + x-2*y-1*z-1
159 ? x + y + z + x-1*z + z-1 + y-1 + 3*x-1 + x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-2*y-1*z + x-1*y-1*z-1 + 2*x-2*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 23 2 Lattice Minkowski decompositions of facet 23
Polytope 2334
Image of polytope 2334 PALP id: 2334
grdb id: 61355
Integer points: [ 1 0 1 0 0 -1 -1 0 -1 -2 -2 -1 0 -1 0]
[ 0 1 -1 0 0 1 1 -1 -1 1 0 0 -1 0 0]
[ 0 0 0 1 -1 0 1 -1 0 1 1 0 0 1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + x-1*y*z + x*y-1 + x-1*y + 2*x-1*z + x-2*y*z + z-1 + 2*y-1 + 3*x-1 + x-2*z + y-1*z-1 + x-1*y-1
17 rank 1, V22 x + y + z + x-1*y*z + x*y-1 + x-1*y + 2*x-1*z + x-2*y*z + z-1 + 2*y-1 + 2*x-1 + x-2*z + y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2335
Image of polytope 2335 PALP id: 2335
grdb id: 61320
Integer points: [ 1 0 1 0 0 1 0 -1 0 -1 -2 0 -1 0 -1]
[ 0 1 -1 0 0 -1 -1 0 -1 0 1 -1 0 0 1]
[ 0 0 0 1 -1 -1 1 1 -1 -1 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + x*y-1 + 2*x-1*y + y-1*z + x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 3*x-1 + x-2*y + y-1*z-1 + x-1*z-1
52 rank 2, number 52 x + y + z + x*y-1 + 2*x-1*y + y-1*z + x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + x-2*y + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2336
Image of polytope 2336 PALP id: 2336
grdb id: 61365
Integer points: [ 1 0 0 1 -1 0 0 2 0 1 -2 1 -1 0 -1]
[ 0 1 0 0 0 -1 0 -1 -1 -1 1 -1 0 0 1]
[ 0 0 1 -1 1 0 -1 -1 1 -1 0 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x2*y-1*z-1 + x*z-1 + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + x*y-1*z-1 + z-1 + y-1 + 2*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 6 Lattice Minkowski decompositions of facet 11
Polytope 2337
Image of polytope 2337 PALP id: 2337
grdb id: 61130
Integer points: [ 1 0 0 0 -1 0 0 -1 -1 -1 -1 -1 0 -1 0]
[ 0 1 0 0 1 -1 -1 0 0 -1 -1 -1 -1 0 0]
[ 0 0 1 -1 0 -1 1 1 -1 1 -1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
3 ? x + y + z + x-1*y + y-1*z + x-1*z + z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
36 rank 3, number 7 x + y + z + x-1*y + y-1*z + x-1*z + z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2338
Image of polytope 2338 PALP id: 2338
grdb id: 61098
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 -1 0 -1 1 0 -1 1 -1 -1 0 0 0]
[ 0 0 1 0 -1 -1 0 1 1 -1 -1 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y + x-1*z + z-1 + x-1*y*z-1 + y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2339
Image of polytope 2339 PALP id: 2339
grdb id: 61054
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 0 1 -1 1 -1 -1 0 0 0]
[ 0 0 1 -1 0 -1 1 0 1 -1 -1 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + y*z-1 + x-1*y + x-1*z + z-1 + x-1*y*z-1 + y-1 + 3*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2340
Image of polytope 2340 PALP id: 2340
grdb id: 61261
Integer points: [ 1 0 0 1 -1 0 -1 -1 1 -1 0 0 -1 0 0]
[ 0 1 0 -1 1 -1 0 1 -1 0 -1 -1 0 0 0]
[ 0 0 1 0 0 1 1 -1 -1 -1 -1 0 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*y-1 + x-1*y + y-1*z + x-1*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2341
Image of polytope 2341 PALP id: 2341
grdb id: 61252
Integer points: [ 1 0 0 1 1 -1 -1 0 1 0 -1 0 -1 0 0]
[ 0 1 0 0 -1 1 0 -1 -1 -1 0 -1 0 0 0]
[ 0 0 1 -1 0 0 1 1 -1 -1 -1 0 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + x*z-1 + x*y-1 + x-1*y + y-1*z + x-1*z + x*y-1*z-1 + 2*z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2342
Image of polytope 2342 PALP id: 2342
grdb id: 61055
Integer points: [ 1 0 0 -1 1 -1 1 0 -1 -1 1 -1 0 0 0]
[ 0 1 0 1 -1 1 -1 0 0 0 -2 0 -1 0 -1]
[ 0 0 1 1 0 0 -1 -1 1 -1 -1 0 0 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y*z + x*y-1 + x-1*y + x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2343
Image of polytope 2343 PALP id: 2343
grdb id: 61081
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 1 1 0 0 -2 -1 0 -1 0]
[ 0 0 1 -1 0 1 0 -1 1 -1 1 0 0 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y + y-1*z + x-1*z + z-1 + x-1*y*z-1 + y-1 + 3*x-1 + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2344
Image of polytope 2344 PALP id: 2344
grdb id: 61283
Integer points: [ 1 0 0 0 0 0 0 -1 -1 -2 -2 -1 -1 -1 0]
[ 0 1 0 1 -1 -1 0 1 -1 0 -1 0 -1 0 0]
[ 0 0 1 -1 1 0 -1 -1 -1 -1 -1 0 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + y*z-1 + y-1*z + z-1 + x-1*y*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-1
36 rank 3, number 7 x + y + z + y*z-1 + y-1*z + z-1 + x-1*y*z-1 + y-1 + 2*x-1 + 3*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2345
Image of polytope 2345 PALP id: 2345
grdb id: 61239
Integer points: [ 1 0 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 1 -1 -1 0 -1 1 1 -2 0 -1 0 0]
[ 0 0 1 -1 1 0 -1 1 -1 -2 1 0 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + y*z-1 + y-1*z + z-1 + x-1*y*z-1 + y-1 + 2*x-1 + x-1*y-1*z + x-1*y*z-2 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2346
Image of polytope 2346 PALP id: 2346
grdb id: 61240
Integer points: [ 1 0 0 1 0 0 -1 0 -1 -1 -1 0 -1 0 -1]
[ 0 1 0 0 1 -1 0 0 1 -1 -2 -1 0 0 -1]
[ 0 0 1 -1 -1 1 1 -1 0 0 1 0 0 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*z-1 + y*z-1 + x-1*y + y-1*z + x-1*z + z-1 + 2*y-1 + 2*x-1 + 2*x-1*y-1*z + x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2347
Image of polytope 2347 PALP id: 2347
grdb id: 60878
Integer points: [ 1 0 0 0 0 0 0 -1 -1 -2 -2 -1 -1 0 -1]
[ 0 1 0 1 -1 0 -1 -1 1 0 1 0 1 0 0]
[ 0 0 1 -1 1 -1 0 1 -1 1 0 0 0 0 1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
3 ? x + y + z + y*z-1 + 2*x-1*y + y-1*z + 2*x-1*z + z-1 + x-1*y*z-1 + y-1 + 3*x-1 + x-2*y + x-1*y-1*z + x-2*z
36 rank 3, number 7 x + y + z + y*z-1 + 2*x-1*y + y-1*z + 2*x-1*z + z-1 + x-1*y*z-1 + y-1 + 2*x-1 + x-2*y + x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 8 irreducible and admissible
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2348
Image of polytope 2348 PALP id: 2348
grdb id: 12613
Integer points: [ 1 0 0 1 -1 0 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 1 -1 0 0 1 0 -1 -1 0 -1 0]
[ 0 0 1 -1 1 0 -1 1 0 -1 0 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y*z + x-1*y + x-1*z + x*y-1*z-1 + z-1 + y-1 + 3*x-1 + 2*y-1*z-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
59 rank 2, number 16 x + y + z + x-1*y*z + x-1*y + x-1*z + x*y-1*z-1 + z-1 + y-1 + 2*x-1 + 2*y-1*z-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 5 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Polytope 2349
Image of polytope 2349 PALP id: 2349
grdb id: 12608
Integer points: [ 1 0 0 -1 1 -1 1 0 0 0 -1 -1 0 -1 0]
[ 0 1 0 1 -1 1 -1 0 -1 -1 0 0 -1 0 0]
[ 0 0 1 1 0 0 -1 -1 1 -1 1 -1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + x-1*y*z + x*y-1 + x-1*y + y-1*z + x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 6 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2350
Image of polytope 2350 PALP id: 2350
grdb id: 12611
Integer points: [ 1 0 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 0 1 1 -1 0 0 -1 -1 0 -1 0]
[ 0 0 0 1 -1 0 -1 1 1 -1 0 1 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*y-1 + x-1*y + y-1*z + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
146 ? x + y + z + x*y-1 + x-1*y + y-1*z + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Polytope 2351
Image of polytope 2351 PALP id: 2351
grdb id: 12607
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -1 0 0 0 -1 -1 -2 -2 -1 -1 0]
[ 0 0 1 -1 1 -1 0 -1 1 -1 1 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + y*z-1 + y-1*z + z-1 + 2*y-1 + x-1 + x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
38 ? x + y + z + y*z-1 + y-1*z + z-1 + 2*y-1 + x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Polytope 2352
Image of polytope 2352 PALP id: 2352
grdb id: 12598
Integer points: [ 1 0 0 1 0 1 -1 0 -1 0 -1 -1 -1 0 0]
[ 0 1 0 0 1 -1 1 -1 0 0 -1 -1 0 -1 0]
[ 0 0 1 -1 -1 0 0 1 1 -1 1 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + x*z-1 + y*z-1 + x*y-1 + x-1*y + y-1*z + x-1*z + z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Polytope 2353
Image of polytope 2353 PALP id: 2353
grdb id: 1520
Integer points: [ 1 0 0 1 1 -1 1 0 -1 -1 0 -2 0 -1 0]
[ 0 1 0 0 -1 1 -1 -1 0 1 0 1 -1 0 0]
[ 0 0 1 -1 0 1 -1 0 1 0 -1 1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y*z + x*z-1 + x*y-1 + x-1*y + x-1*z + x-2*y*z + x*y-1*z-1 + z-1 + y-1 + 2*x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 8 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 2354
Image of polytope 2354 PALP id: 2354
grdb id: 1517
Integer points: [ 1 0 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 1 -1 0 -1 0 -1 -1 1 0 1 0 0]
[ 0 0 1 -1 1 -1 0 1 0 1 -1 -1 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
3 ? x + y + z + y*z-1 + x-1*y + y-1*z + x-1*z + z-1 + x-1*y*z-1 + y-1 + 3*x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
36 rank 3, number 7 x + y + z + y*z-1 + x-1*y + y-1*z + x-1*z + z-1 + x-1*y*z-1 + y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 3 6 Lattice Minkowski decompositions of facet 3
Polytope 2355
Image of polytope 2355 PALP id: 2355
grdb id: 10
Integer points: [ 1 0 0 -1 2 1 1 -1 -1 -2 1 0 0 -1 0]
[ 0 1 0 1 -1 0 -1 1 0 1 -1 0 -1 0 0]
[ 0 0 1 1 -1 -1 0 0 1 1 -1 -1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + x-1*y*z + x2*y-1*z-1 + x*z-1 + x*y-1 + x-1*y + x-1*z + x-2*y*z + x*y-1*z-1 + z-1 + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 12 Lattice Minkowski decompositions of facet 3
Polytope 2356
Image of polytope 2356 PALP id: 2356
grdb id: 545796
Integer points: [ 1 0 0 -1 -4 -3 -2 -3 -2 -1 -2 -1 -1 -1 0 0]
[ 0 1 0 2 -4 -2 0 -3 -1 1 -2 0 -1 -1 1 0]
[ 0 0 1 -2 1 0 -1 1 0 -1 1 0 1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 148 1 none
Image of facet 13 1 irreducible and admissible
Image of facet 14 1 none
Polytope 2357
Image of polytope 2357 PALP id: 2357
grdb id: 545810
Integer points: [ 1 0 0 -5 -1 -2 -3 -4 -1 -2 -3 -1 0 -1 -2 0]
[ 0 1 0 -2 -2 -2 -2 -2 -1 -1 -1 0 -1 -1 -1 0]
[ 0 0 1 -2 2 1 0 -1 1 0 -1 0 1 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 149 1 none
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 2358
Image of polytope 2358 PALP id: 2358
grdb id: 545831
Integer points: [ 1 1 0 -1 -6 -5 -4 -3 -2 -3 -2 -1 0 -1 0 1]
[ 0 2 0 1 -4 -3 -2 -1 0 -2 -1 0 1 -1 0 1]
[ 0 0 1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 43 1 irreducible and admissible
Image of facet 4 1 none
Image of facet 150 1 Lattice Minkowski decompositions of facet 150
Polytope 2359
Image of polytope 2359 PALP id: 2359
grdb id: 545808
Integer points: [ 1 1 0 -1 -7 -3 -5 -2 -4 -1 -3 0 -1 -3 0 1]
[ 0 2 0 -1 -4 -2 -3 -1 -2 0 -1 1 -1 -2 0 1]
[ 0 0 1 1 -2 0 -1 0 -1 0 -1 0 0 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 14 1 none
Image of facet 151 1 none
Polytope 2360
Image of polytope 2360 PALP id: 2360
grdb id: 545736
Integer points: [ 1 0 0 -7 -9 -6 -3 -8 -5 -2 -4 -1 -4 -1 -3 0]
[ 0 1 0 -4 -6 -4 -2 -5 -3 -1 -2 0 -3 -1 -2 0]
[ 0 0 1 -2 -2 -1 0 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 152 1 none
Image of facet 14 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2361
Image of polytope 2361 PALP id: 2361
grdb id: 545799
Integer points: [ 1 0 0 -1 -9 -3 -5 -7 -2 -4 -6 -1 -3 -1 -3 0]
[ 0 1 0 -1 -5 -2 -3 -4 -1 -2 -3 0 -1 -1 -2 0]
[ 0 0 1 1 -3 0 -1 -2 0 -1 -2 0 -1 0 -1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 123 1 none
Image of facet 148 1 none
Polytope 2362
Image of polytope 2362 PALP id: 2362
grdb id: 545690
Integer points: [ 1 0 0 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0]
[ 0 1 0 2 -4 -3 -2 -1 0 1 -2 -1 0 1 -1 0]
[ 0 0 1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 4 1 none
Image of facet 53 1 irreducible and admissible
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Polytope 2363
Image of polytope 2363 PALP id: 2363
grdb id: 532597
Integer points: [ 1 0 0 1 -2 -2 -2 -2 -1 -1 -1 0 0 -1 -1 0]
[ 0 1 0 -1 -1 2 0 1 -1 0 1 -1 0 0 1 0]
[ 0 0 1 -1 2 -1 1 0 1 0 -1 0 -1 1 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 95 1 none
Polytope 2364
Image of polytope 2364 PALP id: 2364
grdb id: 532601
Integer points: [ 1 1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 1]
[ 0 2 0 -1 1 -3 -2 -1 0 -2 -1 0 -1 0 1 1]
[ 0 0 1 1 -1 -1 0 0 0 -1 -1 -1 0 0 0 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 2 none
Image of facet 1 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 2365
Image of polytope 2365 PALP id: 2365
grdb id: 532085
Integer points: [ 1 0 0 2 -2 -2 1 0 -1 0 -1 -2 1 0 -1 -1]
[ 0 1 0 -1 1 -1 -1 -1 -1 0 0 0 0 0 0 1]
[ 0 0 1 -2 0 2 -1 0 1 -1 0 1 -1 0 1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*x*z-1 + 2*x-1*y + 2*x-1*z + x2*y-1*z-2 + 4*x*y-1*z-1 + 2*z-1 + 6*y-1 + 4*x-1 + x-2*y + 4*x-1*y-1*z + 2*x-2*z + x-2*y-1*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 2366
Image of polytope 2366 PALP id: 2366
grdb id: 532208
Integer points: [ 1 1 -1 0 -1 -1 -1 -1 0 0 -1 -1 0 0 1 0]
[ 0 2 -2 0 -1 2 1 0 2 1 0 -1 1 0 1 -1]
[ 0 0 0 1 1 -2 -1 0 -1 0 -1 0 -1 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2367
Image of polytope 2367 PALP id: 2367
grdb id: 532198
Integer points: [ 1 0 0 -2 0 -2 -2 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 1 0 1 -3 -1 0 -2 -1 0 -2 -1 0 1 -1 0]
[ 0 0 1 0 -2 -2 -1 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + 2*x-1*y + 3*y-1 + 2*x-1 + x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + 3*y-2*z-1 + 4*x-1*y-1*z-1 + 2*x-2*z-1 + y-3*z-2 + 2*x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Polytope 2368
Image of polytope 2368 PALP id: 2368
grdb id: 532022
Integer points: [ 1 0 0 -1 -3 -3 -2 -1 -3 -2 -1 -3 -2 -1 0 -1]
[ 0 1 0 -1 -2 -2 -1 0 -2 -1 0 -2 -1 -1 0 -1]
[ 0 0 1 1 0 -3 0 0 -1 -1 -1 -2 -2 0 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 42 1 none
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Polytope 2369
Image of polytope 2369 PALP id: 2369
grdb id: 532021
Integer points: [ 1 0 0 -1 -3 -3 -3 -3 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 0 1 0 -3 -2 -1 -2 -1 0 -1 0 -1 0 0]
[ 0 0 1 -1 -2 1 0 -1 1 0 -1 1 0 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 14 1 none
Image of facet 153 1 Lattice Minkowski decompositions of facet 153
Polytope 2370
Image of polytope 2370 PALP id: 2370
grdb id: 532132
Integer points: [ 1 0 0 0 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 3 -1 2 1 0 2 1 0 1 0 -1 0]
[ 0 0 0 1 -2 2 -1 0 1 -1 0 1 -1 0 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 80 1 none
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 2371
Image of polytope 2371 PALP id: 2371
grdb id: 532070
Integer points: [ 1 0 0 -3 -3 -1 -2 -3 -2 -1 -2 -1 -1 0 -1 0]
[ 0 1 0 0 -2 -2 -2 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 -2 0 2 1 -1 0 1 -1 0 0 1 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 154 1 none
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 2372
Image of polytope 2372 PALP id: 2372
grdb id: 531930
Integer points: [ 1 0 0 -1 -3 -3 -2 -2 -2 -1 -1 -1 0 -1 0 0]
[ 0 1 1 0 -2 -2 -1 -1 -1 0 0 0 1 -1 0 0]
[ 0 0 2 2 -2 -3 0 -1 -2 1 0 -1 1 -1 1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 y*z2 + 2*y*z + x + y + 2*z + x-1*z2 + 3*x-1*z + 5*x-1 + 3*x-1*z-1 + 2*x-1*y-1*z-1 + 2*x-2*y-1 + 4*x-2*y-1*z-1 + 3*x-2*y-1*z-2 + x-3*y-2*z-2 + x-3*y-2*z-3
17 rank 1, V22 y*z2 + 2*y*z + x + y + 2*z + x-1*z2 + 4*x-1*z + 6*x-1 + 3*x-1*z-1 + 2*x-1*y-1*z-1 + 2*x-2*y-1 + 5*x-2*y-1*z-1 + 3*x-2*y-1*z-2 + x-3*y-2*z-2 + x-3*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 3 irreducible and admissible
Image of facet 155 1 Lattice Minkowski decompositions of facet 155
Image of facet 9 1 irreducible and admissible
Polytope 2373
Image of polytope 2373 PALP id: 2373
grdb id: 532216
Integer points: [ 1 0 0 -1 -3 1 0 -2 -1 0 -2 -1 0 1 -1 0]
[ 0 1 0 -2 0 -2 -2 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 0 -2 2 1 -1 0 1 -1 0 0 1 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*y-1*z + 2*y-1 + 3*x-1 + 2*y-2*z + 2*x-1*z-1 + 4*x-1*y-1 + 3*x-2*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Image of facet 9 1 irreducible and admissible
Polytope 2374
Image of polytope 2374 PALP id: 2374
grdb id: 532205
Integer points: [ 1 0 0 -1 -1 -3 -2 -1 -2 -1 -2 -1 -1 0 0 0]
[ 0 1 0 -2 2 0 0 0 1 1 -1 -1 0 0 1 -1]
[ 0 0 1 0 -2 -2 -1 0 -2 -1 -1 0 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 14 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2375
Image of polytope 2375 PALP id: 2375
grdb id: 532065
Integer points: [ 1 0 0 -1 -1 -3 -2 -2 -1 -2 -1 -1 -1 0 0 0]
[ 0 1 0 2 -2 -2 0 -1 1 -2 0 -1 -1 1 0 -1]
[ 0 0 1 -2 2 0 -1 0 -1 1 0 1 0 -1 0 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 156 1 none
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 2376
Image of polytope 2376 PALP id: 2376
grdb id: 532084
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 2 -2 -4 1 0 -1 -1 -2 -3 1 0 -1 -2]
[ 0 0 1 -2 2 2 -1 0 1 0 1 2 -1 0 1 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 4*x-1*y*z-1 + 6*x-1 + 2*y-2*z + 4*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*y-1 + 4*x-1*y-2*z + 2*x-1*y-3*z2 + x-1*y-4*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 2377
Image of polytope 2377 PALP id: 2377
grdb id: 532077
Integer points: [ 1 0 0 0 -2 -4 -1 -3 -2 -1 0 -3 -2 -1 -1 0]
[ 0 1 0 -2 2 2 1 2 1 0 -1 1 0 -1 1 0]
[ 0 0 1 1 -1 -3 0 -2 -1 0 1 -2 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 8 1 none
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 2378
Image of polytope 2378 PALP id: 2378
grdb id: 532234
Integer points: [ 1 0 1 -3 1 -4 0 -1 -2 0 -1 -2 -3 1 0 -1]
[ 0 1 0 0 -1 -1 0 0 0 -1 -1 -1 -1 0 0 0]
[ 0 0 2 -2 2 -3 1 0 -1 1 0 -1 -2 1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 43 1 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 6 1 none
Image of facet 157 1 Lattice Minkowski decompositions of facet 157
Polytope 2379
Image of polytope 2379 PALP id: 2379
grdb id: 532581
Integer points: [ 1 0 1 0 1 -4 -2 -1 0 -3 -2 -1 0 -1 0 1]
[ 0 1 -2 0 -3 2 1 0 -1 1 0 -1 -2 1 0 -1]
[ 0 0 0 1 -1 -1 0 0 0 -1 -1 -1 -1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 58 1 Lattice Minkowski decompositions of facet 58
Image of facet 4 1 none
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Polytope 2380
Image of polytope 2380 PALP id: 2380
grdb id: 532107
Integer points: [ 1 1 0 -1 -2 -4 -1 -3 -2 -1 0 -3 -2 -1 0 1]
[ 0 2 0 1 -2 -2 -1 -2 -1 0 1 -1 0 -1 0 1]
[ 0 0 1 -1 1 -1 1 0 0 0 0 -1 -1 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 4 1 none
Image of facet 158 1 Lattice Minkowski decompositions of facet 158
Image of facet 9 1 irreducible and admissible
Polytope 2381
Image of polytope 2381 PALP id: 2381
grdb id: 531981
Integer points: [ 1 0 0 -4 -2 -5 -4 -3 -3 -2 -1 -2 -1 -2 -1 0]
[ 0 1 0 -1 -2 -2 -2 -2 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 1 -2 1 -2 -1 0 -1 0 1 -1 0 -1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 155 1 Lattice Minkowski decompositions of facet 155
Image of facet 14 1 none
Polytope 2382
Image of polytope 2382 PALP id: 2382
grdb id: 532222
Integer points: [ 1 0 0 -3 -3 -5 -2 -1 -4 -3 -2 -1 0 -4 -2 -1]
[ 0 1 0 -2 -2 -4 -1 0 -3 -2 -1 -1 0 -3 -2 -1]
[ 0 0 1 0 -2 -2 0 0 -1 -1 -1 0 0 -2 -1 -1]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
76 ? x + y + z + 3*x-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*y-1 + 2*x-2*y-1*z-1 + 2*x-2*y-2*z-1 + x-3*y-2 + 4*x-3*y-2*z-1 + x-3*y-2*z-2 + 2*x-4*y-3*z-1 + 2*x-4*y-3*z-2 + x-5*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Polytope 2383
Image of polytope 2383 PALP id: 2383
grdb id: 532230
Integer points: [ 1 0 0 -3 -3 -5 -4 -4 -3 -2 -2 -1 -2 -1 -1 0]
[ 0 1 0 0 -2 -2 -2 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 -2 0 -2 -1 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 159 1 none
Polytope 2384
Image of polytope 2384 PALP id: 2384
grdb id: 532505
Integer points: [ 1 0 1 -3 -4 1 0 -1 -2 -3 0 -1 -2 1 0 -1]
[ 0 1 0 0 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 0 2 -2 -2 3 2 1 0 -1 1 0 -1 1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
91 ? x*z2 + x*y-1*z3 + 2*x*z + x + y + 5*z + 5*y-1*z2 + 7*x-1 + 10*x-1*y-1*z + 2*x-1*z-1 + 4*x-2*z-1 + 10*x-2*y-1 + x-3*z-2 + 5*x-3*y-1*z-1 + x-4*y-1*z-2
94 ? x*z2 + x*y-1*z3 + 2*x*z + x + y + 3*z + 5*y-1*z2 + 4*x-1 + 10*x-1*y-1*z + 2*x-1*z-1 + 3*x-2*z-1 + 10*x-2*y-1 + x-3*z-2 + 5*x-3*y-1*z-1 + x-4*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 160 1 Lattice Minkowski decompositions of facet 160
Image of facet 1 4 irreducible and admissible
Image of facet 43 1 irreducible and admissible
Polytope 2385
Image of polytope 2385 PALP id: 2385
grdb id: 532515
Integer points: [ 1 0 1 -3 -1 -5 -4 -2 -3 -1 -2 0 -1 -2 0 1]
[ 0 1 0 0 1 -2 -1 0 -1 0 -1 0 0 -1 0 0]
[ 0 0 2 -2 -1 -2 -2 -1 -1 0 0 1 -1 -1 0 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 161 1 none
Polytope 2386
Image of polytope 2386 PALP id: 2386
grdb id: 532088
Integer points: [ 1 1 0 -1 -1 -5 -3 -2 -1 0 -4 -3 -2 -1 0 1]
[ 0 2 0 -1 1 -3 -2 -1 0 1 -2 -1 0 -1 0 1]
[ 0 0 1 1 -1 -1 0 0 0 0 -1 -1 -1 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 162 1 Lattice Minkowski decompositions of facet 162
Image of facet 4 1 none
Image of facet 13 1 irreducible and admissible
Polytope 2387
Image of polytope 2387 PALP id: 2387
grdb id: 532020
Integer points: [ 1 0 0 -1 -3 -6 -4 -5 -2 -3 -4 -1 -2 -1 -2 0]
[ 0 1 0 -1 -2 -2 -2 -2 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 1 1 0 -3 -1 -2 0 -1 -2 0 -1 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 14 1 none
Image of facet 153 1 Lattice Minkowski decompositions of facet 153
Polytope 2388
Image of polytope 2388 PALP id: 2388
grdb id: 532180
Integer points: [ 1 0 0 -3 -5 -7 -5 -6 -4 -2 -3 -1 -3 -1 -2 0]
[ 0 1 0 -2 -2 -4 -3 -3 -2 -1 -1 0 -2 -1 -1 0]
[ 0 0 1 0 -2 -2 -1 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
42 rank 2, number 29 x + y + z + 2*x-1 + 2*x-1*y-1 + x-2*y-1 + 2*x-2*y-1*z-1 + x-3*y-1*z-1 + x-3*y-2 + 2*x-3*y-2*z-1 + 2*x-4*y-2*z-1 + x-5*y-2*z-2 + 2*x-5*y-3*z-1 + 2*x-6*y-3*z-2 + x-7*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 163 1 Lattice Minkowski decompositions of facet 163
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 2389
Image of polytope 2389 PALP id: 2389
grdb id: 532206
Integer points: [ 1 0 0 0 -4 -6 -4 -2 -5 -3 -1 -2 -3 -1 -2 0]
[ 0 1 -1 0 1 3 2 1 2 1 0 0 2 1 1 0]
[ 0 0 0 1 -2 -2 -1 0 -2 -1 0 -1 -1 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 14 1 none
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Polytope 2390
Image of polytope 2390 PALP id: 2390
grdb id: 532120
Integer points: [ 1 0 0 -2 -5 -8 -2 -4 -6 -1 -3 -1 -3 -5 0 -2]
[ 0 1 0 -2 -2 -4 -1 -2 -3 0 -1 -1 -2 -3 0 -1]
[ 0 0 1 -1 -2 -3 0 -1 -2 0 -1 0 -1 -2 0 -1]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 64 1 none
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 2391
Image of polytope 2391 PALP id: 2391
grdb id: 531125
Integer points: [ 1 0 0 -2 0 -2 0 -1 -1 -1 -1 -2 -2 -2 0 0]
[ 0 1 0 2 -2 -2 -1 1 0 -1 -2 1 0 -1 0 -1]
[ 0 0 1 -1 1 -1 1 0 0 0 0 -1 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 4 1 none
Image of facet 13 1 irreducible and admissible
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 2392
Image of polytope 2392 PALP id: 2392
grdb id: 530958
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 -2 -2 -2 -2 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 1 -1 -1 2 1 0 1 0 -1 0 -1 1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Image of facet 14 1 none
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Polytope 2393
Image of polytope 2393 PALP id: 2393
grdb id: 531049
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 2 -2 -2 1 0 -1 0 -1 -2 1 0 -1 -1]
[ 0 0 1 -2 2 0 -1 0 1 -1 0 1 -1 0 1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 4*x-1*y*z-1 + 2*y-1 + 6*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-2*z + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Polytope 2394
Image of polytope 2394 PALP id: 2394
grdb id: 531025
Integer points: [ 1 0 0 0 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0]
[ 0 0 0 1 -2 2 -1 0 1 -1 0 1 -1 0 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + 2*x-1*z + y-1 + 4*x-1 + 2*x-1*y-1*z + x-2*y-1*z2 + 2*x-1*z-1 + 4*x-1*y-1 + 4*x-2*y-1*z + 2*x-1*y-1*z-1 + 6*x-2*y-1 + 4*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 32 2 Lattice Minkowski decompositions of facet 32
Polytope 2395
Image of polytope 2395 PALP id: 2395
grdb id: 531279
Integer points: [ 1 0 0 -1 -3 -3 -2 -1 -3 -2 -1 -2 -1 0 -1 0]
[ 0 1 0 -2 0 -2 0 0 -1 -1 -1 -2 0 0 -1 -1]
[ 0 0 1 0 -2 -2 -1 0 -2 -1 0 -1 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
32 ? x + y + z + 2*y-1 + 3*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2 + 4*x-2*y-1*z-1 + x-3*z-2 + 2*x-2*y-2*z-1 + 2*x-3*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 2396
Image of polytope 2396 PALP id: 2396
grdb id: 531277
Integer points: [ 1 0 0 -2 -2 0 -1 0 -1 -2 0 -1 -2 -1 0 0]
[ 0 1 0 2 -1 -3 1 -1 0 1 -2 -1 0 -2 0 -1]
[ 0 0 1 -1 -1 1 0 1 0 -1 1 0 -1 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 4 1 none
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Image of facet 9 2 irreducible and admissible
Polytope 2397
Image of polytope 2397 PALP id: 2397
grdb id: 531870
Integer points: [ 1 0 0 0 -2 -2 -1 -1 -1 -1 -2 -2 -2 -2 0 0]
[ 0 1 0 -1 2 -3 1 0 -1 -2 1 0 -1 -2 0 -1]
[ 0 0 1 1 -1 -1 0 0 0 0 -1 -1 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 43 1 irreducible and admissible
Image of facet 4 1 none
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Polytope 2398
Image of polytope 2398 PALP id: 2398
grdb id: 531257
Integer points: [ 1 0 0 0 -4 -6 -4 -2 -3 -1 -5 -3 -1 -2 0 -2]
[ 0 1 -1 0 -3 -3 -2 -1 -1 0 -3 -2 -1 -1 0 -2]
[ 0 0 0 1 -2 -2 -1 0 -1 0 -2 -1 0 -1 0 -1]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 14 1 none
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2399
Image of polytope 2399 PALP id: 2399
grdb id: 483095
Integer points: [ 1 0 0 0 -2 -1 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 -2 2 1 0 -1 1 0 -1 0 -1 1 0]
[ 0 0 0 1 1 -2 -2 -1 0 -1 0 1 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2400
Image of polytope 2400 PALP id: 2400
grdb id: 483089
Integer points: [ 1 0 1 -1 1 0 -2 -1 0 -1 0 0 -1 0 1 0]
[ 0 1 0 0 -1 1 -1 0 0 -1 -1 1 0 0 0 0]
[ 0 0 2 -2 1 2 -2 0 1 -1 0 1 -1 0 1 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x*z2 + y*z2 + 2*x*z + 2*y*z + x + y + x*y-1*z + 3*z + 2*z-1 + 3*y-1 + 2*x-1 + 2*x-1*z-1 + x-1*z-2 + 3*x-1*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2401
Image of polytope 2401 PALP id: 2401
grdb id: 483090
Integer points: [ 1 0 0 -1 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -2 0 -3 -1 -2 0 -1 0 -1 -2 0 -1]
[ 0 0 1 1 -1 1 -2 0 -1 0 -1 1 0 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
25 ? x + y + z + x-1*y*z + 2*x-1*z + 2*y-1 + 3*x-1 + x-2*z + 4*x-1*y-1 + y-2*z-1 + 2*x-1*y-1*z-1 + 3*x-2*y-1 + 2*x-1*y-2*z-1 + 3*x-2*y-2*z-1 + x-2*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2402
Image of polytope 2402 PALP id: 2402
grdb id: 483006
Integer points: [ 1 0 1 0 -1 1 -3 -2 -1 0 -2 -1 0 -1 0 1]
[ 0 1 -2 0 1 -3 1 1 0 -1 0 -1 -2 1 0 -1]
[ 0 0 0 1 1 -1 -1 0 0 0 -1 -1 -1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 1 2 irreducible and admissible
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 4 1 none
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Polytope 2403
Image of polytope 2403 PALP id: 2403
grdb id: 483103
Integer points: [ 1 0 0 -2 1 -3 2 0 -1 1 0 -1 -2 1 0 -1]
[ 0 1 0 1 -2 2 -3 -1 0 -2 -1 0 1 -1 0 1]
[ 0 0 1 0 0 -1 -1 0 0 -1 -1 -1 -1 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 58 1 Lattice Minkowski decompositions of facet 58
Image of facet 146 1 Lattice Minkowski decompositions of facet 146
Image of facet 6 2 none
Polytope 2404
Image of polytope 2404 PALP id: 2404
grdb id: 483096
Integer points: [ 1 0 1 0 1 -2 -2 -2 -1 -1 -1 0 0 -1 0 1]
[ 0 1 -2 0 -3 2 0 1 1 0 -1 -1 -2 1 0 -1]
[ 0 0 0 1 -1 1 -1 0 1 0 -1 0 -1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 4 1 none
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 2405
Image of polytope 2405 PALP id: 2405
grdb id: 483014
Integer points: [ 1 1 0 0 -3 -1 -3 -2 -1 -3 -2 -1 0 -1 0 1]
[ 0 2 0 1 -2 -1 -2 -1 0 -2 -1 0 1 -1 0 1]
[ 0 0 1 1 -1 1 1 1 1 0 0 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 101 1 none
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2406
Image of polytope 2406 PALP id: 2406
grdb id: 483027
Integer points: [ 1 1 0 -2 0 -4 -2 -1 -3 -2 -1 0 -3 -1 0 1]
[ 0 2 0 -1 1 -3 -1 0 -2 -1 0 1 -2 -1 0 1]
[ 0 0 1 -1 1 -1 1 1 0 0 0 0 -1 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 1 none
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 140 1 Lattice Minkowski decompositions of facet 140
Polytope 2407
Image of polytope 2407 PALP id: 2407
grdb id: 483097
Integer points: [ 1 0 0 -1 -2 -1 -5 -4 -3 -3 -2 -1 -3 -2 -1 0]
[ 0 1 0 -1 0 -1 -3 -2 -1 -2 -1 0 -2 -1 -1 0]
[ 0 0 1 -1 -1 1 -1 -1 -1 0 0 0 -1 -1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 14 1 none
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 2408
Image of polytope 2408 PALP id: 2408
grdb id: 481045
Integer points: [ 1 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 1 0 -2 -1 -2 -2 -2 -1 -1 0 0 -1 -1 0]
[ 0 0 0 1 -1 2 2 1 0 1 0 1 0 1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 104 1 none
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Polytope 2409
Image of polytope 2409 PALP id: 2409
grdb id: 482426
Integer points: [ 1 0 -1 0 0 -1 -1 -1 0 0 -1 -1 0 0 0 0]
[ 0 1 0 1 -2 0 -2 -1 -1 0 -1 0 -1 0 1 0]
[ 0 0 0 2 -1 -2 -2 -1 0 1 -2 -1 -1 0 1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 y*z2 + 2*y*z + x + y + 3*z + 2*z-1 + 3*y-1 + x-1 + 2*y-1*z-1 + 2*x-1*z-1 + x-1*z-2 + y-2*z-1 + 2*x-1*y-1*z-1 + 2*x-1*y-1*z-2 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 9 1 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2410
Image of polytope 2410 PALP id: 2410
grdb id: 482313
Integer points: [ 1 0 0 0 -1 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 -2 -1 1 0 1 0 -1 1 0 1 0 -1]
[ 0 0 1 2 -2 -2 0 -1 1 0 -1 0 -1 1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 y*z2 + 2*y*z + x + y + z + 2*x-1*y*z + 2*x-1*y + 3*x-1 + x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1*z-1 + 2*x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Polytope 2411
Image of polytope 2411 PALP id: 2411
grdb id: 482428
Integer points: [ 1 0 0 0 0 -2 -2 -2 -1 -1 -1 0 -1 -1 0 0]
[ 0 1 0 0 -2 0 2 1 -1 0 1 -1 0 1 -1 0]
[ 0 0 1 -1 1 1 -1 0 1 0 -1 0 1 0 1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + 2*x-1*y + 2*y-1*z + 2*x-1*z + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 4*x-1 + 2*x-2*y + y-2*z + 2*x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2412
Image of polytope 2412 PALP id: 2412
grdb id: 482354
Integer points: [ 1 0 1 0 -2 0 -2 -1 0 -1 0 1 -1 -2 -1 0]
[ 0 1 -2 0 2 -2 0 0 -1 1 0 -1 -1 1 0 -1]
[ 0 0 0 1 -1 1 1 1 1 0 0 0 1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 37 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2413
Image of polytope 2413 PALP id: 2413
grdb id: 482431
Integer points: [ 1 1 0 -1 -1 -1 -1 0 -1 -1 0 0 1 -1 0 0]
[ 0 2 0 -2 0 -1 -2 -1 -2 -1 -1 0 1 -1 0 1]
[ 0 0 1 0 0 1 -2 0 -1 0 -1 0 0 -1 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x*y2 + 2*x*y + x + 2*y + z + 2*z-1 + 2*y-1 + x-1 + x-1*y-1*z + 2*y-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 3 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 2414
Image of polytope 2414 PALP id: 2414
grdb id: 482045
Integer points: [ 1 0 0 -2 -2 -3 -3 -3 -2 -1 -2 -1 -1 -1 -1 0]
[ 0 1 0 -2 1 -2 0 -1 0 1 -1 0 -1 0 -1 0]
[ 0 0 1 1 -2 0 -2 -1 -1 -1 0 0 1 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + 2*x-1*y*z-1 + 4*x-1 + 2*x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + x-2*y*z-2 + 4*x-2*z-1 + 4*x-2*y-1 + x-2*y-2*z + x-3*z-2 + 2*x-3*y-1*z-1 + x-3*y-2
32 ? x + y + z + 2*x-1*y*z-1 + 5*x-1 + 2*x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + x-2*y*z-2 + 5*x-2*z-1 + 5*x-2*y-1 + x-2*y-2*z + x-3*z-2 + 2*x-3*y-1*z-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 164 1 Lattice Minkowski decompositions of facet 164
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2415
Image of polytope 2415 PALP id: 2415
grdb id: 480868
Integer points: [ 1 0 0 -1 -1 -3 -3 -2 -3 -2 -1 -3 -2 -1 0 -1]
[ 0 1 0 0 -1 -2 -2 -1 -2 -1 0 -2 -1 -1 0 -1]
[ 0 0 1 1 1 -2 1 1 0 0 0 -1 -1 0 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 102 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2416
Image of polytope 2416 PALP id: 2416
grdb id: 481410
Integer points: [ 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 -1 -2 -3 0 -1 -2 0 -1 -2 -1 0 -1]
[ 0 0 1 1 -1 1 1 1 1 1 0 0 0 1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 8 1 none
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Polytope 2417
Image of polytope 2417 PALP id: 2417
grdb id: 482243
Integer points: [ 1 0 0 0 -2 -1 -2 -1 -1 -1 -2 -2 0 0 -1 -1]
[ 0 1 -1 0 0 -2 -3 -2 -1 0 -2 -1 -1 0 -1 0]
[ 0 0 0 1 1 -2 -2 -1 0 1 -1 0 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 42 1 none
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2418
Image of polytope 2418 PALP id: 2418
grdb id: 482199
Integer points: [ 1 0 0 0 -1 -2 -3 -2 -1 -1 -2 -1 0 -1 0 0]
[ 0 1 0 -2 -2 1 0 0 0 1 -1 -1 -1 0 0 -1]
[ 0 0 1 1 0 -2 -2 -1 0 -1 -1 0 1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + 2*y-1*z + 2*x-1*y*z-1 + 2*y-1 + 3*x-1 + y-2*z + 2*x-1*z-1 + 4*x-1*y-1 + x-2*y*z-2 + 3*x-2*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 2419
Image of polytope 2419 PALP id: 2419
grdb id: 482425
Integer points: [ 1 0 0 0 0 -2 -2 -2 -1 -1 -1 0 -1 -1 0 0]
[ 0 1 0 0 -2 0 -2 -1 -2 -1 0 -1 -1 0 -1 0]
[ 0 0 1 -1 -1 -1 -3 -2 -2 -1 0 0 -2 -1 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
25 ? x + y + z + z-1 + 2*y-1 + 2*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + y-2*z-1 + 4*x-1*y-1*z-1 + x-2*z-1 + 2*x-1*y-1*z-2 + 2*x-1*y-2*z-2 + 2*x-2*y-1*z-2 + x-2*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Polytope 2420
Image of polytope 2420 PALP id: 2420
grdb id: 480908
Integer points: [ 1 0 1 0 0 -2 -2 -2 -2 -1 -1 -1 0 -1 -1 0]
[ 0 1 -1 0 -2 0 -3 -2 -1 -2 -1 0 -1 -1 0 0]
[ 0 0 0 1 -1 1 -2 -1 0 -1 0 1 0 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 138 1 Lattice Minkowski decompositions of facet 138
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Polytope 2421
Image of polytope 2421 PALP id: 2421
grdb id: 481004
Integer points: [ 1 0 0 -2 -3 -2 -3 -3 -2 -1 -3 -2 -1 -1 -1 0]
[ 0 1 0 -1 -2 -1 -2 -2 -1 0 -2 -1 0 -1 -1 0]
[ 0 0 1 -1 -1 2 2 1 1 1 0 0 0 1 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 136 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Polytope 2422
Image of polytope 2422 PALP id: 2422
grdb id: 481662
Integer points: [ 1 0 0 -1 -1 -2 -2 -2 -1 -2 -1 -2 -1 0 0 0]
[ 0 1 0 2 -2 -2 2 -1 -1 0 0 1 1 -1 0 1]
[ 0 0 1 -2 2 1 -3 0 1 -1 0 -2 -1 1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
94 ? x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 3*x-1*y*z-1 + 4*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + x-2*y2*z-3 + 4*x-2*y*z-2 + 6*x-2*z-1 + 4*x-2*y-1 + x-2*y-2*z
91 ? x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 5*x-1*y*z-1 + 7*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + x-2*y2*z-3 + 4*x-2*y*z-2 + 6*x-2*z-1 + 4*x-2*y-1 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 165 1 Lattice Minkowski decompositions of facet 165
Polytope 2423
Image of polytope 2423 PALP id: 2423
grdb id: 482062
Integer points: [ 1 0 0 -1 -1 -2 -2 0 -1 -1 -1 -2 -2 0 0 0]
[ 0 1 1 0 0 -1 -1 1 0 0 0 -1 -1 0 0 0]
[ 0 0 2 -2 2 0 -3 1 -1 0 1 -2 -1 -1 0 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
94 ? y*z2 + 2*y*z + x + y + 2*z + x-1*z2 + 3*x-1*z + 2*z-1 + 4*x-1 + 3*x-1*z-1 + x-1*z-2 + x-2*y-1 + 3*x-2*y-1*z-1 + 3*x-2*y-1*z-2 + x-2*y-1*z-3
91 ? y*z2 + 2*y*z + x + y + 2*z + x-1*z2 + 4*x-1*z + 2*z-1 + 7*x-1 + 5*x-1*z-1 + x-1*z-2 + x-2*y-1 + 3*x-2*y-1*z-1 + 3*x-2*y-1*z-2 + x-2*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 5 irreducible and admissible
Image of facet 166 1 Lattice Minkowski decompositions of facet 166
Image of facet 9 1 irreducible and admissible
Polytope 2424
Image of polytope 2424 PALP id: 2424
grdb id: 482405
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 2 1 -2 -3 1 0 -1 0 -1 -2 1 0 -1]
[ 0 0 1 -2 -2 2 2 -1 0 1 -1 0 1 -1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 134 1 Lattice Minkowski decompositions of facet 134
Image of facet 6 1 none
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 13 1 irreducible and admissible
Polytope 2425
Image of polytope 2425 PALP id: 2425
grdb id: 481589
Integer points: [ 1 0 0 0 -2 -1 -3 -1 0 -1 -2 -1 -2 0 -1 0]
[ 0 1 0 -2 2 -2 2 1 -1 0 1 -1 0 0 1 -1]
[ 0 0 1 1 -1 0 -2 0 1 0 -1 0 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + 2*x-1*y + 2*y-1*z + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 3*x-1 + y-2*z + 2*x-2*y*z-1 + 2*x-1*y-1 + x-3*y2*z-2 + 2*x-2*z-1 + x-1*y-2
94 ? x + y + z + 2*x-1*y + 2*y-1*z + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 6*x-1 + y-2*z + 4*x-2*y*z-1 + 4*x-1*y-1 + x-3*y2*z-2 + 2*x-2*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 135 1 Lattice Minkowski decompositions of facet 135
Polytope 2426
Image of polytope 2426 PALP id: 2426
grdb id: 482412
Integer points: [ 1 0 1 -2 1 -2 -3 0 -1 -2 0 -1 -1 1 0 -1]
[ 0 1 1 -1 2 -2 -2 1 0 -1 0 -1 0 1 0 -1]
[ 0 0 2 -2 2 -1 -2 1 0 -1 1 0 -1 1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 6 1 none
Image of facet 9 1 irreducible and admissible
Polytope 2427
Image of polytope 2427 PALP id: 2427
grdb id: 481414
Integer points: [ 1 0 0 -2 0 -2 -4 -1 -2 -3 -1 -2 -3 -1 0 -1]
[ 0 1 0 0 -1 -3 -4 -1 -2 -3 0 -1 -2 -2 0 -1]
[ 0 0 1 -1 1 1 1 1 1 1 0 0 0 1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Image of facet 8 1 none
Polytope 2428
Image of polytope 2428 PALP id: 2428
grdb id: 482266
Integer points: [ 1 0 0 -2 0 -1 -4 -2 -3 -1 -2 -1 -2 -3 0 -1]
[ 0 1 0 -1 -1 0 -3 -1 -2 -1 -2 0 -1 -2 0 -1]
[ 0 0 1 -1 1 1 1 1 1 1 1 0 0 0 0 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
123 ? x + y + z + y-1*z + x-1*z + 3*x-1 + 3*x-1*y-1*z + 2*x-1*y-1 + 3*x-2*y-1*z + 3*x-2*y-1 + 2*x-2*y-2*z + x-2*y-1*z-1 + 3*x-3*y-2*z + 2*x-3*y-2 + x-4*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 56 1 Lattice Minkowski decompositions of facet 56
Polytope 2429
Image of polytope 2429 PALP id: 2429
grdb id: 482111
Integer points: [ 1 0 0 -1 -2 -2 -4 -3 -2 -3 -2 -1 -1 -1 -1 0]
[ 0 1 0 1 -1 -2 -2 -1 0 -2 -1 0 -1 0 -1 0]
[ 0 0 1 0 -2 -1 -3 -2 -1 -2 -1 0 0 -1 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Image of facet 8 1 none
Polytope 2430
Image of polytope 2430 PALP id: 2430
grdb id: 482432
Integer points: [ 1 0 0 0 -2 -2 -4 -3 -1 -2 -1 -2 0 -3 -1 -1]
[ 0 1 -1 0 -1 -1 -3 -2 -1 -2 0 -1 0 -2 -1 0]
[ 0 0 0 1 0 -2 -2 -1 0 -1 0 -1 0 -2 -1 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + y-1 + 2*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + 4*x-2*y-1*z-1 + x-2*y-1*z-2 + 2*x-2*y-2*z-1 + 2*x-3*y-2*z-1 + 2*x-3*y-2*z-2 + x-4*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Polytope 2431
Image of polytope 2431 PALP id: 2431
grdb id: 482353
Integer points: [ 1 0 0 0 -2 -2 -4 -3 -3 -2 -1 -1 -2 -1 -1 0]
[ 0 1 -1 0 1 -1 1 1 0 0 0 -1 1 1 0 0]
[ 0 0 0 1 0 -2 -2 -1 -2 -1 0 -1 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
32 ? x + y + z + 2*x-1*y + y-1 + 4*x-1 + x-2*y + 2*x-1*z-1 + 2*x-2*y*z-1 + 2*x-1*y-1*z-1 + 5*x-2*z-1 + 2*x-3*y*z-1 + x-2*y-1*z-2 + 2*x-3*z-2 + x-4*y*z-2
8 ? x + y + z + 2*x-1*y + y-1 + 3*x-1 + x-2*y + 2*x-1*z-1 + 2*x-2*y*z-1 + 2*x-1*y-1*z-1 + 4*x-2*z-1 + 2*x-3*y*z-1 + x-2*y-1*z-2 + 2*x-3*z-2 + x-4*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2432
Image of polytope 2432 PALP id: 2432
grdb id: 480992
Integer points: [ 1 0 0 -1 -1 -3 -3 -2 -1 -2 -1 -2 -1 -1 0 0]
[ 0 1 0 -2 2 2 3 2 1 1 0 0 -1 1 0 -1]
[ 0 0 1 0 -1 -2 -2 -1 0 -1 0 -1 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 104 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2433
Image of polytope 2433 PALP id: 2433
grdb id: 482128
Integer points: [ 1 0 0 2 -3 1 2 -2 -1 -1 0 1 -1 0 1 1]
[ 0 1 0 -1 0 -2 -2 0 0 -1 -1 -1 0 0 0 -1]
[ 0 0 1 2 -2 2 3 -1 0 0 1 2 -1 0 1 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x2*y-1*z2 + x2*y-2*z3 + 2*x*z + 2*x*y-1*z2 + x + y + 2*x*y-1*z + z + x*y-2*z2 + 4*y-1*z + 3*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + 3*x-2*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2434
Image of polytope 2434 PALP id: 2434
grdb id: 481361
Integer points: [ 1 0 0 -2 0 -3 -4 -1 -2 -3 -1 0 -1 -2 0 -1]
[ 0 1 0 -2 1 -2 -3 0 -1 -2 -1 1 0 -1 0 -1]
[ 0 0 1 -1 2 -2 -2 1 0 -1 0 1 0 -1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? y*z2 + 2*y*z + x + y + z + 4*x-1*z + 4*x-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 6*x-2*y-1 + 3*x-2*y-1*z-1 + x-2*y-2*z-1 + 4*x-3*y-2*z-1 + x-3*y-2*z-2 + x-4*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Polytope 2435
Image of polytope 2435 PALP id: 2435
grdb id: 482268
Integer points: [ 1 0 0 -1 -1 -2 -4 -2 -3 -1 -2 -3 -1 -2 0 -1]
[ 0 1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 1 -1 1 2 2 0 1 0 1 2 0 1 0 1]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 14 1 none
Polytope 2436
Image of polytope 2436 PALP id: 2436
grdb id: 482420
Integer points: [ 1 1 -1 -1 0 0 -3 -2 -1 -2 0 -1 0 -1 0 1]
[ 0 2 0 -2 0 1 -4 -2 -1 -3 1 -1 0 -2 -1 1]
[ 0 0 0 0 1 1 -2 -1 0 -1 0 -1 0 -1 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x*y2 + 2*x*y + y*z + x + 2*y + z + 2*y-1 + x-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 2*x-2*y-2*z-1 + 2*x-2*y-3*z-1 + x-3*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 3 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2437
Image of polytope 2437 PALP id: 2437
grdb id: 480933
Integer points: [ 1 0 0 -2 0 -2 -5 -1 -3 -2 -1 -4 -3 -1 0 -2]
[ 0 1 0 0 -1 -2 -2 -1 -2 -1 0 -2 -1 -1 0 -1]
[ 0 0 1 -1 1 1 -2 1 0 0 0 -1 -1 0 0 -1]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
95 ? x + y + z + y-1*z + 4*x-1 + 2*x-1*y-1*z + 3*x-1*y-1 + x-2*z-1 + 5*x-2*y-1 + x-2*y-2*z + 2*x-2*y-1*z-1 + 3*x-3*y-1*z-1 + 3*x-3*y-2 + 3*x-4*y-2*z-1 + x-5*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 138 1 Lattice Minkowski decompositions of facet 138
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2438
Image of polytope 2438 PALP id: 2438
grdb id: 481385
Integer points: [ 1 0 0 -1 -3 -3 -5 -4 -3 -2 -2 -1 -2 -1 -1 0]
[ 0 1 0 0 -2 -3 -4 -3 -2 -1 -2 -1 -1 0 -1 0]
[ 0 0 1 1 -2 -2 -3 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 64 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2439
Image of polytope 2439 PALP id: 2439
grdb id: 481002
Integer points: [ 1 0 0 -1 -2 -4 -5 -3 -4 -2 -3 -1 -2 -1 -2 0]
[ 0 1 0 0 -1 -3 -4 -2 -3 -1 -2 0 -1 -1 -2 0]
[ 0 0 1 1 1 -2 -2 0 -1 0 -1 0 -1 0 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 136 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2440
Image of polytope 2440 PALP id: 2440
grdb id: 482135
Integer points: [ 1 0 0 -1 -2 -3 -5 -3 -4 -1 -2 -1 -2 -3 0 -1]
[ 0 1 0 0 -1 -3 -4 -2 -3 -1 -2 0 -1 -2 0 -1]
[ 0 0 1 -1 0 -2 -3 -1 -2 0 -1 0 -1 -2 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 8 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2441
Image of polytope 2441 PALP id: 2441
grdb id: 481415
Integer points: [ 1 0 -1 0 -2 -2 -4 -1 -2 -3 -1 -1 -2 -3 0 -1]
[ 0 1 -1 0 0 3 4 1 2 3 2 0 1 2 0 1]
[ 0 0 0 1 -1 -2 -3 0 -1 -2 -1 0 -1 -2 0 -1]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 8 1 none
Image of facet 80 1 none
Polytope 2442
Image of polytope 2442 PALP id: 2442
grdb id: 481366
Integer points: [ 1 0 0 0 -2 -2 -4 -1 -2 -3 -1 -1 -2 -3 0 -1]
[ 0 1 -1 0 0 3 4 1 2 3 2 0 1 2 0 1]
[ 0 0 0 1 -1 -2 -3 0 -1 -2 -1 0 -1 -2 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + 2*x-1*y2*z-1 + 4*x-1*y + x-2*y3*z-2 + 3*x-1*y*z-1 + 6*x-2*y2*z-1 + y-1 + 2*x-1 + 4*x-3*y3*z-2 + 4*x-2*y*z-1 + x-4*y4*z-3 + 2*x-3*y2*z-2 + x-2*z-1
50 ? x + y + z + 2*x-1*y2*z-1 + 4*x-1*y + x-2*y3*z-2 + 2*x-1*y*z-1 + 6*x-2*y2*z-1 + y-1 + 2*x-1 + 4*x-3*y3*z-2 + 4*x-2*y*z-1 + x-4*y4*z-3 + 2*x-3*y2*z-2 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 2443
Image of polytope 2443 PALP id: 2443
grdb id: 479735
Integer points: [ 1 0 0 0 0 -2 -2 -1 -2 -1 -1 0 -1 0 -1 0]
[ 0 1 0 0 -2 0 -2 -1 -1 0 -2 -1 -1 0 0 -1]
[ 0 0 1 -1 1 -1 1 1 0 0 1 1 0 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + 2*y-1*z + z-1 + 2*y-1 + 2*x-1 + y-2*z + 2*x-1*y-1*z + 2*x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-2*z + x-2*z-1 + 2*x-2*y-1 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2444
Image of polytope 2444 PALP id: 2444
grdb id: 477857
Integer points: [ 1 0 0 -1 -2 -1 -2 -2 -2 -2 -1 -1 -1 -1 -1 0]
[ 0 1 0 -1 -2 2 2 1 0 -1 1 0 -1 1 0 0]
[ 0 0 1 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
55 rank 2, number 19 x + y + z + x-1*y2*z-1 + 2*x-1*y + 3*x-1*y*z-1 + x-2*y2*z-1 + 4*x-1 + 3*x-1*z-1 + 4*x-2*y*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + 6*x-2*z-1 + 4*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 9 1 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2445
Image of polytope 2445 PALP id: 2445
grdb id: 479727
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 0 0 -2 -2 -1 0 -1 -2 -1 0 -1 0 -1]
[ 0 0 1 0 -2 0 2 -1 -1 0 1 1 -1 0 0 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + 2*y-1*z + 2*z-1 + 2*y-1 + x-1 + 2*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-2*z + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 2446
Image of polytope 2446 PALP id: 2446
grdb id: 479734
Integer points: [ 1 0 0 0 -2 2 0 0 -1 -1 1 1 0 0 -1 1]
[ 0 1 0 0 2 -2 -2 -1 1 0 -1 -2 0 -1 1 -1]
[ 0 0 1 -1 -1 1 1 0 -1 0 0 1 0 1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 x + y + x2*y-2*z + 2*x*y-1*z + z + 2*x*y-1 + 2*x-1*y + 2*x*y-2*z + 2*y-1*z + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 2*x-1 + y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 4 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 2447
Image of polytope 2447 PALP id: 2447
grdb id: 479733
Integer points: [ 1 0 0 0 0 -2 -2 -1 -2 -1 0 -1 -1 0 -1 0]
[ 0 1 0 0 -2 2 0 -1 1 0 -1 1 0 -1 1 0]
[ 0 0 1 -1 -1 1 1 0 1 0 -1 0 1 0 1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + 2*x-1*y*z + x-2*y2*z + 2*x-1*y + 2*x-1*z + 2*x-2*y*z + z-1 + 2*y-1 + 4*x-1 + x-2*z + 2*y-1*z-1 + 2*x-1*y-1 + y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 2448
Image of polytope 2448 PALP id: 2448
grdb id: 479576
Integer points: [ 1 0 -1 0 -1 -3 -3 -2 -3 -2 -1 -2 -1 0 -1 0]
[ 0 1 0 0 -2 -2 -4 -3 -3 -2 -1 -1 -2 -1 -1 0]
[ 0 0 0 1 0 -2 -2 -1 -2 -1 0 -1 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + 2*y-1 + x-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 2*x-2*y-1*z-1 + 4*x-2*y-2*z-1 + 2*x-2*y-3*z-1 + x-3*y-2*z-2 + 2*x-3*y-3*z-2 + x-3*y-4*z-2
103 ? x + y + z + 2*y-1 + x-1 + 4*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 2*x-2*y-1*z-1 + 5*x-2*y-2*z-1 + 2*x-2*y-3*z-1 + x-3*y-2*z-2 + 2*x-3*y-3*z-2 + x-3*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Polytope 2449
Image of polytope 2449 PALP id: 2449
grdb id: 479159
Integer points: [ 1 0 0 -1 -1 -2 -4 -3 -2 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 -1 -1 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
[ 0 0 1 -1 1 -2 -2 -1 0 -1 0 -2 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + 3*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + 2*x-2*z-1 + 3*x-2*y-1 + 4*x-2*y-1*z-1 + x-2*y-1*z-2 + 3*x-3*y-1*z-1 + 2*x-3*y-1*z-2 + x-4*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2450
Image of polytope 2450 PALP id: 2450
grdb id: 479732
Integer points: [ 1 0 0 0 -2 -2 -4 -3 -1 -2 -1 -2 0 -3 -1 -1]
[ 0 1 -1 0 1 1 1 1 0 0 1 1 0 1 0 1]
[ 0 0 0 1 0 -2 -2 -1 0 -1 0 -1 0 -2 -1 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + 2*x-1*y + 2*x-1*y*z-1 + y-1 + 2*x-1 + x-2*y + 2*x-1*z-1 + 4*x-2*y*z-1 + x-2*y*z-2 + 2*x-2*z-1 + 2*x-3*y*z-1 + 2*x-3*y*z-2 + x-4*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2451
Image of polytope 2451 PALP id: 2451
grdb id: 475996
Integer points: [ 1 0 0 0 -2 0 -2 -1 -2 -1 -1 0 -1 0 -1 0]
[ 0 1 0 0 0 -2 -2 -1 -1 0 -2 -1 -1 0 0 -1]
[ 0 0 1 -1 -1 -1 -1 0 -1 0 -1 0 -1 0 -1 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + z-1 + 2*y-1 + 2*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + y-2*z-1 + 4*x-1*y-1*z-1 + x-2*z-1 + 2*x-1*y-2*z-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 2452
Image of polytope 2452 PALP id: 2452
grdb id: 372986
Integer points: [ 1 0 0 0 -2 1 -2 0 -1 -1 0 -1 -1 0 0 1]
[ 0 1 0 0 1 -2 0 -2 -1 0 -1 0 1 -1 0 -1]
[ 0 0 1 -1 -2 2 -1 1 0 -1 0 0 -1 1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
23 ? x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*y-1*z + z-1 + 2*x-1*y*z-1 + 2*y-1 + 2*x-1 + y-2*z + 2*x-1*z-1 + 2*x-1*y-1 + x-2*y*z-2 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2453
Image of polytope 2453 PALP id: 2453
grdb id: 372990
Integer points: [ 1 0 0 0 0 1 -1 -1 0 -1 -1 -1 0 0 0 0]
[ 0 1 1 -1 -1 0 -2 2 0 -1 0 1 -1 0 1 0]
[ 0 0 2 -2 0 -1 -2 2 -1 -1 0 1 -1 0 1 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
26 rank 2, number 8 y*z2 + x-1*y2*z2 + y*z + x + y + 2*z + 4*x-1*y*z + x*z-1 + 2*z-1 + y-1 + 6*x-1 + y-1*z-1 + y-1*z-2 + 4*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 10 2 Lattice Minkowski decompositions of facet 10
Image of facet 59 2 Lattice Minkowski decompositions of facet 59
Polytope 2454
Image of polytope 2454 PALP id: 2454
grdb id: 372987
Integer points: [ 1 0 0 -2 1 2 -1 -2 -1 0 -1 0 1 -1 0 1]
[ 0 1 0 2 -2 -3 0 1 0 -1 1 -1 -2 1 0 -1]
[ 0 0 1 1 0 -1 -1 0 0 0 1 -1 -1 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 6 2 none
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2455
Image of polytope 2455 PALP id: 2455
grdb id: 372989
Integer points: [ 1 0 0 -1 -2 1 -2 2 -1 0 -1 0 1 -1 0 1]
[ 0 1 0 1 1 -2 1 -3 0 -1 0 -1 -2 1 0 -1]
[ 0 0 1 1 0 0 -1 -1 0 0 -1 -1 -1 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 6 2 none
Polytope 2456
Image of polytope 2456 PALP id: 2456
grdb id: 372984
Integer points: [ 1 1 0 0 -1 -1 2 2 1 1 1 0 0 0 -1 -1]
[ 0 2 0 1 -3 0 2 3 1 1 2 -1 0 1 -2 -1]
[ 0 0 1 1 -1 -1 1 1 0 1 1 0 0 0 -1 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 2 none
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2457
Image of polytope 2457 PALP id: 2457
grdb id: 372979
Integer points: [ 1 1 0 0 -2 -2 -1 -3 -2 -1 0 -1 0 1 0 1]
[ 0 3 0 -1 -3 -2 -2 -4 -3 -1 1 -2 0 2 -1 1]
[ 0 0 1 1 -1 -1 1 -1 0 0 0 0 0 0 0 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 45 2 none
Polytope 2458
Image of polytope 2458 PALP id: 2458
grdb id: 372905
Integer points: [ 1 0 0 -1 0 -2 -1 -2 -2 -1 -1 0 -1 -1 0 0]
[ 0 1 0 1 -2 1 -2 -1 0 0 -1 -1 1 0 0 -1]
[ 0 0 1 1 -1 0 -2 -2 -1 0 -1 0 0 -1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y*z + 2*x-1*y + 2*y-1 + 4*x-1 + x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + y-2*z-1 + 4*x-1*y-1*z-1 + 2*x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
59 rank 2, number 16 x + y + z + x-1*y*z + 2*x-1*y + 2*y-1 + 3*x-1 + x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + y-2*z-1 + 3*x-1*y-1*z-1 + 2*x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 96 1 Lattice Minkowski decompositions of facet 96
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2459
Image of polytope 2459 PALP id: 2459
grdb id: 372872
Integer points: [ 1 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 -1 0 -2 2 2 -1 1 0 1 0 -1 1 0 -1]
[ 0 0 0 1 2 -2 -1 2 0 1 -1 0 1 -1 0 1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + 2*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + x-1*y2*z-2 + 2*x-1*y*z-1 + x-1 + x-1*y-1*z + x-1*y-2*z2 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 109 1 Lattice Minkowski decompositions of facet 109
Polytope 2460
Image of polytope 2460 PALP id: 2460
grdb id: 372541
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 0 -2 2 2 1 0 1 -1 0 0 1 -1]
[ 0 0 1 1 1 0 -1 -2 0 0 -1 0 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 106 1 none
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 2461
Image of polytope 2461 PALP id: 2461
grdb id: 372774
Integer points: [ 1 0 0 1 1 -2 1 0 0 -1 0 -1 1 0 -1 0]
[ 0 1 0 -1 -2 1 -2 -1 -1 0 -1 0 -1 0 1 0]
[ 0 0 1 0 -1 2 -2 -2 0 1 -1 0 -1 0 1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + 2*x-1*y*z + x-2*y*z2 + x*y-1 + 3*x-1*z + 2*x*y-1*z-1 + 2*z-1 + 3*y-1 + 2*x-1 + x*y-2*z-1 + 3*y-1*z-1 + x*y-2*z-2 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2462
Image of polytope 2462 PALP id: 2462
grdb id: 372934
Integer points: [ 1 1 -1 0 0 0 -2 -2 -1 -1 -1 0 -1 0 0 1]
[ 0 2 -2 0 1 2 -1 0 0 -1 1 1 0 0 -1 1]
[ 0 0 0 1 -1 -1 -1 -1 0 0 -1 0 -1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 1 none
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2463
Image of polytope 2463 PALP id: 2463
grdb id: 372785
Integer points: [ 1 0 -1 1 0 1 1 -3 -1 0 -2 -1 0 1 -1 1]
[ 0 1 1 -1 0 1 -2 0 0 -1 0 -1 0 -1 0 0]
[ 0 0 0 0 1 -1 -1 1 1 0 1 0 0 -1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x*y*z-1 + x + y + z + 3*x*z-1 + x*y-1 + x-1*y + 3*x-1*z + 3*x*y-1*z-1 + 3*y-1 + 3*x-1 + 3*x-2*z + x*y-2*z-1 + 2*x-1*y-1 + x-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Polytope 2464
Image of polytope 2464 PALP id: 2464
grdb id: 372768
Integer points: [ 1 0 0 -1 -1 1 0 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 1 0 1 0 -1 -3 -3 -2 -1 -2 -1 -1 0 -1 0]
[ 0 0 1 0 1 -1 -2 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 14 1 none
Polytope 2465
Image of polytope 2465 PALP id: 2465
grdb id: 372723
Integer points: [ 1 0 -1 1 -3 -2 1 0 -1 0 -1 -2 0 1 0 -1]
[ 0 1 -1 0 0 1 -1 1 1 0 0 0 -1 0 0 0]
[ 0 0 0 2 -2 -1 2 1 0 1 0 -1 1 1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
127 ? x*z2 + 2*x*z + y*z + x*y-1*z2 + x + y + 5*z + 2*x-1*y + 2*y-1*z + 6*x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + 4*x-2*z-1 + x-3*z-2
146 ? x*z2 + 2*x*z + y*z + x*y-1*z2 + x + y + 2*z + 2*x-1*y + 2*y-1*z + 3*x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + 3*x-2*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 147 1 Lattice Minkowski decompositions of facet 147
Polytope 2466
Image of polytope 2466 PALP id: 2466
grdb id: 372746
Integer points: [ 1 0 0 -2 -3 1 -2 0 -1 0 -1 -2 -1 1 0 -1]
[ 0 1 0 -2 -2 2 0 2 1 1 0 -1 -1 1 0 -1]
[ 0 0 1 -1 -2 2 -1 1 0 1 0 -1 0 1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x*y2*z2 + 2*x*y*z + y2*z + 2*y*z + x + y + z + 2*x-1*y + 2*x-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1 + x-3*y-2*z-2
91 ? x*y2*z2 + 2*x*y*z + y2*z + 4*y*z + x + y + z + 2*x-1*y + 7*x-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + 4*x-2*y-1*z-1 + x-2*y-2*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 144 1 Lattice Minkowski decompositions of facet 144
Image of facet 1 4 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 2467
Image of polytope 2467 PALP id: 2467
grdb id: 372775
Integer points: [ 1 0 0 0 -1 0 -2 -3 -2 -1 -2 -1 0 -1 -1 0]
[ 0 1 0 -1 0 -1 2 2 1 0 1 0 -1 1 1 0]
[ 0 0 1 -1 -1 1 1 1 1 1 0 0 0 1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2468
Image of polytope 2468 PALP id: 2468
grdb id: 372892
Integer points: [ 1 0 0 0 1 -2 -2 -3 -2 -1 0 -1 -1 -1 0 1]
[ 0 1 -1 0 -2 1 2 2 1 0 -1 0 1 1 0 -1]
[ 0 0 0 1 2 -2 -1 -2 -1 0 1 -1 0 -1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*x-1*y + 4*y-1*z + x-1*y*z-1 + x-2*y2*z-1 + y-1 + 6*x-1 + 2*x-1*z-1 + 4*x-2*y*z-1 + x-2*y*z-2 + x-3*y2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 59 2 Lattice Minkowski decompositions of facet 59
Polytope 2469
Image of polytope 2469 PALP id: 2469
grdb id: 372784
Integer points: [ 1 0 0 1 0 0 -1 -3 0 -1 -2 -1 -2 1 0 -1]
[ 0 1 0 -2 -1 -1 0 2 -1 0 1 0 1 -1 0 1]
[ 0 0 1 0 -1 1 1 -1 0 0 0 -1 -1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2470
Image of polytope 2470 PALP id: 2470
grdb id: 372936
Integer points: [ 1 0 1 0 1 -1 0 -1 0 0 -1 -1 -1 0 0 0]
[ 0 1 -1 0 -2 2 -3 -2 -1 -2 1 0 -1 1 0 -1]
[ 0 0 0 1 -1 2 -2 -2 0 -1 1 0 -1 1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x-1*y2*z2 + 2*y*z + x + y + z + 4*x-1*y*z + x*y-1 + 3*y-1 + 6*x-1 + x*y-2*z-1 + y-1*z-1 + 3*y-2*z-1 + 4*x-1*y-1*z-1 + y-3*z-2 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 13 1 irreducible and admissible
Polytope 2471
Image of polytope 2471 PALP id: 2471
grdb id: 372935
Integer points: [ 1 1 -1 -1 0 1 1 -3 0 1 -1 0 -2 1 -1 0]
[ 0 2 0 -2 0 2 0 -3 -1 1 -1 0 -2 1 -1 1]
[ 0 0 0 0 1 -1 -1 1 0 -1 0 0 1 0 1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x*y2 + x*y2*z-1 + 2*x*y + 2*x*y*z-1 + x + 2*y + z + x*z-1 + 2*y-1 + x-1 + 3*x-1*y-1*z + 2*x-1*y-1 + x-1*y-2 + 3*x-2*y-2*z + x-3*y-3*z
51 rank 2, number 7 x*y2 + x*y2*z-1 + 2*x*y + 2*x*y*z-1 + x + 2*y + z + x*z-1 + 2*y-1 + x-1 + 3*x-1*y-1*z + 3*x-1*y-1 + x-1*y-2 + 3*x-2*y-2*z + x-3*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2472
Image of polytope 2472 PALP id: 2472
grdb id: 372821
Integer points: [ 1 0 0 0 -1 -2 -2 -4 -3 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 -1 0 0 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 0 1 -1 -1 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
66 rank 2, number 24 x + y + z + 2*x-1 + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + x-2*z-1 + 2*x-2*y-1 + 3*x-2*y-1*z-1 + x-2*y-2*z-1 + 2*x-3*y-1*z-1 + 2*x-3*y-2*z-1 + x-4*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2473
Image of polytope 2473 PALP id: 2473
grdb id: 372760
Integer points: [ 1 0 0 0 -1 -1 -3 -4 -3 -2 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 -1 1 0 1 1 1 0 0 1 1 0 0]
[ 0 0 0 1 -1 1 -2 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Image of facet 14 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2474
Image of polytope 2474 PALP id: 2474
grdb id: 372464
Integer points: [ 1 0 1 0 -1 0 -1 -4 -2 -3 -1 -2 0 -1 -2 0]
[ 0 1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 0 1 -1 1 1 -2 0 -1 0 -1 0 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 111 1 none
Polytope 2475
Image of polytope 2475 PALP id: 2475
grdb id: 372903
Integer points: [ 1 0 0 -1 1 -1 -3 -3 0 -1 -2 -1 -2 1 0 -1]
[ 0 1 0 0 -2 2 2 3 -1 0 1 1 2 -1 0 1]
[ 0 0 1 -1 2 -1 -2 -2 1 0 -1 0 -1 1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + 2*x*y-1*z + z + x*y-2*z2 + x-1*y2*z-1 + 3*x-1*y + 4*y-1*z + x-1*y*z-1 + 3*x-2*y2*z-1 + 6*x-1 + x-3*y3*z-2 + x-1*z-1 + 4*x-2*y*z-1 + x-3*y2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 13 1 irreducible and admissible
Polytope 2476
Image of polytope 2476 PALP id: 2476
grdb id: 372670
Integer points: [ 1 0 0 1 -3 -2 1 1 -1 0 -2 -1 0 -1 0 1]
[ 0 1 0 2 -2 0 2 3 1 2 -1 0 1 -1 0 1]
[ 0 0 1 2 -2 -1 1 2 0 1 -1 0 1 -1 0 1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
100 ? x*y3*z2 + x*y2*z2 + x*y2*z + 2*x*y*z + 3*y2*z + y*z + x + y + z + 3*x-1*y + 3*x-1 + 2*x-1*y-1*z-1 + x-2*z-1 + 3*x-2*y-1*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 110 1 Lattice Minkowski decompositions of facet 110
Polytope 2477
Image of polytope 2477 PALP id: 2477
grdb id: 370864
Integer points: [ 1 0 1 -1 0 1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 -1 1 0 -1 -1 -1 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 1 -1 -1 2 1 0 1 0 1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 14 1 none
Polytope 2478
Image of polytope 2478 PALP id: 2478
grdb id: 370703
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 1 -1 -2 -2 0 1 0 -1 0 -1 0 -1]
[ 0 0 1 -1 1 1 0 -1 1 0 0 0 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + x-1*y*z-1 + 2*y-1 + 5*x-1 + x-1*y-1*z + 3*x-1*z-1 + 4*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 2479
Image of polytope 2479 PALP id: 2479
grdb id: 370754
Integer points: [ 1 0 0 -1 0 -2 0 -2 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 -1 1 -1 1 1 0 0 0 0 0 -1 -1]
[ 0 0 1 1 1 1 -2 0 0 1 0 -1 0 -1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + 2*z-1 + 3*y-1 + 4*x-1 + x-2*y + 3*y-1*z-1 + 2*x-1*z-1 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Polytope 2480
Image of polytope 2480 PALP id: 2480
grdb id: 372136
Integer points: [ 1 0 0 0 -2 1 -2 0 -1 -1 0 -1 0 -1 0 1]
[ 0 1 0 0 1 -2 0 -2 -1 0 -1 0 -1 1 0 -1]
[ 0 0 1 -1 0 0 1 1 1 0 0 1 1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + 2*x*y-1 + 2*x-1*y + 2*y-1*z + 2*x-1*z + z-1 + x*y-2 + y-1 + x-1 + x-2*y + y-2*z + 2*x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 48 1 Lattice Minkowski decompositions of facet 48
Polytope 2481
Image of polytope 2481 PALP id: 2481
grdb id: 372120
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 1 -2 1 -1 1 1 0 0 1 0 -1 0 -1]
[ 0 0 1 -2 1 -1 1 1 0 1 0 -1 0 1 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y*z + 2*y*z-1 + 2*x-1*y + 2*y-1*z + 2*x-1*z + y*z-2 + 3*z-1 + x-1*y*z-1 + 3*y-1 + 2*x-1 + y-2*z + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2482
Image of polytope 2482 PALP id: 2482
grdb id: 371917
Integer points: [ 1 0 0 1 -2 1 -2 0 -1 0 -1 0 -1 1 0 -1]
[ 0 1 0 -1 1 -2 0 -2 -1 -1 0 -1 0 -1 0 1]
[ 0 0 1 -1 0 0 1 1 1 0 0 1 1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + 2*x*y-1 + 2*x-1*y + 2*y-1*z + 2*x-1*z + x*y-1*z-1 + x*y-2 + y-1 + 2*x-1 + x-2*y + y-2*z + 2*x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 47 1 Lattice Minkowski decompositions of facet 47
Polytope 2483
Image of polytope 2483 PALP id: 2483
grdb id: 370843
Integer points: [ 1 0 0 1 0 -1 -2 -2 -1 -2 -1 0 -1 0 -1 0]
[ 0 1 0 -1 1 1 -1 1 1 0 0 0 0 0 -1 -1]
[ 0 0 1 0 -1 -2 0 -2 -1 -1 -1 -1 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + y*z-1 + x*y-1 + 2*z-1 + 2*x-1*y*z-1 + 3*y-1 + 2*x-1 + x-1*y*z-2 + 4*x-1*z-1 + 3*x-1*y-1 + x-2*y*z-2 + 2*x-2*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Polytope 2484
Image of polytope 2484 PALP id: 2484
grdb id: 370581
Integer points: [ 1 0 0 1 1 -2 0 -2 0 -1 -1 0 -1 0 -1 0]
[ 0 1 0 -1 -1 0 -1 -1 -1 -1 0 -1 -1 0 0 0]
[ 0 0 1 0 -1 1 -2 0 0 0 1 -1 -1 0 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*y-1 + 2*x-1*z + x*y-1*z-1 + 2*z-1 + 3*y-1 + 2*x-1 + x-2*z + 3*y-1*z-1 + 3*x-1*y-1 + y-1*z-2 + 2*x-1*y-1*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2485
Image of polytope 2485 PALP id: 2485
grdb id: 371631
Integer points: [ 1 0 1 0 -2 0 -1 -2 0 -1 -1 -2 0 0 -1 -1]
[ 0 1 -1 0 1 -2 -2 -1 -1 -1 0 0 -1 0 0 1]
[ 0 0 0 1 0 -1 -2 -2 0 -1 0 -1 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + x*y-1 + 2*x-1*y + 2*y-1 + x-1 + x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + y-2*z-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 71 1 Lattice Minkowski decompositions of facet 71
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2486
Image of polytope 2486 PALP id: 2486
grdb id: 370321
Integer points: [ 1 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 1 0 -1 -2 -1 -2 -2 -1 -1 0 0 -1 -1 0]
[ 0 0 0 1 -1 0 2 2 1 0 1 0 1 0 1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 105 1 none
Polytope 2487
Image of polytope 2487 PALP id: 2487
grdb id: 370592
Integer points: [ 1 0 0 -1 -1 -1 -2 -2 -2 -2 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -2 2 -1 2 1 0 1 0 -1 1 0 -1]
[ 0 0 1 -1 0 -1 -1 -1 -1 -1 0 0 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*y2*z-1 + 2*x-1*y + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 3*x-1 + x-1*z-1 + 3*x-2*y*z-1 + 3*x-1*y-1 + 3*x-2*z-1 + x-1*y-2 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 56 1 Lattice Minkowski decompositions of facet 56
Polytope 2488
Image of polytope 2488 PALP id: 2488
grdb id: 368601
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 -1 -1 -1]
[ 0 1 0 0 -1 -2 2 -2 1 0 -1 0 -1 1 0 -1]
[ 0 0 1 1 1 0 -1 -1 0 0 0 0 0 -1 -1 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y2*z-1 + 2*x-1*y + x-1*z + 4*x-1*y*z-1 + 2*y-1 + 5*x-1 + x-1*y-1*z + 6*x-1*z-1 + 4*x-1*y-1 + 4*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 13 1 irreducible and admissible
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Polytope 2489
Image of polytope 2489 PALP id: 2489
grdb id: 370548
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 2 -2 -1 -2 0 1 -1 0 1 -1 -1 0]
[ 0 0 1 -1 -1 1 2 2 1 0 1 0 -1 0 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y2*z-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + 2*x-1*y*z-1 + 5*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 2490
Image of polytope 2490 PALP id: 2490
grdb id: 371033
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 0 -2 -1 -2 0 -1 -2 0 -1 -1 0 -1]
[ 0 0 1 0 -1 0 2 2 1 1 1 0 0 1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + 2*y-1 + 2*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + x-1*z-1 + x-1*y-1 + 2*x-1*y-2*z + x-1*y-2
107 rank 3, number 11 x + y + z + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + 2*y-1 + x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-2*z + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 112 1 Lattice Minkowski decompositions of facet 112
Polytope 2491
Image of polytope 2491 PALP id: 2491
grdb id: 372074
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 -1 0 -2 2 2 -1 1 0 -1 1 0 1 0 -1]
[ 0 0 0 1 2 -1 -2 2 -1 0 1 0 1 -1 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
109 ? x + y + z + 2*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + x-1*y2*z-2 + 4*x-1*y*z-1 + y-1 + 6*x-1 + 4*x-1*y-1*z + x-1*y-2*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 13 1 irreducible and admissible
Polytope 2492
Image of polytope 2492 PALP id: 2492
grdb id: 372059
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 0 -1 0 0 0]
[ 0 1 0 -2 2 0 -2 2 -1 0 1 -1 1 -1 0 1]
[ 0 0 1 -1 1 -1 -2 2 -1 0 1 0 0 -1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? x-1*y2*z2 + 2*y*z + x-1*y2*z + x + y + z + 4*x-1*y*z + 2*x-1*y + 2*y-1 + 6*x-1 + 2*y-1*z-1 + x-1*z-1 + y-2*z-1 + 4*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 59 2 Lattice Minkowski decompositions of facet 59
Polytope 2493
Image of polytope 2493 PALP id: 2493
grdb id: 370852
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 0 -1 -1 0 0 0]
[ 0 1 0 -2 2 1 2 -2 0 -1 -1 1 0 0 -1 1]
[ 0 0 1 1 -1 0 -2 0 0 0 1 -1 -1 0 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + 2*y*z-1 + x-1*y2*z-1 + x-1*y + 2*y-1*z + x-1*y2*z-2 + 3*x-1*y*z-1 + 2*y-1 + 3*x-1 + y-2*z + 2*x-1*z-1 + 3*x-1*y-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2494
Image of polytope 2494 PALP id: 2494
grdb id: 370851
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 1 -1 -2 -2 0 -1 -2 0 -1 -1 0 -1]
[ 0 0 1 -1 -1 -1 0 2 -1 0 1 0 1 0 0 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + 2*y-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Polytope 2495
Image of polytope 2495 PALP id: 2495
grdb id: 370863
Integer points: [ 1 0 0 0 0 -1 -2 -2 -2 -2 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 0 -1 -1 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 1 -1 -1 -1 2 0 1 0 1 -1 0 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + 2*x-1*z + y-1 + 3*x-1 + 2*x-1*y-1*z + x-2*y-1*z2 + y-1*z-1 + x-1*z-1 + 4*x-1*y-1 + 3*x-2*y-1*z + 2*x-1*y-1*z-1 + 3*x-2*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2496
Image of polytope 2496 PALP id: 2496
grdb id: 370586
Integer points: [ 1 0 0 0 0 -1 -2 -2 -2 -2 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 1 2 -1 2 0 1 0 1 -1 0 1 0]
[ 0 0 0 1 1 1 -2 1 -1 0 -1 0 -1 0 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? y*z + x-1*y2*z + x + y + z + 2*x-1*y*z + x-2*y2*z + 3*x-1*y + y-1 + 4*x-1 + 3*x-2*y + 2*x-1*z-1 + 2*x-1*y-1*z-1 + 3*x-2*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2497
Image of polytope 2497 PALP id: 2497
grdb id: 372105
Integer points: [ 1 0 0 0 0 2 -2 -2 -1 1 -1 1 -2 0 -1 -1]
[ 0 1 0 0 -1 -2 1 1 0 -1 0 -1 1 0 1 1]
[ 0 0 1 -1 0 -1 0 2 1 0 0 -1 1 0 1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + 2*x-1*y*z + x-2*y*z2 + 2*x*y-1 + 2*x-1*y + 2*x-1*z + 2*x-2*y*z + x2*y-2*z-1 + 2*x*y-1*z-1 + z-1 + y-1 + 2*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2498
Image of polytope 2498 PALP id: 2498
grdb id: 372128
Integer points: [ 1 0 0 2 -2 2 -1 0 1 0 1 0 1 -1 0 -1]
[ 0 1 0 -1 1 -2 -1 -2 -2 -1 -1 -1 -1 0 0 1]
[ 0 0 1 -1 0 -1 -1 -1 -1 0 0 -1 -1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Polytope 2499
Image of polytope 2499 PALP id: 2499
grdb id: 370782
Integer points: [ 1 0 1 0 1 -1 -2 -2 0 -1 0 -1 -2 0 -1 -1]
[ 0 1 -1 0 -2 0 1 1 -1 0 -1 0 1 0 1 1]
[ 0 0 0 1 -1 -1 0 2 0 1 -1 0 1 0 1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + 2*x-1*y*z + x-2*y*z2 + x*y-1 + 2*x-1*y + 3*x-1*z + 2*x-2*y*z + 3*y-1 + 4*x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 2500
Image of polytope 2500 PALP id: 2500
grdb id: 370816
Integer points: [ 1 0 -1 0 -1 -2 -2 0 -2 -1 -1 -1 0 0 0 0]
[ 0 1 1 0 0 1 -1 -3 0 0 -1 -2 -1 -2 0 -1]
[ 0 0 0 1 -1 -1 -1 1 -1 0 0 0 1 1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 2501
Image of polytope 2501 PALP id: 2501
grdb id: 370624
Integer points: [ 1 0 -1 0 -1 -1 0 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 1 0 -1 0 -2 -3 -2 -1 -2 -1 0 -1 -1 0]
[ 0 0 0 1 -1 1 1 1 1 1 0 0 0 1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 56 1 Lattice Minkowski decompositions of facet 56
Image of facet 8 1 none
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2502
Image of polytope 2502 PALP id: 2502
grdb id: 370599
Integer points: [ 1 0 -1 0 -1 -1 0 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 1 0 1 0 -3 -3 -1 -2 0 -1 -1 -2 0 -1]
[ 0 0 0 1 1 1 -2 -2 0 -1 0 -1 0 -1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y*z + x-1*y + x-1*z + 3*y-1 + 3*x-1 + 2*y-1*z-1 + 3*x-1*y-1 + 3*y-2*z-1 + 2*x-1*y-1*z-1 + 3*x-1*y-2*z-1 + y-3*z-2 + x-1*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2503
Image of polytope 2503 PALP id: 2503
grdb id: 371265
Integer points: [ 1 0 -1 0 0 0 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 1 0 -1 -1 -1 -3 -2 -2 -1 0 -2 -1 -1 0]
[ 0 0 0 1 -1 1 -1 -1 -1 0 0 0 -1 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + x-1*y + y-1*z + 2*y-1 + 3*x-1 + y-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-1*y-2 + 2*x-1*y-2*z-1 + x-2*y-1*z-1 + 2*x-2*y-2*z-1 + x-2*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Polytope 2504
Image of polytope 2504 PALP id: 2504
grdb id: 370044
Integer points: [ 1 0 0 -1 -2 -2 -3 -3 -3 -2 -1 -2 -1 -1 -1 0]
[ 0 1 0 1 1 -2 0 -2 -1 -1 -1 0 0 -1 0 0]
[ 0 0 1 0 -1 -1 -2 -2 -2 -1 0 -1 0 -1 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
66 rank 2, number 24 x + y + z + x-1*y + 2*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*z-1 + 3*x-2*y-1*z-1 + x-3*z-2 + x-2*y-2*z-1 + 2*x-3*y-1*z-2 + x-3*y-2*z-2
16 ? x + y + z + x-1*y + 3*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*z-1 + 4*x-2*y-1*z-1 + x-3*z-2 + x-2*y-2*z-1 + 2*x-3*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 143 1 Lattice Minkowski decompositions of facet 143
Polytope 2505
Image of polytope 2505 PALP id: 2505
grdb id: 369255
Integer points: [ 1 0 0 -1 -2 -1 0 -3 -1 0 -2 -1 -2 0 -1 0]
[ 0 1 0 1 1 -2 -2 0 0 -1 0 -1 -1 0 0 -1]
[ 0 0 1 0 -1 0 1 -2 0 1 -1 0 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y + 2*y-1*z + 2*y-1 + 3*x-1 + y-2*z + 2*x-1*z-1 + x-2*y*z-1 + 3*x-1*y-1 + 2*x-2*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + x-3*z-2
36 rank 3, number 7 x + y + z + x-1*y + 2*y-1*z + 2*y-1 + 3*x-1 + y-2*z + 2*x-1*z-1 + x-2*y*z-1 + 4*x-1*y-1 + 3*x-2*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 143 1 Lattice Minkowski decompositions of facet 143
Polytope 2506
Image of polytope 2506 PALP id: 2506
grdb id: 370605
Integer points: [ 1 0 0 -1 -1 -2 -1 -2 -2 -2 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -2 0 -2 -3 -1 -2 0 -1 0 -1 0 -1]
[ 0 0 1 -1 0 -1 -1 -1 -1 -1 0 0 -1 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y*z-1 + 2*y-1 + 2*x-1 + 3*x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + x-2*z-1 + x-1*y-2 + x-1*y-2*z-1 + 3*x-2*y-1*z-1 + 3*x-2*y-2*z-1 + x-2*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2507
Image of polytope 2507 PALP id: 2507
grdb id: 369931
Integer points: [ 1 0 0 -1 -1 -1 -3 -3 -2 -1 -2 -1 -2 0 -1 0]
[ 0 1 0 1 1 -2 0 1 1 0 0 -1 -1 0 0 -1]
[ 0 0 1 0 -1 0 -2 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 105 1 none
Polytope 2508
Image of polytope 2508 PALP id: 2508
grdb id: 368624
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 -1 -1 -1]
[ 0 1 0 1 1 0 -1 -3 -2 -1 0 -1 0 -2 -1 0]
[ 0 0 1 0 -1 1 1 -1 0 0 0 0 0 -1 -1 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 8 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 13 1 irreducible and admissible
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Polytope 2509
Image of polytope 2509 PALP id: 2509
grdb id: 370632
Integer points: [ 1 0 0 -1 0 -1 -3 -3 -2 -1 -3 -2 -1 -2 -1 0]
[ 0 1 0 -1 1 1 -1 1 1 1 0 0 0 -1 0 0]
[ 0 0 1 0 1 -1 -2 -2 -1 0 -2 -1 0 -1 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 8 1 none
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 2510
Image of polytope 2510 PALP id: 2510
grdb id: 372096
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 -2 -1 -1 -3 -2 -2 -1 0 0 -1 -1 0]
[ 0 0 1 -1 1 1 -1 1 0 1 0 -1 0 0 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2511
Image of polytope 2511 PALP id: 2511
grdb id: 370577
Integer points: [ 1 0 0 -1 0 0 -2 -3 -2 -1 -2 -1 -1 0 -1 0]
[ 0 1 0 1 -1 -1 -1 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 0 -1 1 -2 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*y + y-1*z + 2*y-1 + 3*x-1 + y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + 2*x-2*z-1 + 3*x-2*y-1*z-1 + x-2*y-1*z-2 + x-3*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Polytope 2512
Image of polytope 2512 PALP id: 2512
grdb id: 369371
Integer points: [ 1 0 0 0 -1 -2 -3 -3 -1 -2 -1 -3 -2 -1 0 -1]
[ 0 1 0 1 -1 1 -2 0 1 0 0 -1 -1 0 0 -1]
[ 0 0 1 1 0 -1 -2 -2 0 -1 0 -2 -1 -1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
80 ? y*z + x + y + z + 2*x-1*y + 3*x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + 4*x-2*z-1 + 3*x-2*y-1*z-1 + x-3*z-2 + 2*x-3*y-1*z-2 + x-3*y-2*z-2
107 rank 3, number 11 y*z + x + y + z + 2*x-1*y + 3*x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*z-1 + 2*x-2*y-1*z-1 + x-3*z-2 + 2*x-3*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 143 1 Lattice Minkowski decompositions of facet 143
Polytope 2513
Image of polytope 2513 PALP id: 2513
grdb id: 370588
Integer points: [ 1 0 0 0 -1 -2 -1 -2 -2 -2 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 0 0 -2 -3 -1 -2 0 -1 -1 -2 0 -1]
[ 0 0 1 -1 -1 -1 0 -1 -1 -1 0 0 -1 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + x-2*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 3*x-2*y-1*z-1 + 3*x-2*y-2*z-1 + x-2*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Polytope 2514
Image of polytope 2514 PALP id: 2514
grdb id: 370823
Integer points: [ 1 0 0 0 -1 -1 -3 -3 -2 -3 -2 -1 -2 -1 -1 0]
[ 0 1 0 -1 1 1 1 -1 1 0 0 0 -1 -1 0 0]
[ 0 0 1 1 -1 0 -2 -2 -1 -2 -1 0 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 9 1 irreducible and admissible
Polytope 2515
Image of polytope 2515 PALP id: 2515
grdb id: 370866
Integer points: [ 1 0 0 0 -1 -1 0 -3 -2 -1 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 1 -1 1 1 1 1 1 1 0 0 0 0]
[ 0 0 0 1 -1 1 1 1 1 1 0 0 1 1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 y*z + x + y + z + 3*x-1*y*z + 3*x-1*y + 3*x-1*z + 3*x-2*y*z + x-1*y*z-1 + y-1 + 2*x-1 + 2*x-2*y + x-1*y-1*z + 2*x-2*z + x-3*y*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 2516
Image of polytope 2516 PALP id: 2516
grdb id: 370580
Integer points: [ 1 0 0 1 -2 1 -2 0 0 0 -1 -1 -1 0 0 -1]
[ 0 1 0 -1 0 -2 -1 -3 -2 -1 -2 -1 0 -1 0 0]
[ 0 0 1 0 -1 -1 -2 -2 -1 0 -2 -1 0 -1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x*y-1 + 3*y-1 + 2*x-1 + x*y-2*z-1 + 3*y-1*z-1 + 2*x-1*z-1 + 3*y-2*z-1 + 4*x-1*y-1*z-1 + x-2*z-1 + y-3*z-2 + 2*x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2517
Image of polytope 2517 PALP id: 2517
grdb id: 370912
Integer points: [ 1 0 1 -1 0 0 -2 -3 -2 -1 -2 -1 -1 0 -1 0]
[ 0 1 -1 1 0 -2 -3 -3 -2 -1 -1 0 -2 -1 -1 0]
[ 0 0 0 0 1 -1 -2 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 66 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2518
Image of polytope 2518 PALP id: 2518
grdb id: 370920
Integer points: [ 1 0 1 0 1 -2 1 0 0 0 1 -1 -1 0 0 -1]
[ 0 1 -1 0 -1 1 -3 -3 -1 -2 -2 0 -1 0 -1 1]
[ 0 0 0 1 -1 0 -2 -2 0 -1 -1 0 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 14 1 none
Polytope 2519
Image of polytope 2519 PALP id: 2519
grdb id: 372147
Integer points: [ 1 0 0 0 0 -1 -2 -2 -1 -1 0 0 0 -1 -1 0]
[ 0 1 0 0 -2 2 2 3 1 2 -1 0 1 0 1 -1]
[ 0 0 1 -1 1 -2 -1 -2 0 -1 1 0 -1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + 2*y*z-1 + 2*x-1*y2*z-1 + 2*x-1*y + 2*y-1*z + x-1*y2*z-2 + x-2*y3*z-2 + z-1 + 3*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 2*x-1 + y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2520
Image of polytope 2520 PALP id: 2520
grdb id: 370274
Integer points: [ 1 0 0 -1 -2 -3 -2 -3 -1 -2 -1 -3 -2 -1 0 -1]
[ 0 1 0 -1 -1 0 2 2 1 1 0 1 0 1 0 0]
[ 0 0 1 0 -1 -2 -1 -2 0 -1 0 -2 -1 -1 0 -1]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
65 ? x + y + z + 2*x-1*y + 2*x-1*y*z-1 + x-2*y2*z-1 + 3*x-1 + 2*x-1*z-1 + 4*x-2*y*z-1 + x-1*y-1 + x-3*y2*z-2 + 3*x-2*z-1 + 2*x-3*y*z-2 + x-2*y-1*z-1 + x-3*z-2
119 ? x + y + z + 2*x-1*y + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*x-1 + 2*x-1*z-1 + 3*x-2*y*z-1 + x-1*y-1 + x-3*y2*z-2 + 3*x-2*z-1 + 2*x-3*y*z-2 + x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 143 1 Lattice Minkowski decompositions of facet 143
Polytope 2521
Image of polytope 2521 PALP id: 2521
grdb id: 370589
Integer points: [ 1 0 0 0 -1 -2 -3 -3 -1 -2 -1 -2 -3 0 -1 -1]
[ 0 1 -1 0 -1 2 0 2 0 0 1 1 1 0 0 1]
[ 0 0 0 1 -1 -1 -2 -2 0 -1 0 -1 -2 0 -1 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + 2*x-1*y + 2*x-1*y*z-1 + x-2*y2*z-1 + y-1 + 3*x-1 + 2*x-1*z-1 + 4*x-2*y*z-1 + x-3*y2*z-2 + x-1*y-1*z-1 + 3*x-2*z-1 + 2*x-3*y*z-2 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2522
Image of polytope 2522 PALP id: 2522
grdb id: 370618
Integer points: [ 1 0 0 0 0 -1 -2 -3 -2 -1 -2 -1 -1 -1 0 0]
[ 0 1 0 0 1 -2 -1 -2 -1 0 -2 -1 0 -1 0 -1]
[ 0 0 1 -1 -1 0 2 2 1 0 1 0 1 1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + y*z-1 + 2*x-1*z + z-1 + 2*y-1 + 3*x-1 + 3*x-1*y-1*z + x-2*y-1*z2 + 3*x-1*y-1 + 3*x-2*y-1*z + x-1*y-2 + 2*x-2*y-2*z + x-3*y-2*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2523
Image of polytope 2523 PALP id: 2523
grdb id: 372117
Integer points: [ 1 0 0 0 2 -3 -2 1 1 0 -1 1 0 -1 -1 -2]
[ 0 1 -1 0 -1 0 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 0 0 1 2 -2 -1 2 1 1 0 1 0 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x2*y-1*z2 + 2*x*z + x*y-1*z2 + x + y + 2*x*y-1*z + z + 3*y-1*z + y-1 + 3*x-1 + 2*x-1*z-1 + 3*x-1*y-1 + 3*x-2*z-1 + x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 9 1 irreducible and admissible
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2524
Image of polytope 2524 PALP id: 2524
grdb id: 372151
Integer points: [ 1 0 0 1 -1 -1 -2 -3 -2 -1 -2 0 -1 1 0 -1]
[ 0 1 0 -2 2 0 1 2 1 1 2 -1 0 -1 0 1]
[ 0 0 1 0 -1 -1 0 -1 -1 -1 -1 0 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? x + y + z + x-1*y2*z-1 + 2*x*y-1 + 3*x-1*y + 2*x-1*y*z-1 + 2*x-2*y2*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + x-1*z-1 + 2*x-2*y*z-1 + x-3*y2*z-1
31 rank 3, number 3 x + y + z + x-1*y2*z-1 + 2*x*y-1 + 2*x-1*y + 2*x-1*y*z-1 + 2*x-2*y2*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + x-1*z-1 + 2*x-2*y*z-1 + x-3*y2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 9 1 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2525
Image of polytope 2525 PALP id: 2525
grdb id: 370625
Integer points: [ 1 0 0 -1 -1 -2 -2 -4 -2 -3 -1 -1 -2 -3 0 -1]
[ 0 1 0 0 0 -1 -2 -3 -1 -2 -1 0 -1 -2 0 -1]
[ 0 0 1 -1 1 -1 1 1 1 1 1 0 0 0 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 8 1 none
Polytope 2526
Image of polytope 2526 PALP id: 2526
grdb id: 368691
Integer points: [ 1 0 0 -1 0 -3 -2 -4 -1 -2 -3 -1 -2 -1 0 -1]
[ 0 1 0 -1 1 0 1 1 1 1 1 0 0 1 0 0]
[ 0 0 1 0 1 -2 -2 -3 0 -1 -2 0 -1 -1 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
147 ? y*z + x + y + z + 4*x-1*y + 2*x-1*y*z-1 + 4*x-1 + 2*x-1*z-1 + 6*x-2*y*z-1 + x-1*y-1 + x-2*y*z-2 + 4*x-2*z-1 + 4*x-3*y*z-2 + x-3*z-2 + x-4*y*z-3
112 rank 3, number 15 y*z + x + y + z + 4*x-1*y + 2*x-1*y*z-1 + 3*x-1 + 2*x-1*z-1 + 6*x-2*y*z-1 + x-1*y-1 + x-2*y*z-2 + 3*x-2*z-1 + 4*x-3*y*z-2 + x-3*z-2 + x-4*y*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 93 1 Lattice Minkowski decompositions of facet 93
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Polytope 2527
Image of polytope 2527 PALP id: 2527
grdb id: 370583
Integer points: [ 1 0 0 -1 0 -1 -3 -4 -2 -3 -1 -2 -1 -2 0 -1]
[ 0 1 0 0 -1 0 -2 -3 -1 -2 0 -1 -1 -2 0 -1]
[ 0 0 1 -1 1 1 0 1 1 1 0 0 1 1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
126 ? x + y + z + y-1*z + x-1*z + 3*x-1 + 3*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + 3*x-2*y-1*z + 4*x-2*y-1 + 2*x-2*y-2*z + 3*x-3*y-2*z + x-3*y-2 + x-4*y-3*z
119 ? x + y + z + y-1*z + x-1*z + 2*x-1 + 3*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + 3*x-2*y-1*z + 2*x-2*y-1 + 2*x-2*y-2*z + 3*x-3*y-2*z + x-3*y-2 + x-4*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2528
Image of polytope 2528 PALP id: 2528
grdb id: 372132
Integer points: [ 1 0 0 0 -2 -2 -2 -4 -1 -1 -2 -3 -3 0 -1 -1]
[ 0 1 -1 0 0 -1 -2 -2 0 -1 -1 -1 -2 0 0 -1]
[ 0 0 0 1 -1 -2 -1 -3 0 0 -1 -2 -2 0 -1 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + y-1 + 2*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + x-2*z-1 + 4*x-2*y-1*z-1 + x-2*y-1*z-2 + x-2*y-2*z-1 + 2*x-3*y-1*z-2 + 2*x-3*y-2*z-2 + x-4*y-2*z-3
50 ? x + y + z + y-1 + 2*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + 4*x-2*y-1*z-1 + x-2*y-1*z-2 + x-2*y-2*z-1 + 2*x-3*y-1*z-2 + 2*x-3*y-2*z-2 + x-4*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2529
Image of polytope 2529 PALP id: 2529
grdb id: 371259
Integer points: [ 1 0 0 0 -1 -2 -2 -4 -3 -2 -1 -1 0 -3 -2 -1]
[ 0 1 0 -1 0 -1 -1 -3 -2 -1 0 -1 0 -2 -2 -1]
[ 0 0 1 -1 1 -1 1 -1 0 0 0 0 0 -1 -1 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + x-1*z + 3*x-1 + y-1*z-1 + 3*x-1*y-1 + x-2*y-1*z + 2*x-1*y-1*z-1 + 3*x-2*y-1 + x-2*y-1*z-1 + 2*x-2*y-2*z-1 + 2*x-3*y-2 + 2*x-3*y-2*z-1 + x-4*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2530
Image of polytope 2530 PALP id: 2530
grdb id: 370579
Integer points: [ 1 0 0 0 -1 -1 -3 -4 -3 -2 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 0 0 -2 -3 -2 -1 -2 -1 -1 0 -1 0]
[ 0 0 0 1 -1 1 -2 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 66 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2531
Image of polytope 2531 PALP id: 2531
grdb id: 370638
Integer points: [ 1 0 0 0 -1 0 -3 -4 -2 -3 -1 -2 -1 -2 0 -1]
[ 0 1 -1 0 1 1 0 1 1 1 0 0 1 1 0 0]
[ 0 0 0 1 0 -1 -2 -3 -1 -2 0 -1 -1 -2 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + y*z-1 + x-1*y + 3*x-1*y*z-1 + y-1 + 3*x-1 + 2*x-1*z-1 + 3*x-2*y*z-1 + 2*x-2*y*z-2 + 3*x-2*z-1 + 3*x-3*y*z-2 + x-3*z-2 + x-4*y*z-3
144 rank 3, number 12 x + y + z + y*z-1 + x-1*y + 3*x-1*y*z-1 + y-1 + 3*x-1 + 3*x-1*z-1 + 3*x-2*y*z-1 + 2*x-2*y*z-2 + 3*x-2*z-1 + 3*x-3*y*z-2 + x-3*z-2 + x-4*y*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2532
Image of polytope 2532 PALP id: 2532
grdb id: 371689
Integer points: [ 1 0 0 0 0 -2 -3 -4 -1 -2 -3 -1 -2 -1 0 -1]
[ 0 1 -1 0 1 1 0 1 1 1 1 0 0 1 0 0]
[ 0 0 0 1 1 -2 -2 -3 0 -1 -2 0 -1 -1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
55 rank 2, number 19 y*z + x + y + z + 4*x-1*y + 2*x-1*y*z-1 + y-1 + 3*x-1 + x-1*z-1 + 6*x-2*y*z-1 + x-2*y*z-2 + 3*x-2*z-1 + 4*x-3*y*z-2 + x-3*z-2 + x-4*y*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Polytope 2533
Image of polytope 2533 PALP id: 2533
grdb id: 370627
Integer points: [ 1 0 0 0 0 -1 -3 -4 -3 -2 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 -1 -1 0 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 0 1 -1 1 1 1 1 1 0 0 1 1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 8 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2534
Image of polytope 2534 PALP id: 2534
grdb id: 370639
Integer points: [ 1 0 0 0 0 -1 -3 -4 -3 -2 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 1 1 -2 -2 -1 0 -1 0 -1 0 -1 0]
[ 0 0 0 1 -1 -1 -1 -1 -1 -1 0 0 -1 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 8 1 none
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2535
Image of polytope 2535 PALP id: 2535
grdb id: 370608
Integer points: [ 1 0 0 0 0 -1 -3 -4 -2 -3 -1 -2 -1 -2 0 -1]
[ 0 1 -1 0 1 1 0 1 1 1 1 1 0 0 0 0]
[ 0 0 0 1 1 1 -2 -2 0 -1 0 -1 0 -1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 y*z + x + y + z + x-1*y*z + 3*x-1*y + y-1 + 2*x-1 + 3*x-2*y + 2*x-1*z-1 + 2*x-2*y*z-1 + 2*x-2*z-1 + 3*x-3*y*z-1 + x-3*z-2 + x-4*y*z-2
159 ? y*z + x + y + z + x-1*y*z + 3*x-1*y + y-1 + 4*x-1 + 3*x-2*y + 2*x-1*z-1 + 2*x-2*y*z-1 + 3*x-2*z-1 + 3*x-3*y*z-1 + x-3*z-2 + x-4*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2536
Image of polytope 2536 PALP id: 2536
grdb id: 370480
Integer points: [ 1 0 1 0 -1 -2 -3 -4 -1 0 -3 -2 -1 -1 0 -2]
[ 0 1 -1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 0 1 -1 0 -2 -2 0 0 -1 -1 -1 0 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + x*y-1 + 3*y-1 + 2*x-1 + x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1 + 4*x-2*y-1*z-1 + 2*x-3*y-1*z-1 + x-3*y-1*z-2 + x-4*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Polytope 2537
Image of polytope 2537 PALP id: 2537
grdb id: 370613
Integer points: [ 1 0 0 -1 -1 -1 -3 -3 -2 -3 -2 -1 -2 -1 -1 0]
[ 0 1 0 0 -1 -1 -2 -2 -1 -2 -1 0 -1 0 -1 0]
[ 0 0 1 -1 0 2 1 3 0 2 1 0 2 1 1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
37 rank 3, number 17 x + y + z + 3*x-1*z + x-1*y-1*z2 + 2*x-1 + 2*x-1*y-1*z + 3*x-2*y-1*z2 + x-1*z-1 + x-1*y-1 + 4*x-2*y-1*z + x-3*y-2*z3 + 2*x-2*y-1 + 2*x-3*y-2*z2 + x-3*y-2*z
111 ? x + y + z + 3*x-1*z + x-1*y-1*z2 + 2*x-1 + 3*x-1*y-1*z + 3*x-2*y-1*z2 + x-1*z-1 + x-1*y-1 + 4*x-2*y-1*z + x-3*y-2*z3 + 2*x-2*y-1 + 2*x-3*y-2*z2 + x-3*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2538
Image of polytope 2538 PALP id: 2538
grdb id: 372148
Integer points: [ 1 0 0 0 -2 2 3 2 1 1 2 -1 0 0 1 -1]
[ 0 1 -1 0 1 -1 -3 -3 -2 -1 -2 0 -1 0 -1 1]
[ 0 0 0 1 0 -1 -2 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x2*y-1*z-1 + 3*x*y-1 + 2*x-1*y + 3*x2*y-2*z-1 + 3*x*y-1*z-1 + y-1 + 2*x-1 + x-2*y + x3*y-3*z-2 + 2*x*y-2*z-1 + 2*y-1*z-1 + x2*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2539
Image of polytope 2539 PALP id: 2539
grdb id: 359406
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 2 -1 -1 -1 -1 0 0 0 1 1 0]
[ 0 0 0 1 1 -1 -1 2 0 1 -1 0 1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + x-1*y2*z-1 + 3*x-1*y + y-1*z + 3*x-1*z + x-1*y-1*z2 + 3*x-1*y*z-1 + y-1 + 6*x-1 + 3*x-1*y-1*z + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Polytope 2540
Image of polytope 2540 PALP id: 2540
grdb id: 365106
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 1 -2 -1 -2 -1 0 -2 -1 0 -1 0 -1]
[ 0 0 1 -1 0 0 -2 -2 0 0 -1 -1 -1 0 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
85 rank 3, number 8 x + y + z + x-1*y + z-1 + 2*y-1 + 3*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + 4*x-1*y-1*z-1 + x-1*y-2 + x-1*y-1*z-2 + 2*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 2541
Image of polytope 2541 PALP id: 2541
grdb id: 364781
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 1 -2 0 1 0 -1 1 0 -1 0 -1 0]
[ 0 0 1 -1 0 0 -2 -2 0 0 -1 -1 -1 0 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + y*z-1 + x-1*y + 2*z-1 + 2*x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*y*z-2 + 4*x-1*z-1 + 3*x-1*y-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 2542
Image of polytope 2542 PALP id: 2542
grdb id: 364763
Integer points: [ 1 0 0 0 0 -1 -2 -2 -2 -2 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 0 -1 -1 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 1 1 1 1 -2 0 -1 0 -1 1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + y-1*z + x-1*z + y-1 + 3*x-1 + 2*x-1*y-1*z + 2*x-1*z-1 + 4*x-1*y-1 + x-2*y-1*z + 2*x-1*y-1*z-1 + 3*x-2*y-1 + 3*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2543
Image of polytope 2543 PALP id: 2543
grdb id: 367025
Integer points: [ 1 0 0 1 -2 1 -1 1 0 1 -1 0 1 0 -1 0]
[ 0 1 0 -1 0 0 -1 -1 -1 -1 0 0 0 -1 0 0]
[ 0 0 1 0 1 -2 0 -2 0 -1 1 0 -1 -1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? x + y + z + 2*x*z-1 + x*y-1 + 2*x-1*z + x*z-2 + 2*x*y-1*z-1 + 3*z-1 + 2*y-1 + 3*x-1 + x-2*z + x*y-1*z-2 + 2*y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2544
Image of polytope 2544 PALP id: 2544
grdb id: 361261
Integer points: [ 1 0 0 0 -1 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 1 -2 2 -1 0 1 -1 0 1 0 0]
[ 0 0 0 1 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + 2*x-1*y + x-1*y*z-1 + x-2*y2*z-1 + y-1 + 4*x-1 + 2*x-1*z-1 + 4*x-2*y*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + 6*x-2*z-1 + 4*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 2545
Image of polytope 2545 PALP id: 2545
grdb id: 364448
Integer points: [ 1 0 0 0 -1 0 -2 -3 -2 -1 0 -2 -1 -1 0 -1]
[ 0 1 -1 0 1 -2 1 1 1 0 -1 0 -1 1 0 0]
[ 0 0 0 1 0 1 -2 -2 -1 0 1 -1 0 -1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + x-1*y + 2*y-1*z + 2*x-1*y*z-1 + y-1 + 4*x-1 + y-2*z + 2*x-1*z-1 + 2*x-2*y*z-1 + 3*x-1*y-1 + x-2*y*z-2 + 3*x-2*z-1 + x-3*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2546
Image of polytope 2546 PALP id: 2546
grdb id: 364612
Integer points: [ 1 0 0 0 0 -1 -2 -3 -2 -1 -2 -1 0 -1 -1 0]
[ 0 1 0 -1 -1 -1 0 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 1 -1 1 1 1 1 0 0 0 1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 8 1 none
Polytope 2547
Image of polytope 2547 PALP id: 2547
grdb id: 205991
Integer points: [ 1 0 0 1 -1 -1 0 -2 -2 -1 -2 -1 0 -1 0 1]
[ 0 1 0 -2 0 1 -1 1 1 0 1 0 -1 1 0 -1]
[ 0 0 1 0 -1 1 1 -1 1 1 0 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 1 none
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Polytope 2548
Image of polytope 2548 PALP id: 2548
grdb id: 206001
Integer points: [ 1 0 0 1 -1 0 1 -2 0 -1 0 -1 0 -1 1 0]
[ 0 1 0 -1 1 0 -2 0 -2 -1 -1 0 -1 0 -1 0]
[ 0 0 1 -1 1 -1 0 1 1 1 0 0 1 1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + x-1*y*z + 2*x*y-1 + 2*y-1*z + 2*x-1*z + x*y-1*z-1 + z-1 + x*y-2 + 3*y-1 + 2*x-1 + y-2*z + 2*x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2549
Image of polytope 2549 PALP id: 2549
grdb id: 206005
Integer points: [ 1 0 0 -1 0 2 -2 -1 1 1 0 -1 1 0 0 -1]
[ 0 1 0 1 1 -1 0 -1 0 0 0 0 -1 -1 0 0]
[ 0 0 1 1 1 -2 1 1 -2 -1 0 1 -1 0 -1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
26 rank 2, number 8 y*z + x + y + z + x-1*y*z + x*z-1 + x-1*z + x2*y-1*z-2 + x*z-2 + 3*x*y-1*z-1 + 3*z-1 + 3*y-1 + 3*x-1 + x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 10 2 Lattice Minkowski decompositions of facet 10
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2550
Image of polytope 2550 PALP id: 2550
grdb id: 206000
Integer points: [ 1 1 -1 0 -1 1 -1 0 -1 -1 0 0 -1 0 1 0]
[ 0 2 -2 0 -1 2 0 1 0 0 1 1 -1 0 1 -1]
[ 0 0 0 1 1 -1 -1 1 1 0 0 -1 0 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2551
Image of polytope 2551 PALP id: 2551
grdb id: 206002
Integer points: [ 1 0 0 0 0 -1 -1 -1 -3 -2 -2 -1 -2 -1 -1 0]
[ 0 1 0 0 -1 1 1 -1 1 1 0 0 1 1 0 0]
[ 0 0 1 -1 0 -1 1 1 1 0 1 0 1 0 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
25 ? x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + 2*x-2*y*z + z-1 + x-1*y*z-1 + y-1 + 3*x-1 + 2*x-2*y + x-1*y-1*z + 2*x-2*z + x-3*y*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2552
Image of polytope 2552 PALP id: 2552
grdb id: 206003
Integer points: [ 1 -1 0 0 -1 -1 1 0 1 0 0 0 0 0 0 0]
[ 0 0 1 1 0 -1 0 -2 -1 -1 0 -1 0 1 0 1]
[ 0 0 0 3 1 -1 1 -3 -1 -1 1 -2 0 2 -1 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 y*z3 + 3*y*z2 + x*z + 3*y*z + x + y + z + x-1*z + x*y-1*z-1 + 3*z-1 + x-1 + y-1*z-1 + 3*y-1*z-2 + x-1*y-1*z-1 + y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 50 1 Lattice Minkowski decompositions of facet 50
Image of facet 20 4 Lattice Minkowski decompositions of facet 20
Polytope 2553
Image of polytope 2553 PALP id: 2553
grdb id: 205994
Integer points: [ 1 0 1 1 -2 0 -1 1 0 0 -1 1 0 -1 1 0]
[ 0 1 1 3 -3 0 0 2 2 1 -1 2 0 -2 1 -1]
[ 0 0 2 3 -3 1 -1 3 1 1 -1 2 0 -2 1 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
51 rank 2, number 7 x*y3*z3 + x*y2*z3 + 3*x*y2*z2 + x*y*z2 + 3*x*y*z + y2*z + y*z + x + y + z + 3*y-1*z-1 + x-1*z-1 + 2*x-1*y-1*z-1 + 3*x-1*y-2*z-2 + x-2*y-3*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 51 1 Lattice Minkowski decompositions of facet 51
Image of facet 20 4 Lattice Minkowski decompositions of facet 20
Polytope 2554
Image of polytope 2554 PALP id: 2554
grdb id: 205958
Integer points: [ 1 0 1 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 1 -1 1 -1 -1 -1 0 0 0 1 -1 0]
[ 0 0 0 1 -1 1 1 1 -1 0 1 0 -1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 8 1 none
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 2555
Image of polytope 2555 PALP id: 2555
grdb id: 205585
Integer points: [ 1 0 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 -1 2 0 -1 -1 -1 0 1 0 1 -1 0]
[ 0 0 0 1 1 -1 1 1 -1 0 0 0 -1 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2556
Image of polytope 2556 PALP id: 2556
grdb id: 205601
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 1 -1 1 0 -2 0 -1 0 -1 0 -1 0]
[ 0 0 1 1 0 1 -1 -2 0 0 0 -1 -1 0 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
35 rank 2, number 15 x + y + z + x-1*y + x-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 115 1 Lattice Minkowski decompositions of facet 115
Polytope 2557
Image of polytope 2557 PALP id: 2557
grdb id: 205281
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 0 0 -2 -1 -2 -1 -2 0 -1 -1 0 -1]
[ 0 0 1 0 -1 1 0 1 -2 0 -1 0 -1 0 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y + x-1*z + 2*y-1 + 3*x-1 + x-1*y-1*z + 2*y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 117 1 Lattice Minkowski decompositions of facet 117
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2558
Image of polytope 2558 PALP id: 2558
grdb id: 205468
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 1 -1 -1 -2 0 1 0 -1 0 0 -1]
[ 0 0 1 -1 1 -1 -1 1 0 -1 0 0 0 1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + x-1*y-1*z + 2*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
94 ? x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 5*x-1 + x-1*y-1*z + 2*x-1*z-1 + 4*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 1 3 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Polytope 2559
Image of polytope 2559 PALP id: 2559
grdb id: 205721
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 -1 0 0]
[ 0 1 0 1 -1 1 0 -2 1 0 0 -1 0 -1 0 -1]
[ 0 0 1 -1 1 -1 -2 0 -2 0 -1 0 0 -1 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
35 rank 2, number 15 x + y + z + y*z-1 + 2*z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + x-1*y*z-2 + 2*x-1*z-1 + x-1*y-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 71 1 Lattice Minkowski decompositions of facet 71
Polytope 2560
Image of polytope 2560 PALP id: 2560
grdb id: 205921
Integer points: [ 1 0 0 0 -1 -1 -1 0 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 1 1 -1 -2 -2 0 0 -1 0 -1 0 -1]
[ 0 0 1 -1 1 0 1 -1 0 1 0 0 0 0 -1 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
56 rank 2, number 11 x + y + z + x-1*y*z + y*z-1 + x-1*y + 2*x-1*z + 3*z-1 + y-1 + 3*x-1 + x-1*y-1*z + 3*y-1*z-1 + 3*x-1*y-1 + y-2*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2561
Image of polytope 2561 PALP id: 2561
grdb id: 205584
Integer points: [ 1 0 0 0 0 -1 -1 -2 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 0 -1 -1 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 0 1 -1 1 1 1 -2 0 -1 0 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 66 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2562
Image of polytope 2562 PALP id: 2562
grdb id: 205940
Integer points: [ 1 0 0 0 0 -1 -1 -2 -2 -1 -2 -1 -1 0 -1 0]
[ 0 1 0 0 -1 1 -2 0 -2 0 -1 -1 0 0 -1 -1]
[ 0 0 1 -1 1 -1 0 -1 -1 0 -1 0 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + y-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + 2*x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2563
Image of polytope 2563 PALP id: 2563
grdb id: 205576
Integer points: [ 1 0 0 0 1 0 -1 -2 -2 -1 0 -2 -1 -1 0 -1]
[ 0 1 0 0 -1 -1 -1 -1 1 -1 -1 0 0 0 0 1]
[ 0 0 1 -1 0 1 1 0 -2 0 0 -1 -1 0 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*y-1 + y-1*z + z-1 + 2*x-1*y*z-1 + 3*y-1 + 3*x-1 + x-1*y-1*z + 3*x-1*z-1 + 3*x-1*y-1 + x-2*y*z-2 + 2*x-2*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2564
Image of polytope 2564 PALP id: 2564
grdb id: 205912
Integer points: [ 1 0 0 0 1 1 -2 -1 -2 0 0 1 -1 -1 0 -1]
[ 0 1 0 0 -1 -1 1 -1 0 -1 -1 -1 0 0 0 1]
[ 0 0 1 -1 -1 1 0 1 1 0 1 0 0 1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + x*y-1*z + z + 2*x*y-1 + 2*x-1*y + 2*y-1*z + 2*x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 3*x-1 + x-2*y + x-1*y-1*z + x-2*z
10 rank 1, V18 x + y + x*y-1*z + z + 2*x*y-1 + 2*x-1*y + 2*y-1*z + 2*x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + x-2*y + x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2565
Image of polytope 2565 PALP id: 2565
grdb id: 205541
Integer points: [ 1 0 0 1 -2 0 -1 -2 1 0 -1 1 0 -1 0 -1]
[ 0 1 0 -2 1 -1 0 1 -2 -1 0 -1 0 1 -1 0]
[ 0 0 1 0 0 1 1 -1 -1 0 0 0 0 0 -1 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? x + y + z + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + x*y-2 + 4*y-1 + 4*x-1 + x-2*y + x*y-2*z-1 + 3*y-1*z-1 + 3*x-1*z-1 + x-2*y*z-1
31 rank 3, number 3 x + y + z + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + 3*y-1*z-1 + 3*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Polytope 2566
Image of polytope 2566 PALP id: 2566
grdb id: 205948
Integer points: [ 1 0 0 1 -1 1 -2 -1 1 0 0 -1 1 0 0 -1]
[ 0 1 0 0 0 -1 1 0 -2 -1 -1 0 -1 0 0 1]
[ 0 0 1 -1 1 1 0 -1 1 0 1 0 0 -1 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + x*y-1*z + z + x*z-1 + 2*x*y-1 + 2*x-1*y + x*y-2*z + 2*y-1*z + x-1*z + 2*z-1 + 2*y-1 + 2*x-1 + x-2*y + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2567
Image of polytope 2567 PALP id: 2567
grdb id: 205418
Integer points: [ 1 0 1 0 0 -1 -1 -2 -2 -1 -2 -1 0 -1 0 -1]
[ 0 1 -1 0 -2 1 -1 0 -2 0 -1 -1 -1 0 0 -2]
[ 0 0 0 1 -1 1 -1 1 -1 1 0 0 0 0 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
81 ? x + y + z + x-1*y*z + x*y-1 + 2*x-1*z + 4*y-1 + 3*x-1 + x-2*z + 5*x-1*y-1 + y-2*z-1 + x-1*y-1*z-1 + 2*x-2*y-1 + 2*x-1*y-2*z-1 + x-2*y-2*z-1
88 ? x + y + z + x-1*y*z + x*y-1 + 2*x-1*z + 4*y-1 + 2*x-1 + x-2*z + 5*x-1*y-1 + y-2*z-1 + x-1*y-1*z-1 + 2*x-2*y-1 + 2*x-1*y-2*z-1 + x-2*y-2*z-1
88 ? x + y + z + x-1*y*z + x*y-1 + 2*x-1*z + 3*y-1 + 3*x-1 + x-2*z + 4*x-1*y-1 + y-2*z-1 + x-1*y-1*z-1 + 2*x-2*y-1 + 2*x-1*y-2*z-1 + x-2*y-2*z-1
67 ? x + y + z + x-1*y*z + x*y-1 + 2*x-1*z + 3*y-1 + 2*x-1 + x-2*z + 4*x-1*y-1 + y-2*z-1 + x-1*y-1*z-1 + 2*x-2*y-1 + 2*x-1*y-2*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Polytope 2568
Image of polytope 2568 PALP id: 2568
grdb id: 205443
Integer points: [ 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 0 2 -2 0 2 1 1 0 -1 1 0 -1]
[ 0 0 1 0 -1 1 -2 1 1 0 1 0 -1 1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 y2*z + 2*y*z + x-1*y2*z + x + y + z + 2*x-1*y*z + 2*x-1*y + x-1*z + 3*x-1 + 2*y-1*z-1 + x-1*z-1 + x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Polytope 2569
Image of polytope 2569 PALP id: 2569
grdb id: 205970
Integer points: [ 1 0 0 -1 0 1 1 1 -2 1 1 0 0 0 -1 -1]
[ 0 1 -1 0 0 1 1 -2 1 -1 0 -1 0 1 0 1]
[ 0 0 0 0 1 2 1 -1 -1 0 1 -1 0 1 -1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
97 ? x*y*z2 + x*y*z + 3*x*z + 3*y*z + x + y + z + 3*x*y-1 + 3*x-1*y + y-1 + x-1 + x*y-2*z-1 + 3*y-1*z-1 + 3*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 20 6 Lattice Minkowski decompositions of facet 20
Polytope 2570
Image of polytope 2570 PALP id: 2570
grdb id: 205938
Integer points: [ 1 0 0 0 -1 -2 -1 2 1 0 1 0 1 -1 0 -1]
[ 0 1 0 0 0 1 0 -2 -2 -1 -1 -1 -1 0 0 1]
[ 0 0 1 -1 1 0 -1 -1 -1 0 0 -1 -1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + 2*x*y-1 + 2*x-1*y + x-1*z + x2*y-2*z-1 + 2*x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2571
Image of polytope 2571 PALP id: 2571
grdb id: 205575
Integer points: [ 1 0 0 0 -1 0 -2 -1 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 -1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 0 1 -1 1 -1 2 2 1 0 1 0 1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 66 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2572
Image of polytope 2572 PALP id: 2572
grdb id: 205964
Integer points: [ 1 0 0 1 1 0 -1 0 -1 0 0 -1 -1 0 0 0]
[ 0 1 0 0 -1 1 1 -2 -2 0 -1 0 -1 1 0 -1]
[ 0 0 1 -1 0 -2 -1 1 2 -1 0 0 1 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + x*z-1 + 2*y*z-1 + x*y-1 + y-1*z + y*z-2 + 3*z-1 + x-1*y*z-1 + 3*y-1 + 3*x-1 + y-2*z + 3*x-1*y-1*z + x-1*y-2*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2573
Image of polytope 2573 PALP id: 2573
grdb id: 205630
Integer points: [ 1 0 0 -1 -1 -1 0 -1 -1 -1 -1 0 -1 -1 0 0]
[ 0 1 0 1 0 0 -2 -2 -3 -2 -1 -1 -1 0 -1 0]
[ 0 0 1 0 -1 1 -1 -2 -2 -1 0 0 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 66 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2574
Image of polytope 2574 PALP id: 2574
grdb id: 205920
Integer points: [ 1 0 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 1 0 -2 -2 -3 0 -1 -1 -2 0 -1 -1]
[ 0 0 1 -1 1 1 -1 -2 -2 0 -1 0 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
35 rank 2, number 15 x + y + z + x-1*y*z + x-1*z + z-1 + 2*y-1 + 3*x-1 + y-1*z-1 + 3*x-1*y-1 + y-2*z-1 + 3*x-1*y-1*z-1 + 3*x-1*y-2*z-1 + x-1*y-2*z-2 + x-1*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2575
Image of polytope 2575 PALP id: 2575
grdb id: 205959
Integer points: [ 1 0 0 0 0 -1 -1 -1 -3 -2 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 -1 0 0 -2 -2 -1 -2 -1 -1 0 -1 0]
[ 0 0 0 1 -1 -1 1 -1 -1 0 -1 0 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + x-1*z + y-1 + 2*x-1 + y-1*z-1 + x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*y-1 + x-1*y-2*z-1 + 2*x-2*y-1*z-1 + 2*x-2*y-2*z-1 + x-3*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2576
Image of polytope 2576 PALP id: 2576
grdb id: 205713
Integer points: [ 1 0 0 0 0 1 -2 -2 -3 -1 -2 -1 0 -1 0 -1]
[ 0 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 0 -1 -1 0 -1 0 -1 -1 -1 0 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
60 rank 2, number 18 x + y + z + x*y-1*z-1 + z-1 + y-1 + x-1 + 4*y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + 6*x-1*y-1*z-1 + x-2*z-1 + x-2*y-1 + 4*x-2*y-1*z-1 + x-3*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 59 2 Lattice Minkowski decompositions of facet 59
Polytope 2577
Image of polytope 2577 PALP id: 2577
grdb id: 205973
Integer points: [ 1 0 1 -1 0 -1 0 -2 -2 -1 0 1 -1 0 -1 0]
[ 0 1 0 0 -1 0 -1 -1 -1 -1 0 0 -1 0 0 0]
[ 0 0 2 -2 0 0 -1 -2 -3 -1 1 1 -2 0 -1 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x*z2 + 2*x*z + x + y + 2*z + 2*z-1 + y-1 + x-1 + y-1*z-1 + x-1*z-1 + x-1*z-2 + 2*x-1*y-1*z-1 + 2*x-1*y-1*z-2 + x-2*y-1*z-2 + x-2*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 3 Lattice Minkowski decompositions of facet 15
Polytope 2578
Image of polytope 2578 PALP id: 2578
grdb id: 205968
Integer points: [ 1 1 -1 -1 0 -1 -1 -2 -2 -2 -1 0 -1 0 0 1]
[ 0 2 -2 0 0 0 -2 -3 -1 -2 -1 -1 -1 0 1 1]
[ 0 0 0 0 1 -1 -1 -1 -1 -1 0 0 -1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x*y2 + 2*x*y + x + 2*y + z + 2*y-1 + x-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1 + x-2*y-1*z-1 + 2*x-2*y-2*z-1 + x-2*y-3*z-1
151 ? x*y2 + 2*x*y + x + 2*y + z + 2*y-1 + x-1 + x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1 + x-2*y-1*z-1 + 2*x-2*y-2*z-1 + x-2*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Image of facet 1 3 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2579
Image of polytope 2579 PALP id: 2579
grdb id: 204760
Integer points: [ 1 0 0 0 1 -1 1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 -1 -1 1 -1 -1 -1 0 -1 0 -1 0 -1 0]
[ 0 0 1 1 0 -1 -1 1 -1 -1 0 0 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + x*y-1 + y-1*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 3*y-1 + 2*x-1 + x-1*y-1*z + 2*y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 2580
Image of polytope 2580 PALP id: 2580
grdb id: 203196
Integer points: [ 1 0 0 -1 -1 -1 -1 -2 -2 -2 -2 -1 -1 -1 0 0]
[ 0 1 0 1 1 -1 -2 1 -2 -1 0 -1 0 0 -1 0]
[ 0 0 1 0 -1 -1 0 -1 -1 -1 -1 0 0 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
88 ? x + y + z + x-1*y + x-1*y*z-1 + 2*y-1 + 4*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2 + 3*x-2*y-1*z-1 + x-2*y-2*z-1
46 ? x + y + z + x-1*y + x-1*y*z-1 + 2*y-1 + 2*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2 + 3*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2581
Image of polytope 2581 PALP id: 2581
grdb id: 202927
Integer points: [ 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 -1]
[ 0 1 0 1 0 -1 0 -2 -2 -1 -2 -1 0 -1 0 -1]
[ 0 0 1 0 -1 1 1 -1 1 1 0 0 0 0 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2582
Image of polytope 2582 PALP id: 2582
grdb id: 202533
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -1 0 -2 1 -2 0 -1 1 0 -1 0 -1]
[ 0 0 1 -1 1 -1 0 1 1 1 1 0 0 0 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
85 rank 3, number 8 x + y + z + x-1*y*z + 2*x-1*y + y-1*z + 3*x-1*z + x-1*y*z-1 + 2*y-1 + 4*x-1 + 3*x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2583
Image of polytope 2583 PALP id: 2583
grdb id: 204801
Integer points: [ 1 0 0 -1 0 -1 0 -2 -2 -1 -2 -1 -1 0 -1 0]
[ 0 1 0 1 -1 0 -2 0 -2 -1 -1 0 -2 -1 -1 0]
[ 0 0 1 0 -1 -1 -1 -1 -1 0 -1 0 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + y-2*z-1 + 3*x-1*y-1*z-1 + x-2*z-1 + 2*x-1*y-2*z-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2584
Image of polytope 2584 PALP id: 2584
grdb id: 202565
Integer points: [ 1 0 0 0 -1 -1 -1 0 -1 -1 -1 0 -1 -1 0 0]
[ 0 1 0 0 1 0 1 -2 -2 -1 0 -1 -1 0 -1 0]
[ 0 0 1 -1 0 1 -1 -1 -1 -1 -1 -1 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + 2*y-1*z-1 + 3*x-1*z-1 + 2*x-1*y-1 + y-2*z-1 + 3*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2585
Image of polytope 2585 PALP id: 2585
grdb id: 202543
Integer points: [ 1 0 0 0 -1 0 -2 -1 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 -1 0 1 -1 1 -2 -2 -1 0 -1 0 -1 0 0]
[ 0 0 0 1 0 -1 -1 -1 -1 -1 -1 0 0 -1 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y + y-1 + 3*x-1 + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2*z-1 + 3*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Polytope 2586
Image of polytope 2586 PALP id: 2586
grdb id: 204255
Integer points: [ 1 0 0 0 -1 0 -2 -1 -2 -2 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 -1 0 -2 -2 -1 -1 0 -1 0 -1 0]
[ 0 0 1 -1 0 -1 1 0 1 1 0 0 1 1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y + 2*x-1*z + z-1 + 2*y-1 + 2*x-1 + 2*x-1*y-1*z + x-2*z + y-1*z-1 + 2*x-1*y-1 + 2*x-2*y-1*z + x-1*y-2 + x-2*y-2*z
85 rank 3, number 8 x + y + z + x-1*y + 2*x-1*z + z-1 + 2*y-1 + 3*x-1 + 2*x-1*y-1*z + x-2*z + y-1*z-1 + 4*x-1*y-1 + 2*x-2*y-1*z + x-1*y-2 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2587
Image of polytope 2587 PALP id: 2587
grdb id: 205060
Integer points: [ 1 0 0 0 -1 0 -1 -2 -2 -1 -2 -1 -1 0 0 -1]
[ 0 1 0 -1 0 -1 0 -1 -1 -1 -1 0 -1 0 -1 -1]
[ 0 0 1 -1 -1 1 1 -1 1 1 0 0 0 0 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + y-1*z + x-1*z + 2*y-1 + 2*x-1 + 2*x-1*y-1*z + y-1*z-1 + x-1*z-1 + 4*x-1*y-1 + x-2*y-1*z + 2*x-1*y-1*z-1 + 2*x-2*y-1 + x-2*y-1*z-1
67 ? x + y + z + y-1*z + x-1*z + 2*y-1 + 3*x-1 + 2*x-1*y-1*z + y-1*z-1 + x-1*z-1 + 4*x-1*y-1 + x-2*y-1*z + 2*x-1*y-1*z-1 + 2*x-2*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2588
Image of polytope 2588 PALP id: 2588
grdb id: 205076
Integer points: [ 1 0 0 0 0 -1 -2 -1 -2 -1 -2 -1 -1 0 -1 0]
[ 0 1 0 0 1 1 0 -2 -2 0 -1 -1 0 0 -1 -1]
[ 0 0 1 -1 -1 -1 -1 0 -1 0 -1 0 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + y*z-1 + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + 3*x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2589
Image of polytope 2589 PALP id: 2589
grdb id: 204381
Integer points: [ 1 0 0 0 0 -1 -2 -1 -2 -2 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 1 0 -2 -2 -1 0 -1 0 -1 0 -1]
[ 0 0 1 -1 -1 0 1 0 1 1 0 0 1 1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + y*z-1 + x-1*y + 2*x-1*z + z-1 + 2*y-1 + 2*x-1 + 2*x-1*y-1*z + x-2*z + 2*x-1*y-1 + 2*x-2*y-1*z + x-1*y-2 + x-2*y-2*z
146 ? x + y + z + y*z-1 + x-1*y + 2*x-1*z + z-1 + 2*y-1 + 4*x-1 + 2*x-1*y-1*z + x-2*z + 3*x-1*y-1 + 2*x-2*y-1*z + x-1*y-2 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2590
Image of polytope 2590 PALP id: 2590
grdb id: 202591
Integer points: [ 1 0 0 0 0 -1 -1 -2 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 0 -1 -1 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 1 -1 0 1 1 1 -2 0 -1 0 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + x-1*z + z-1 + y-1 + 3*x-1 + x-1*y-1*z + 2*x-1*z-1 + 3*x-1*y-1 + x-2*y-1*z + 2*x-1*y-1*z-1 + 3*x-2*y-1 + 3*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Polytope 2591
Image of polytope 2591 PALP id: 2591
grdb id: 202512
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 -1 -1 1 -2 -2 0 -1 0 -1 0 0 -1]
[ 0 0 1 -1 -1 1 -1 0 -1 -1 -1 0 0 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + y*z-1 + 2*z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + 3*x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2592
Image of polytope 2592 PALP id: 2592
grdb id: 205078
Integer points: [ 1 0 0 1 0 -1 0 -2 -2 -1 -1 0 -1 0 -1 0]
[ 0 1 0 0 -1 1 -1 0 -1 -1 -1 -1 0 0 0 0]
[ 0 0 1 -1 1 0 -1 -1 -1 -1 0 0 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*z-1 + x-1*y + y-1*z + 3*z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + 3*x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-1
39 ? x + y + z + x*z-1 + x-1*y + y-1*z + 3*z-1 + 2*y-1 + 3*x-1 + y-1*z-1 + 3*x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2593
Image of polytope 2593 PALP id: 2593
grdb id: 202609
Integer points: [ 1 0 0 1 0 -1 1 -2 0 0 0 -1 -1 0 0 -1]
[ 0 1 0 -1 -1 0 -1 1 -1 -1 -1 0 0 0 0 1]
[ 0 0 1 0 1 1 -1 0 -2 0 -1 0 -1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + z + x*y-1 + 2*x-1*y + y-1*z + x-1*z + x*y-1*z-1 + 2*z-1 + 3*y-1 + 3*x-1 + x-2*y + 3*y-1*z-1 + 2*x-1*z-1 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 2594
Image of polytope 2594 PALP id: 2594
grdb id: 204885
Integer points: [ 1 0 0 1 1 -1 -2 -1 1 0 -1 1 0 0 -1 0]
[ 0 1 0 -1 0 1 0 -1 -1 -1 0 -1 0 -1 0 0]
[ 0 0 1 0 -1 0 1 0 -2 0 1 -1 0 -1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*z-1 + x*y-1 + x-1*y + 2*x-1*z + 2*x*y-1*z-1 + 2*z-1 + 2*y-1 + 2*x-1 + x-2*z + x*y-1*z-2 + 2*y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2595
Image of polytope 2595 PALP id: 2595
grdb id: 202545
Integer points: [ 1 0 1 -1 0 -1 -2 -1 -2 -2 -2 -1 -1 -1 0 0]
[ 0 1 -1 1 0 0 1 -2 -2 -1 0 -1 0 -1 -1 0]
[ 0 0 0 0 1 -1 -1 -1 -1 -1 -1 0 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2596
Image of polytope 2596 PALP id: 2596
grdb id: 204789
Integer points: [ 1 0 1 -1 0 -1 1 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 1 -1 1 0 0 -2 0 -2 -1 -2 -1 -1 0 -1 0]
[ 0 0 0 0 1 -1 -1 1 -1 0 -1 0 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*y-1 + x-1*y + x-1*z + 3*y-1 + 2*x-1 + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + 2*y-2*z-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2597
Image of polytope 2597 PALP id: 2597
grdb id: 204737
Integer points: [ 1 0 1 0 0 -1 -2 0 -2 0 -1 -1 0 0 -1 -1]
[ 0 1 -1 0 0 1 1 -2 0 -1 -1 0 -1 0 0 1]
[ 0 0 0 1 -1 -1 0 1 1 0 1 0 1 0 1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + x*y-1 + 2*x-1*y + 2*y-1*z + 2*x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-2*y + y-2*z + 2*x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2598
Image of polytope 2598 PALP id: 2598
grdb id: 204086
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 -1 0 -2 -1 -2 -2 -1 -1 0 -1 -1 0]
[ 0 0 1 -1 -1 1 0 2 2 1 0 1 0 0 1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + 2*y-1*z + x-1*z + x-1*y-1*z2 + 2*y-1 + 2*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
8 ? x + y + z + 2*y-1*z + x-1*z + x-1*y-1*z2 + 2*y-1 + 2*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 96 1 Lattice Minkowski decompositions of facet 96
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2599
Image of polytope 2599 PALP id: 2599
grdb id: 203231
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 0 2 0 -2 -2 -1 1 0 -1 1 0 -1]
[ 0 0 1 1 -1 -1 1 0 1 1 0 0 0 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y2*z-1 + 2*x-1*y + y-1*z + x-1*z + 2*x-1*y*z-1 + 2*y-1 + 4*x-1 + 2*x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z + x-1*y-2
146 ? x + y + z + x-1*y2*z-1 + 2*x-1*y + y-1*z + x-1*z + 2*x-1*y*z-1 + 2*y-1 + 5*x-1 + 2*x-1*y-1*z + x-1*z-1 + 4*x-1*y-1 + x-1*y-2*z + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Polytope 2600
Image of polytope 2600 PALP id: 2600
grdb id: 202454
Integer points: [ 1 0 0 0 -1 0 -2 -1 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 0 1 -1 1 -1 2 2 1 0 1 0 1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Image of facet 14 1 none
Polytope 2601
Image of polytope 2601 PALP id: 2601
grdb id: 204893
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 0 0 0 -1 -1 0]
[ 0 1 0 0 -2 2 0 -1 2 1 -1 0 1 0 1 -1]
[ 0 0 1 -1 1 -1 1 1 -2 0 1 0 -1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + z + 2*y*z-1 + x-1*y2*z-1 + 2*x-1*y + 2*y-1*z + x-1*z + x-1*y2*z-2 + z-1 + 3*x-1*y*z-1 + 2*y-1 + 3*x-1 + y-2*z + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Polytope 2602
Image of polytope 2602 PALP id: 2602
grdb id: 205096
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 0 0 -1 0 0 0]
[ 0 1 1 -1 -1 0 1 1 0 0 -1 0 1 0 0 1]
[ 0 0 2 -2 0 -1 2 0 1 0 -1 -1 1 0 1 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? y*z2 + 2*y*z + x-1*y*z2 + x + y + 2*z + 2*x-1*y*z + x-1*y + x-1*z + 2*z-1 + y-1 + 2*x-1 + 2*y-1*z-1 + x-1*z-1 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 3 Lattice Minkowski decompositions of facet 15
Polytope 2603
Image of polytope 2603 PALP id: 2603
grdb id: 204951
Integer points: [ 1 0 0 0 0 0 -1 -2 -2 0 -1 -1 0 0 -1 -1]
[ 0 1 0 1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 1 -1 1 -1 2 1 2 0 0 1 -1 0 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + y*z-1 + y-1*z + 2*x-1*z + x-1*y-1*z2 + 2*z-1 + 2*y-1 + 2*x-1 + 3*x-1*y-1*z + x-2*y-1*z2 + y-1*z-1 + 2*x-1*y-1 + x-2*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2604
Image of polytope 2604 PALP id: 2604
grdb id: 204865
Integer points: [ 1 0 0 0 1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 0 1 0 -2 -2 -1 0 -1 0 -1 0 -1]
[ 0 0 1 -1 -1 -1 -1 2 1 0 0 1 -1 0 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*z-1 + y*z-1 + 2*y-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Polytope 2605
Image of polytope 2605 PALP id: 2605
grdb id: 204826
Integer points: [ 1 0 0 1 0 1 0 -1 -2 -1 0 0 -1 0 -1 0]
[ 0 1 0 -1 0 0 -2 2 2 1 1 -1 0 0 1 -1]
[ 0 0 1 0 -1 -1 1 -1 -1 -1 -1 0 0 0 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + x*z-1 + 2*y*z-1 + x-1*y2*z-1 + x*y-1 + 2*x-1*y + 2*y-1*z + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 2*x-1 + y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2606
Image of polytope 2606 PALP id: 2606
grdb id: 202581
Integer points: [ 1 0 -1 0 -1 -2 0 -1 -2 -2 -2 -1 -1 -1 0 0]
[ 0 1 1 0 -1 0 -1 -2 -3 -2 -1 -2 -1 0 -1 0]
[ 0 0 0 1 -1 -1 1 -1 -1 -1 -1 0 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 8 1 none
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Polytope 2607
Image of polytope 2607 PALP id: 2607
grdb id: 201900
Integer points: [ 1 0 0 -1 -1 -1 -1 -3 -3 -2 -3 -2 -1 -1 0 -2]
[ 0 1 0 0 -1 0 -1 -2 -2 -1 -2 -1 0 -1 0 -1]
[ 0 0 1 -1 -1 1 1 -1 1 1 0 0 0 0 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
103 ? x + y + z + x-1*z + 3*x-1 + x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + 2*x-2*y-1*z + x-1*y-1*z-1 + 4*x-2*y-1 + 2*x-2*y-1*z-1 + x-3*y-2*z + 2*x-3*y-2 + x-3*y-2*z-1
147 ? x + y + z + x-1*z + 4*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + 2*x-2*y-1*z + x-1*y-1*z-1 + 5*x-2*y-1 + 2*x-2*y-1*z-1 + x-3*y-2*z + 2*x-3*y-2 + x-3*y-2*z-1
145 ? x + y + z + x-1*z + 4*x-1 + x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + 2*x-2*y-1*z + x-1*y-1*z-1 + 5*x-2*y-1 + 2*x-2*y-1*z-1 + x-3*y-2*z + 2*x-3*y-2 + x-3*y-2*z-1
112 rank 3, number 15 x + y + z + x-1*z + 3*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + 2*x-2*y-1*z + x-1*y-1*z-1 + 4*x-2*y-1 + 2*x-2*y-1*z-1 + x-3*y-2*z + 2*x-3*y-2 + x-3*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Polytope 2608
Image of polytope 2608 PALP id: 2608
grdb id: 203259
Integer points: [ 1 0 0 -1 -1 -1 -1 0 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 0 0 -2 -2 -3 -1 -2 0 -1 -1 0 -1]
[ 0 0 1 0 -1 1 0 1 1 1 1 0 0 1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
114 ? x + y + z + x-1*y + 2*y-1*z + x-1*z + 2*y-1 + 3*x-1 + y-2*z + 3*x-1*y-1*z + x-1*z-1 + 4*x-1*y-1 + 3*x-1*y-2*z + x-1*y-2 + x-1*y-3*z
144 rank 3, number 12 x + y + z + x-1*y + 2*y-1*z + x-1*z + 2*y-1 + 2*x-1 + y-2*z + 3*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + 3*x-1*y-2*z + x-1*y-2 + x-1*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2609
Image of polytope 2609 PALP id: 2609
grdb id: 202559
Integer points: [ 1 0 0 -1 0 -2 -1 -3 -3 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 0 -1 0 -2 -1 -3 -2 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 1 -1 1 -1 1 1 1 0 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + y-1*z + 3*x-1 + 3*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z + x-2*z-1 + 4*x-2*y-1 + 3*x-2*y-2*z + x-3*y-1*z-1 + 2*x-3*y-2 + x-3*y-3*z
103 ? x + y + z + y-1*z + 3*x-1 + 3*x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z + x-2*z-1 + 4*x-2*y-1 + 3*x-2*y-2*z + x-3*y-1*z-1 + 2*x-3*y-2 + x-3*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2610
Image of polytope 2610 PALP id: 2610
grdb id: 202555
Integer points: [ 1 0 0 0 -1 -2 -1 -3 -3 -1 -2 -1 -2 -3 0 -1]
[ 0 1 -1 0 0 0 -2 -1 -3 -1 -2 0 -1 -2 0 -1]
[ 0 0 0 1 -1 -1 -1 -2 -2 0 -1 0 -1 -2 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + y-1 + 2*x-1 + x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + x-1*y-2*z-1 + 4*x-2*y-1*z-1 + 3*x-2*y-2*z-1 + x-3*y-1*z-2 + 2*x-3*y-2*z-2 + x-3*y-3*z-2
16 ? x + y + z + y-1 + 2*x-1 + x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + x-2*z-1 + x-1*y-2*z-1 + 4*x-2*y-1*z-1 + 3*x-2*y-2*z-1 + x-3*y-1*z-2 + 2*x-3*y-2*z-2 + x-3*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2611
Image of polytope 2611 PALP id: 2611
grdb id: 202529
Integer points: [ 1 0 0 0 -1 0 -2 -1 -3 -2 -1 0 -1 0 -2 -1]
[ 0 1 0 -1 0 -1 0 -1 -1 -1 -1 -1 0 0 -1 -1]
[ 0 0 1 -1 -1 1 -1 1 -1 0 0 0 0 0 -1 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + y-1*z + 2*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 4*x-1*y-1 + 3*x-1*y-1*z-1 + x-2*z-1 + 2*x-2*y-1 + 3*x-2*y-1*z-1 + x-3*y-1*z-1
67 ? x + y + z + y-1*z + 2*y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 4*x-1*y-1 + 3*x-1*y-1*z-1 + x-2*z-1 + 2*x-2*y-1 + 3*x-2*y-1*z-1 + x-3*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2612
Image of polytope 2612 PALP id: 2612
grdb id: 204861
Integer points: [ 1 0 0 0 -1 0 -1 -1 -3 -2 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 0 -1 0 -2 -2 -1 -1 0 -2 -1 -1 0]
[ 0 0 0 1 -1 1 1 1 1 0 1 0 1 0 1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + y-1*z + x-1*z + y-1 + 2*x-1 + 3*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z + 2*x-2*y-1*z + 2*x-2*y-1 + 2*x-2*y-2*z + x-3*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2613
Image of polytope 2613 PALP id: 2613
grdb id: 205079
Integer points: [ 1 0 0 0 0 -1 -2 -1 -2 -1 -1 -2 0 0 -1 -1]
[ 0 1 0 0 -1 0 -1 -2 -3 -2 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 0 1 0 -2 -2 -1 0 -1 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*z + z-1 + y-1 + 2*x-1 + 2*y-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + x-2*y-1 + 2*x-1*y-2*z-1 + x-1*y-2*z-2 + 2*x-2*y-2*z-1 + x-2*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2614
Image of polytope 2614 PALP id: 2614
grdb id: 202520
Integer points: [ 1 0 0 0 0 0 -1 -2 -3 -2 -1 -2 -1 -1 -1 0]
[ 0 1 0 -1 0 -1 1 -1 -1 -1 -1 0 0 -1 0 0]
[ 0 0 1 0 -1 1 0 -2 -2 -1 0 -1 0 -1 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*y + y-1*z + z-1 + y-1 + 3*x-1 + 3*x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + 3*x-2*y-1*z-1 + x-2*y-1*z-2 + x-3*y-1*z-2
38 ? x + y + z + x-1*y + y-1*z + z-1 + y-1 + 3*x-1 + 2*x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + 3*x-2*y-1*z-1 + x-2*y-1*z-2 + x-3*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2615
Image of polytope 2615 PALP id: 2615
grdb id: 202546
Integer points: [ 1 0 0 0 0 0 -1 -2 -3 -2 -1 -2 -1 -1 -1 0]
[ 0 1 0 0 -1 1 -1 1 1 1 1 0 0 1 0 0]
[ 0 0 1 -1 0 -1 -1 0 -1 -1 -1 -1 -1 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + y*z-1 + 2*x-1*y + z-1 + 3*x-1*y*z-1 + y-1 + 2*x-1 + x-2*y + 3*x-1*z-1 + 3*x-2*y*z-1 + x-1*y-1*z-1 + 2*x-2*z-1 + x-3*y*z-1
67 ? x + y + z + y*z-1 + 2*x-1*y + z-1 + 3*x-1*y*z-1 + y-1 + 3*x-1 + x-2*y + 3*x-1*z-1 + 3*x-2*y*z-1 + x-1*y-1*z-1 + 2*x-2*z-1 + x-3*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2616
Image of polytope 2616 PALP id: 2616
grdb id: 205057
Integer points: [ 1 0 0 0 1 0 -2 -2 -3 -1 0 -2 -1 -1 0 -1]
[ 0 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 0 1 1 0 1 0 0 1 1 0 0 1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x*y-1 + y-1*z + 2*x-1*z + z-1 + 3*y-1 + x-1 + 3*x-1*y-1*z + x-2*z + 3*x-1*y-1 + 3*x-2*y-1*z + x-2*y-1 + x-3*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2617
Image of polytope 2617 PALP id: 2617
grdb id: 204738
Integer points: [ 1 0 0 1 -1 0 -1 -2 -3 -2 -1 -2 -1 0 -1 0]
[ 0 1 0 -1 1 0 -1 1 1 1 0 0 1 0 0 -1]
[ 0 0 1 0 0 -1 0 -2 -2 -1 0 -1 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*y-1 + x-1*y + z-1 + 2*x-1*y*z-1 + 2*y-1 + 2*x-1 + 3*x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1 + x-2*y*z-2 + 2*x-2*z-1 + x-3*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2618
Image of polytope 2618 PALP id: 2618
grdb id: 204551
Integer points: [ 1 0 1 -1 0 -1 -2 -3 -3 -2 -1 -2 0 -1 0 -1]
[ 0 1 -1 1 0 -1 1 0 -1 -1 0 0 -1 -1 0 0]
[ 0 0 0 0 1 0 -1 -2 -2 -1 0 -1 0 -1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x*y-1 + x-1*y + 2*y-1 + 2*x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + 2*x-2*y-1*z-1 + x-3*z-2 + x-3*y-1*z-2
3 ? x + y + z + x*y-1 + x-1*y + 2*y-1 + 3*x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + 4*x-2*z-1 + 2*x-2*y-1*z-1 + x-3*z-2 + x-3*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2619
Image of polytope 2619 PALP id: 2619
grdb id: 202590
Integer points: [ 1 0 1 -1 0 -1 0 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 -1 1 0 1 -1 0 -3 -1 -2 0 -1 -1 -2 0]
[ 0 0 0 0 1 1 -1 1 -2 0 -1 0 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + x-1*y*z + x*y-1 + x-1*y + x-1*z + 3*y-1 + 3*x-1 + y-1*z-1 + 3*x-1*y-1 + 2*y-2*z-1 + 2*x-1*y-1*z-1 + 3*x-1*y-2*z-1 + x-1*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Polytope 2620
Image of polytope 2620 PALP id: 2620
grdb id: 205034
Integer points: [ 1 0 1 -1 0 0 -1 -2 -3 -2 -1 -2 0 -1 0 -1]
[ 0 1 -1 1 0 -1 -1 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 0 0 1 -1 0 -2 -2 -1 0 -1 0 -1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x*y-1 + x-1*y + 2*y-1 + 2*x-1 + y-1*z-1 + 2*x-1*z-1 + x-1*y-1 + 3*x-1*y-1*z-1 + 2*x-2*z-1 + 2*x-2*y-1*z-1 + x-2*y-1*z-2 + x-3*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2621
Image of polytope 2621 PALP id: 2621
grdb id: 202510
Integer points: [ 1 0 1 0 0 -2 -2 0 -3 -1 -2 0 -1 -1 0 -1]
[ 0 1 -1 0 -1 1 1 -2 1 -1 0 -1 0 0 0 1]
[ 0 0 0 1 -1 0 -1 -1 -1 -1 -1 0 0 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + x*y-1 + 2*x-1*y + 2*y-1 + 3*x-1 + x-2*y + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1 + y-2*z-1 + 3*x-1*y-1*z-1 + 3*x-2*z-1 + x-3*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2622
Image of polytope 2622 PALP id: 2622
grdb id: 203149
Integer points: [ 1 0 0 0 -1 -1 -2 -3 -4 -2 -3 -1 -2 -1 0 -1]
[ 0 1 0 1 -1 1 -1 -2 -2 0 -1 0 -1 0 0 -1]
[ 0 0 1 1 0 0 -2 -2 -3 -1 -2 0 -1 -1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 y*z + x + y + z + x-1*y + 4*x-1 + 2*x-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*z-1 + 4*x-2*y-1*z-1 + x-2*y-1*z-2 + 3*x-3*y-1*z-2 + x-3*y-2*z-2 + x-4*y-2*z-3
107 rank 3, number 11 y*z + x + y + z + x-1*y + 3*x-1 + 2*x-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*z-1 + 3*x-2*y-1*z-1 + x-2*y-1*z-2 + 3*x-3*y-1*z-2 + x-3*y-2*z-2 + x-4*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Polytope 2623
Image of polytope 2623 PALP id: 2623
grdb id: 215827
Integer points: [ 1 0 0 0 -1 -1 -1 -2 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 -1 0 1 1 -2 1 -2 -1 0 -1 0 -1 0 0]
[ 0 0 0 1 0 -1 -1 -1 -1 -1 -1 0 0 -1 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y + x-1*y*z-1 + y-1 + 3*x-1 + 3*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2*z-1 + 3*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2624
Image of polytope 2624 PALP id: 2624
grdb id: 219192
Integer points: [ 1 0 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 0 -1 -1 0 -1 -1 -1 0 0 -1 0 0]
[ 0 0 1 1 1 -1 1 -2 -2 0 -1 0 -1 0 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + y-1*z + x-1*z + 2*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*z-2 + 3*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2625
Image of polytope 2625 PALP id: 2625
grdb id: 219437
Integer points: [ 1 0 0 0 0 -1 0 -2 -2 -1 -1 0 -1 0 -1 0]
[ 0 1 0 1 -1 0 -1 1 1 0 0 -1 1 0 1 0]
[ 0 0 1 -1 1 1 -1 0 -1 -1 0 0 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + y*z-1 + 2*x-1*y + y-1*z + x-1*z + 2*z-1 + 2*x-1*y*z-1 + 2*y-1 + 3*x-1 + x-2*y + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2626
Image of polytope 2626 PALP id: 2626
grdb id: 219121
Integer points: [ 1 0 0 0 0 -1 0 -2 -2 -1 -1 -1 0 -1 0 0]
[ 0 1 0 1 -1 1 -1 0 -1 -1 0 -1 -1 0 0 0]
[ 0 0 1 -1 1 -1 -1 -1 -1 0 0 -1 0 -1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + y*z-1 + y-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + 3*x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2627
Image of polytope 2627 PALP id: 2627
grdb id: 215852
Integer points: [ 1 0 0 0 0 -1 -1 -2 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 0 2 2 -1 1 0 1 0 -1 1 0]
[ 0 0 0 1 1 -1 -1 -1 -1 -1 -1 0 0 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y2*z-1 + 2*x-1*y + y-1*z + 2*x-1*y*z-1 + x-2*y2*z-1 + y-1 + 4*x-1 + x-1*z-1 + 3*x-2*y*z-1 + 2*x-1*y-1 + 3*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2628
Image of polytope 2628 PALP id: 2628
grdb id: 219443
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 2 0 -2 0 2 -1 1 0 -1 1 1 0]
[ 0 0 0 1 1 -1 -1 1 1 0 1 0 -1 0 1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 y2*z + 2*y*z + x-1*y2*z + x + y + z + 2*x-1*y*z + 2*x-1*y + x-1*z + y-1 + 4*x-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2629
Image of polytope 2629 PALP id: 2629
grdb id: 219188
Integer points: [ 1 0 0 0 0 -1 -1 -1 -3 -2 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 -1 0 2 0 2 1 1 0 2 1 1 0]
[ 0 0 0 1 1 -1 -1 1 -1 -1 0 0 -1 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y2*z-1 + 3*x-1*y + y-1*z + x-1*z + 2*x-1*y*z-1 + 2*x-2*y2*z-1 + y-1 + 3*x-1 + 2*x-2*y + x-1*z-1 + 2*x-2*y*z-1 + x-3*y2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2630
Image of polytope 2630 PALP id: 2630
grdb id: 652784
Integer points: [ 1 0 0 -1 1 0 1 -2 0 -2 -1 -1 0 -1 0 1]
[ 0 1 0 1 -2 -1 -2 1 -1 1 0 0 -1 1 0 -1]
[ 0 0 1 1 -1 -1 0 0 1 1 1 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
109 ? x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + x*y-2 + 4*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + y-1*z-1
39 ? x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + x*y-2 + 2*y-1 + 2*x-1 + x-2*y + x*y-2*z-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 1 2 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Polytope 2631
Image of polytope 2631 PALP id: 2631
grdb id: 652808
Integer points: [ 1 0 0 0 -1 -1 1 -1 0 -1 -1 0 -1 -1 0 0]
[ 0 1 0 0 1 0 -1 0 -2 -2 -1 -1 -1 0 -1 0]
[ 0 0 1 -1 0 1 -1 -1 -1 -1 0 0 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
128 ? x + y + z + x-1*y + x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + 3*y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1
59 rank 2, number 16 x + y + z + x-1*y + x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + 2*y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2632
Image of polytope 2632 PALP id: 2632
grdb id: 652803
Integer points: [ 1 0 0 0 1 -1 -1 0 -2 -2 -1 0 -1 -1 0 1]
[ 0 1 0 0 -2 1 1 -1 1 1 0 -1 0 1 0 -1]
[ 0 0 1 -1 0 -1 1 1 0 1 0 0 1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + 2*x*y-1 + x-1*y + y-1*z + 2*x-1*z + x-2*y*z + z-1 + x-1*y*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2633
Image of polytope 2633 PALP id: 2633
grdb id: 652813
Integer points: [ 1 0 0 1 -1 1 0 1 -1 -2 0 0 -1 1 0 -1]
[ 0 1 0 -1 1 0 1 -2 1 1 0 -1 0 -1 0 1]
[ 0 0 1 -1 1 -1 -1 0 -1 0 -1 0 0 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + x-1*y*z + x*z-1 + y*z-1 + 2*x*y-1 + x-1*y + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2634
Image of polytope 2634 PALP id: 2634
grdb id: 652811
Integer points: [ 1 0 0 1 -1 0 0 1 1 -1 0 0 -1 0 0 0]
[ 0 1 1 -1 1 -1 -1 0 -1 -1 -1 0 0 0 0 1]
[ 0 0 2 -1 1 0 -2 -1 -2 -1 -1 -1 0 0 1 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 y*z2 + 2*y*z + x + y + 2*z + x-1*y*z + x*z-1 + x*y-1*z-1 + 2*z-1 + y-1 + 2*x-1 + x*y-1*z-2 + y-1*z-1 + y-1*z-2 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2635
Image of polytope 2635 PALP id: 2635
grdb id: 652672
Integer points: [ 1 0 0 -1 1 0 1 0 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 -1 0 -1 -1 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 1 1 -1 -1 0 1 -1 1 0 0 1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y*z + x*y-1 + y-1*z + 2*x-1*z + x*y-1*z-1 + z-1 + 3*y-1 + 2*x-1 + x-1*y-1*z + 2*y-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2636
Image of polytope 2636 PALP id: 2636
grdb id: 652240
Integer points: [ 1 0 -1 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 1 0 -1 0 -1 -1 -2 -2 -1 -2 -1 0 -1 0]
[ 0 0 0 1 -1 1 1 -1 -1 1 1 0 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + x-1*y + y-1*z + x-1*z + 2*y-1 + 3*x-1 + 2*x-1*y-1*z + y-1*z-1 + 3*x-1*y-1 + x-1*y-2*z + x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-2*z-1
88 ? x + y + z + x-1*y + y-1*z + x-1*z + 3*y-1 + 3*x-1 + 2*x-1*y-1*z + y-1*z-1 + 3*x-1*y-1 + x-1*y-2*z + x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Polytope 2637
Image of polytope 2637 PALP id: 2637
grdb id: 652771
Integer points: [ 1 0 0 -1 -1 1 1 -1 1 -1 0 -1 0 0 1 0]
[ 0 1 0 1 0 -1 0 -1 -1 -1 0 0 -1 0 0 -1]
[ 0 0 1 1 0 -1 -2 1 -2 0 -1 1 -1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + z + x-1*y*z + 2*x*z-1 + 2*x-1*z + x*z-2 + x*y-1*z-1 + 2*z-1 + 2*y-1 + x-1 + x-1*y-1*z + x*y-1*z-2 + 2*y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 1 2 irreducible and admissible
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2638
Image of polytope 2638 PALP id: 2638
grdb id: 652299
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -1 1 0 -2 -2 -1 0 0 -1 -1 0 -1]
[ 0 0 1 0 -1 1 -1 0 -1 1 1 0 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*y*z + x-1*y + 2*x-1*z + 2*y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
85 rank 3, number 8 x + y + z + x-1*y*z + x-1*y + 2*x-1*z + 2*y-1 + 4*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 96 1 Lattice Minkowski decompositions of facet 96
Polytope 2639
Image of polytope 2639 PALP id: 2639
grdb id: 652759
Integer points: [ 1 0 0 -1 1 0 1 0 -2 -2 0 -1 -1 1 0 -1]
[ 0 1 0 1 -1 0 -2 -1 1 1 -1 0 0 -1 0 1]
[ 0 0 1 1 -1 -1 0 1 0 1 0 0 1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + x*y-1*z-1 + z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 1 2 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2640
Image of polytope 2640 PALP id: 2640
grdb id: 652547
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 -1]
[ 0 1 0 0 -1 1 0 -1 -2 -2 -1 -1 0 -1 0 0]
[ 0 0 1 -1 0 0 1 -2 -1 -2 0 -1 0 -1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
60 rank 2, number 18 x + y + z + x-1*y + x-1*z + z-1 + y-1 + x-1 + 2*y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-1*z-2 + x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 71 1 Lattice Minkowski decompositions of facet 71
Polytope 2641
Image of polytope 2641 PALP id: 2641
grdb id: 652695
Integer points: [ 1 0 0 1 -1 -1 -1 1 0 1 0 1 0 0 -1 0]
[ 0 1 0 -1 1 0 0 -2 -1 -2 -1 -1 -1 0 0 0]
[ 0 0 1 0 0 1 -1 -1 -2 -2 0 -1 -1 0 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*y-1 + x-1*y + x-1*z + 2*x*y-1*z-1 + 2*z-1 + 2*y-1 + 2*x-1 + x*y-2*z-1 + 3*y-1*z-1 + x-1*z-1 + x*y-2*z-2 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2642
Image of polytope 2642 PALP id: 2642
grdb id: 652718
Integer points: [ 1 0 0 1 -1 0 -1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 1 0 0 0 -2 -2 -1 -1 0 -1 -1 0]
[ 0 0 1 0 0 -1 -1 1 1 1 0 1 0 0 1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + x*y-1 + x-1*y + 2*y-1*z + x-1*z + z-1 + 3*y-1 + 2*x-1 + y-2*z + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
17 rank 1, V22 x + y + z + x*y-1 + x-1*y + 2*y-1*z + x-1*z + z-1 + 2*y-1 + 2*x-1 + y-2*z + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2643
Image of polytope 2643 PALP id: 2643
grdb id: 652681
Integer points: [ 1 0 0 1 -1 0 1 -2 -1 -2 -1 -1 0 -1 0 0]
[ 0 1 0 -1 1 0 -1 0 -1 -1 0 -1 -1 0 0 -1]
[ 0 0 1 0 0 -1 1 -1 -2 -2 0 -1 0 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + x*y-1*z + z + x*y-1 + x-1*y + z-1 + 3*y-1 + 2*x-1 + 2*y-1*z-1 + 3*x-1*z-1 + 3*x-1*y-1*z-1 + x-2*z-1 + x-1*y-1*z-2 + x-2*y-1*z-2
13 rank 2, number 12 x + y + x*y-1*z + z + x*y-1 + x-1*y + z-1 + 3*y-1 + 2*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1*z-1 + x-2*z-1 + x-1*y-1*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Polytope 2644
Image of polytope 2644 PALP id: 2644
grdb id: 652662
Integer points: [ 1 0 0 1 -1 0 1 1 0 -2 0 -1 -1 0 0 -1]
[ 0 1 0 -1 1 0 -1 -2 -2 0 -1 0 -1 0 -1 0]
[ 0 0 1 0 0 -1 1 1 1 -1 1 0 0 0 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + x*y-1*z + z + x*y-1 + x-1*y + x*y-2*z + 2*y-1*z + z-1 + 3*y-1 + 2*x-1 + y-2*z + 2*x-1*z-1 + 2*x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2645
Image of polytope 2645 PALP id: 2645
grdb id: 652691
Integer points: [ 1 0 0 1 0 1 -1 -2 -1 -2 0 -1 0 -1 0 -1]
[ 0 1 0 0 1 -1 -1 0 1 1 0 0 -1 1 0 0]
[ 0 0 1 -1 -1 -1 1 1 -1 0 -1 0 0 0 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*z-1 + y*z-1 + 2*x-1*y + 2*x-1*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-2*y + x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2646
Image of polytope 2646 PALP id: 2646
grdb id: 652716
Integer points: [ 1 0 1 -1 0 1 0 0 -2 -2 -1 -1 0 -1 -1 0]
[ 0 1 -1 1 0 -1 -1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 0 0 0 1 -1 -1 1 1 1 0 1 0 0 1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2647
Image of polytope 2647 PALP id: 2647
grdb id: 652669
Integer points: [ 1 0 1 0 -1 0 -1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 1 -1 0 1 -1 0 1 -1 0 1 0 0 0 0 -1]
[ 0 0 0 1 1 1 1 -1 -1 -2 0 0 -1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + x*y-1 + 2*x-1*y + y-1*z + x-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + y-1*z-1 + 3*x-1*z-1 + x-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Polytope 2648
Image of polytope 2648 PALP id: 2648
grdb id: 652706
Integer points: [ 1 0 1 0 -1 1 -1 -2 0 -2 -1 0 -1 0 0 -1]
[ 0 1 -1 0 1 -2 0 1 -2 0 -1 -1 0 -1 0 1]
[ 0 0 0 1 1 -1 -1 0 -1 -1 -1 0 0 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y*z + x*y-1 + 2*x-1*y + 2*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2649
Image of polytope 2649 PALP id: 2649
grdb id: 652773
Integer points: [ 1 0 0 0 -1 1 -2 1 1 0 1 1 0 -1 0 -1]
[ 0 1 0 0 0 0 2 -2 -2 -1 -1 -1 0 1 -1 1]
[ 0 0 1 -1 0 1 -1 0 1 1 0 1 0 -1 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x*z + x + y + 2*x*y-1*z + z + 2*x*y-1 + 2*x-1*y + x*y-2*z + y-1*z + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + x*y-2 + 2*y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 5 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2650
Image of polytope 2650 PALP id: 2650
grdb id: 652478
Integer points: [ 1 0 0 0 0 0 -1 -2 -1 -2 -2 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 0 1 -1 0 2 2 1 0 1 0 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
55 rank 2, number 19 x + y + z + y-1*z + 2*x-1*z + x-1*y-1*z2 + z-1 + y-1 + 2*x-1 + 2*x-1*y-1*z + x-2*y-1*z2 + 2*x-1*y-1 + 2*x-2*y-1*z + x-1*y-1*z-1 + x-2*y-1
46 ? x + y + z + y-1*z + 2*x-1*z + x-1*y-1*z2 + z-1 + y-1 + 2*x-1 + 4*x-1*y-1*z + x-2*y-1*z2 + 3*x-1*y-1 + 2*x-2*y-1*z + x-1*y-1*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Polytope 2651
Image of polytope 2651 PALP id: 2651
grdb id: 652700
Integer points: [ 1 0 0 0 0 0 -1 -2 -1 -2 -2 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 -1 0 2 2 1 0 1 0 1 0]
[ 0 0 1 -1 0 1 -1 -1 1 1 0 0 1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? y*z + x-1*y2*z + x + y + z + 2*x-1*y*z + x-2*y2*z + 3*x-1*y + z-1 + y-1 + 3*x-1 + 2*x-2*y + 2*x-1*z-1 + x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2652
Image of polytope 2652 PALP id: 2652
grdb id: 652688
Integer points: [ 1 0 0 1 0 0 0 -2 -2 -3 -2 -1 -1 -1 -1 0]
[ 0 1 0 -1 -1 0 1 0 1 1 1 1 0 1 0 0]
[ 0 0 1 -1 0 -1 1 1 0 1 1 1 1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 y*z + x + y + z + 3*x-1*y*z + 2*x-1*y + 2*x-1*z + 3*x-2*y*z + x*y-1*z-1 + z-1 + y-1 + 2*x-1 + x-2*y + x-2*z + x-3*y*z
39 ? y*z + x + y + z + 3*x-1*y*z + 2*x-1*y + 2*x-1*z + 3*x-2*y*z + x*y-1*z-1 + z-1 + y-1 + 3*x-1 + x-2*y + x-2*z + x-3*y*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Polytope 2653
Image of polytope 2653 PALP id: 2653
grdb id: 652715
Integer points: [ 1 0 1 -1 0 -1 1 -1 0 -1 -1 -1 0 0 0 0]
[ 0 1 -1 1 0 1 -2 0 -3 -2 -1 0 -2 -1 -1 0]
[ 0 0 0 0 1 1 -1 -1 -2 -2 -1 0 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + x-1*y*z + x*y-1 + x-1*y + 3*y-1 + 3*x-1 + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1 + 3*y-2*z-1 + 3*x-1*y-1*z-1 + y-3*z-2 + x-1*y-2*z-2
52 rank 2, number 52 x + y + z + x-1*y*z + x*y-1 + x-1*y + 3*y-1 + 3*x-1 + x*y-2*z-1 + 3*y-1*z-1 + x-1*z-1 + 3*y-2*z-1 + 3*x-1*y-1*z-1 + y-3*z-2 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2654
Image of polytope 2654 PALP id: 2654
grdb id: 662248
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 -1 1 -1 1 -1 0 0 0 1 0]
[ 0 0 1 -1 0 1 -1 -1 1 1 0 -1 0 1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 y*z + x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + z-1 + x-1*y*z-1 + y-1 + 4*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 2655
Image of polytope 2655 PALP id: 2655
grdb id: 662536
Integer points: [ 1 0 0 1 -1 -1 1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 -1 1 0 -1 1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 0 0 1 -1 -1 0 -1 -1 0 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + x*y-1 + x-1*y + x-1*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
52 rank 2, number 52 x + y + z + x*y-1 + x-1*y + x-1*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2656
Image of polytope 2656 PALP id: 2656
grdb id: 660114
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 1 1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 1 -1 0 1 0 -1 -1 2 0 1 -1 0 1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y + y-1*z + 2*x-1*z + x-1*y-1*z2 + z-1 + x-1*y*z-1 + y-1 + 4*x-1 + 3*x-1*y-1*z + 2*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2657
Image of polytope 2657 PALP id: 2657
grdb id: 662250
Integer points: [ 1 0 0 1 0 0 -1 -1 0 -1 -1 0 -1 0 -1 0]
[ 0 1 0 0 1 -1 1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 1 -1 -1 1 0 2 -1 0 1 0 0 -1 1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*z-1 + y*z-1 + x-1*y + y-1*z + 2*x-1*z + x-1*y-1*z2 + 2*z-1 + 2*y-1 + 2*x-1 + 2*x-1*y-1*z + y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2658
Image of polytope 2658 PALP id: 2658
grdb id: 660370
Integer points: [ 1 0 0 -1 -1 0 -1 -2 -1 -2 -2 -2 -1 -1 0 0]
[ 0 1 0 0 1 -1 -1 1 -2 -2 -1 0 -1 0 -1 0]
[ 0 0 1 -1 0 1 -1 -1 0 -1 -1 -1 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
88 ? x + y + z + x-1*y + y-1*z + 2*y-1 + 4*x-1 + x-1*z-1 + x-2*y*z-1 + 4*x-1*y-1 + x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2 + 3*x-2*y-1*z-1 + x-2*y-2*z-1
67 ? x + y + z + x-1*y + y-1*z + 2*y-1 + 3*x-1 + x-1*z-1 + x-2*y*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2 + 3*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2659
Image of polytope 2659 PALP id: 2659
grdb id: 660595
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 1 1 0 -1 -2 -2 -1 -1 0 0 -1 0]
[ 0 0 1 1 0 -1 1 -1 0 1 1 0 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
85 rank 3, number 8 x + y + z + x-1*y + y-1*z + x-1*z + x-1*y*z-1 + 2*y-1 + 4*x-1 + 2*x-1*y-1*z + 2*x-1*z-1 + 4*x-1*y-1 + x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
36 rank 3, number 7 x + y + z + x-1*y + y-1*z + x-1*z + x-1*y*z-1 + 2*y-1 + 3*x-1 + 2*x-1*y-1*z + 2*x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 96 1 Lattice Minkowski decompositions of facet 96
Polytope 2660
Image of polytope 2660 PALP id: 2660
grdb id: 662294
Integer points: [ 1 0 0 0 -1 -1 -1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 1 1 0 0 -2 -2 -1 0 -1 -1 0 -1]
[ 0 0 1 -1 0 -1 1 -1 1 1 0 0 1 0 0 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y + 2*y-1*z + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + y-2*z + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2661
Image of polytope 2661 PALP id: 2661
grdb id: 662301
Integer points: [ 1 0 0 0 -1 -1 0 -1 -1 -1 -1 -1 0 -1 0 0]
[ 0 1 0 -1 1 1 -1 -1 0 -1 0 -1 -1 0 0 0]
[ 0 0 1 1 0 -1 -1 0 -2 -2 0 -1 0 -1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y + y-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + 3*x-1*z-1 + x-1*y-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2662
Image of polytope 2662 PALP id: 2662
grdb id: 662356
Integer points: [ 1 0 0 0 -1 -1 0 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 1 -1 -1 -2 -2 -1 0 -1 0 -1 0]
[ 0 0 1 -1 0 -1 1 -1 0 -1 0 0 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + x-1*y + y-1*z + z-1 + x-1*y*z-1 + y-1 + 3*x-1 + y-1*z-1 + 3*x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2663
Image of polytope 2663 PALP id: 2663
grdb id: 662177
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 0 -1 0 0]
[ 0 1 0 1 -1 0 1 1 -2 0 -1 0 0 -1 -1 0]
[ 0 0 1 -1 1 0 -1 -2 0 -2 0 -1 0 -1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + y*z-1 + y-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + x-1 + x-1*y*z-2 + 3*x-1*z-1 + 2*x-1*y-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2664
Image of polytope 2664 PALP id: 2664
grdb id: 660113
Integer points: [ 1 0 0 0 0 -1 -1 0 -1 -1 -1 -1 0 -1 -1 0]
[ 0 1 0 0 -1 1 0 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 1 0 1 -1 1 -2 0 -1 0 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y + y-1*z + x-1*z + z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2665
Image of polytope 2665 PALP id: 2665
grdb id: 662262
Integer points: [ 1 0 0 0 0 -1 -1 0 -1 -1 -1 -1 0 -1 0 0]
[ 0 1 0 1 -1 1 0 -1 -2 -2 -1 0 0 -1 -1 0]
[ 0 0 1 -1 1 0 1 -1 1 0 0 0 -1 1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + y*z-1 + x-1*y + y-1*z + x-1*z + 2*z-1 + y-1 + 3*x-1 + 2*x-1*y-1*z + y-1*z-1 + 3*x-1*y-1 + x-1*y-2*z + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Polytope 2666
Image of polytope 2666 PALP id: 2666
grdb id: 662510
Integer points: [ 1 0 0 0 0 -1 0 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 0 1 -2 -1 1 -2 0 -1 0 -1 0 -1]
[ 0 0 1 -1 -1 -1 1 1 -2 1 0 0 -1 1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + y*z-1 + 2*y-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + y-2*z + x-1*y-1*z + x-1*y*z-2 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 2667
Image of polytope 2667 PALP id: 2667
grdb id: 662367
Integer points: [ 1 0 0 0 0 0 -1 -2 -1 -2 -1 -2 -1 -1 0 -1]
[ 0 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 0 -1 0 0]
[ 0 0 1 -1 0 -1 1 0 -2 -2 0 -1 0 -1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*z + z-1 + y-1 + 2*x-1 + y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + x-2*y-1 + x-1*y-1*z-2 + 2*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2668
Image of polytope 2668 PALP id: 2668
grdb id: 662326
Integer points: [ 1 0 0 1 -1 0 1 -1 -2 -2 0 -1 0 -1 0 -1]
[ 0 1 0 -1 1 0 -1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 0 1 0 0 -1 -1 0 -1 -1 0 -1 -1 0 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + x*y-1 + x-1*y + x*y-1*z-1 + z-1 + 2*y-1 + x-1 + 3*y-1*z-1 + 2*x-1*z-1 + x-1*y-1 + 3*x-1*y-1*z-1 + x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Polytope 2669
Image of polytope 2669 PALP id: 2669
grdb id: 662154
Integer points: [ 1 0 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 -1 0 0 1 1 0 -1 -1 0 0 -1 0 -1 -1]
[ 0 0 0 1 -1 0 1 1 0 -2 -1 0 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y*z + x*y-1 + x-1*y + x-1*z + z-1 + 2*y-1 + 3*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2670
Image of polytope 2670 PALP id: 2670
grdb id: 662109
Integer points: [ 1 0 0 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 0 -1 0 -1 -1 -1 -1 -1 0 -1 0]
[ 0 0 1 -1 -1 -1 1 1 -2 2 -1 0 1 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + y-1*z + x-1*z + x-1*y-1*z2 + z-1 + 2*y-1 + 2*x-1 + 4*x-1*y-1*z + y-1*z-1 + x-1*z-1 + 6*x-1*y-1 + 4*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 59 2 Lattice Minkowski decompositions of facet 59
Polytope 2671
Image of polytope 2671 PALP id: 2671
grdb id: 662129
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -1 -1 0 -1 0 -1 0 0 -1 -1 0 0]
[ 0 0 1 -1 1 0 1 2 -2 -1 -1 0 0 1 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + y*z-1 + y-1*z + x-1*z + x-1*y-1*z2 + 2*z-1 + y-1 + 3*x-1 + 3*x-1*y-1*z + 3*x-1*z-1 + 3*x-1*y-1 + x-1*z-2 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2672
Image of polytope 2672 PALP id: 2672
grdb id: 660322
Integer points: [ 1 0 0 0 -1 0 -1 -2 -3 -3 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 1 -1 -1 1 0 -1 -1 -1 0 0 0 0]
[ 0 0 0 1 0 1 -1 -1 -2 -2 -1 0 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + x-1*y + y-1*z + y-1 + 4*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + 4*x-2*z-1 + 3*x-2*y-1*z-1 + x-3*z-2 + x-3*y-1*z-2
46 ? x + y + z + x-1*y + y-1*z + y-1 + 3*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + 3*x-2*z-1 + 3*x-2*y-1*z-1 + x-3*z-2 + x-3*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Polytope 2673
Image of polytope 2673 PALP id: 2673
grdb id: 660594
Integer points: [ 1 0 0 0 0 -1 -1 -2 -3 -3 -2 -1 -2 -1 0 -1]
[ 0 1 -1 0 -1 1 1 -1 1 0 1 0 0 -1 0 0]
[ 0 0 0 1 1 -1 0 -1 -2 -2 -1 0 -1 0 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y + y-1*z + x-1*y*z-1 + y-1 + 3*x-1 + 2*x-1*z-1 + 2*x-2*y*z-1 + 2*x-1*y-1 + 3*x-2*z-1 + x-3*y*z-2 + x-2*y-1*z-1 + x-3*z-2
67 ? x + y + z + x-1*y + y-1*z + x-1*y*z-1 + y-1 + 4*x-1 + 2*x-1*z-1 + 2*x-2*y*z-1 + 2*x-1*y-1 + 4*x-2*z-1 + x-3*y*z-2 + x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 96 1 Lattice Minkowski decompositions of facet 96
Polytope 2674
Image of polytope 2674 PALP id: 2674
grdb id: 662260
Integer points: [ 1 0 0 0 0 0 -1 -2 -1 -3 -2 -1 -2 -1 -1 0]
[ 0 1 0 0 -1 -1 0 -1 -2 -2 -2 -1 -1 -1 0 0]
[ 0 0 1 -1 0 1 1 0 1 1 1 0 1 1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + y-1*z + x-1*z + z-1 + y-1 + 2*x-1 + 3*x-1*y-1*z + 3*x-1*y-1 + x-1*y-2*z + 2*x-2*y-1*z + x-2*y-1 + 2*x-2*y-2*z + x-3*y-2*z
8 ? x + y + z + y-1*z + x-1*z + z-1 + y-1 + 2*x-1 + 3*x-1*y-1*z + 2*x-1*y-1 + x-1*y-2*z + 2*x-2*y-1*z + x-2*y-1 + 2*x-2*y-2*z + x-3*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2675
Image of polytope 2675 PALP id: 2675
grdb id: 662247
Integer points: [ 1 0 0 0 0 0 -1 -1 -2 -3 -2 -1 -2 -1 0 -1]
[ 0 1 0 0 -1 -1 -1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 0 -1 -1 1 1 1 0 0 1 0 0 1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + 2*x-1*z + z-1 + y-1 + 3*x-1 + x-1*y-1*z + x-2*z + y-1*z-1 + 3*x-1*y-1 + 2*x-2*y-1*z + x-1*y-1*z-1 + 2*x-2*y-1 + x-3*y-1*z
46 ? x + y + z + 2*x-1*z + z-1 + y-1 + 2*x-1 + x-1*y-1*z + x-2*z + y-1*z-1 + 3*x-1*y-1 + 2*x-2*y-1*z + x-1*y-1*z-1 + 2*x-2*y-1 + x-3*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2676
Image of polytope 2676 PALP id: 2676
grdb id: 662358
Integer points: [ 1 0 0 0 0 0 -1 -1 -2 -3 -2 -1 -2 -1 0 -1]
[ 0 1 0 0 -1 1 0 0 -2 -2 -1 0 -1 -1 0 -1]
[ 0 0 1 -1 0 1 -1 1 -1 -1 0 0 -1 0 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? y*z + x + y + z + x-1*z + z-1 + y-1 + 3*x-1 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*y-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1 + x-3*y-2*z-1
36 rank 3, number 7 y*z + x + y + z + x-1*z + z-1 + y-1 + 3*x-1 + x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*y-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1 + x-3*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2677
Image of polytope 2677 PALP id: 2677
grdb id: 658964
Integer points: [ 1 0 0 -1 -1 -1 1 1 1 -1 -1 0 0 0 0 1]
[ 0 1 0 1 1 0 0 -1 -1 -1 0 0 0 -1 -1 -1]
[ 0 0 1 1 0 1 -1 0 -2 0 0 -1 0 -1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + z + x-1*y*z + x*z-1 + x*y-1 + x-1*y + x-1*z + 2*x*y-1*z-1 + 2*z-1 + 2*y-1 + 2*x-1 + x*y-1*z-2 + 2*y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 2678
Image of polytope 2678 PALP id: 2678
grdb id: 57390
Integer points: [ 1 0 0 1 1 -1 -1 1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 0 -1 1 0 -1 -1 0 -1 0 -1 0 -1 0]
[ 0 0 1 -1 0 0 1 1 1 -1 0 0 0 -1 1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
56 rank 2, number 11 x + y + x*y-1*z + z + x*z-1 + x*y-1 + x-1*y + 2*y-1*z + x-1*z + 2*z-1 + 2*y-1 + x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2679
Image of polytope 2679 PALP id: 2679
grdb id: 57386
Integer points: [ 1 0 0 0 1 1 -1 0 -2 -1 0 0 1 -1 0 -1]
[ 0 1 0 0 -1 -1 0 -1 1 0 -1 -1 -1 0 0 1]
[ 0 0 1 -1 -1 1 -1 1 0 1 -1 0 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + x*y-1*z + z + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + x-2*y + y-1*z-1 + x-1*z-1
31 rank 3, number 3 x + y + x*y-1*z + z + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 3*x-1 + x-2*y + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2680
Image of polytope 2680 PALP id: 2680
grdb id: 59969
Integer points: [ 1 0 0 1 -1 0 -1 -1 0 -1 -1 -1 0 -1 0 0]
[ 0 1 0 0 0 -1 1 -1 -1 0 -1 -1 -1 0 0 0]
[ 0 0 1 -1 1 1 0 1 -1 -1 -1 0 0 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + x*z-1 + x-1*y + y-1*z + x-1*z + 2*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
52 rank 2, number 52 x + y + z + x*z-1 + x-1*y + y-1*z + x-1*z + 2*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2681
Image of polytope 2681 PALP id: 2681
grdb id: 60032
Integer points: [ 1 0 0 1 1 -1 -1 1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 0 -1 0 1 -1 0 -1 -1 0 -1 0 -1 0]
[ 0 0 1 -1 0 1 0 -1 -1 0 -1 0 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + x*z-1 + x*y-1 + x-1*y + x-1*z + x*y-1*z-1 + 2*z-1 + 2*y-1 + x-1 + 2*y-1*z-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2682
Image of polytope 2682 PALP id: 2682
grdb id: 60038
Integer points: [ 1 0 1 0 0 0 -1 -1 0 -1 -1 0 -1 0 0 -1]
[ 0 1 -1 0 -1 1 1 0 -1 1 0 -1 0 0 0 1]
[ 0 0 0 1 1 -1 1 1 -1 -1 -1 0 0 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + y*z-1 + x*y-1 + 2*x-1*y + y-1*z + x-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2683
Image of polytope 2683 PALP id: 2683
grdb id: 60041
Integer points: [ 1 0 0 -1 -1 1 0 -2 -1 1 1 -1 0 0 0 1]
[ 0 1 0 1 1 -1 0 1 0 -2 -2 0 -1 -1 0 -1]
[ 0 0 1 1 0 0 -1 1 1 -1 -2 0 -1 0 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + x*y-1 + x-1*y + x-1*z + x-2*y*z + 2*x*y-1*z-1 + z-1 + 2*y-1 + 3*x-1 + x*y-2*z-1 + 3*y-1*z-1 + x*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2684
Image of polytope 2684 PALP id: 2684
grdb id: 59845
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 1 0 0 -1 -2 -2 -1 0 -1 -1 0]
[ 0 0 1 -1 1 0 -1 1 -1 0 1 0 0 1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
85 rank 3, number 8 x + y + z + x-1*y + y-1*z + x-1*z + z-1 + 2*y-1 + 3*x-1 + 2*x-1*y-1*z + x-1*z-1 + 4*x-1*y-1 + x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
38 ? x + y + z + x-1*y + y-1*z + x-1*z + z-1 + 2*y-1 + 2*x-1 + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Polytope 2685
Image of polytope 2685 PALP id: 2685
grdb id: 59847
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 1 0 -1 1 -1 -2 0 -1 0 -1 0]
[ 0 0 1 -1 -1 0 1 1 -1 -1 0 -1 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + y*z-1 + x-1*y + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
146 ? x + y + z + y*z-1 + x-1*y + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + x-1*y-1*z + 2*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Polytope 2686
Image of polytope 2686 PALP id: 2686
grdb id: 60022
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -2 -2 -1 -2 -1 -1 0]
[ 0 1 0 0 -1 -1 1 1 -1 1 -1 -1 0 0 0 0]
[ 0 0 1 -1 0 1 0 -1 -1 -1 -1 0 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y + y-1*z + z-1 + x-1*y*z-1 + y-1 + 3*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1*z-1
36 rank 3, number 7 x + y + z + x-1*y + y-1*z + z-1 + x-1*y*z-1 + y-1 + 3*x-1 + 3*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2687
Image of polytope 2687 PALP id: 2687
grdb id: 60017
Integer points: [ 1 0 0 0 0 0 1 -1 -1 -2 -2 -1 0 -1 0 -1]
[ 0 1 0 1 0 -1 -1 0 0 -1 -1 -1 -1 0 0 -1]
[ 0 0 1 -1 -1 1 0 1 -1 1 0 0 0 0 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + y*z-1 + x*y-1 + y-1*z + x-1*z + z-1 + 3*y-1 + 2*x-1 + 2*x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-2*y-1*z + x-2*y-1
39 ? x + y + z + y*z-1 + x*y-1 + y-1*z + x-1*z + z-1 + 3*y-1 + 3*x-1 + 2*x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-2*y-1*z + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2688
Image of polytope 2688 PALP id: 2688
grdb id: 60031
Integer points: [ 1 0 0 1 0 0 0 -1 -2 -1 -2 -1 -1 0 0 -1]
[ 0 1 0 0 1 0 -1 0 -1 -2 -2 -1 0 -1 0 -1]
[ 0 0 1 -1 -1 -1 1 1 1 1 1 0 0 0 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*z-1 + y*z-1 + y-1*z + x-1*z + z-1 + 2*y-1 + 2*x-1 + 3*x-1*y-1*z + 2*x-1*y-1 + x-1*y-2*z + x-2*y-1*z + x-2*y-2*z
13 rank 2, number 12 x + y + z + x*z-1 + y*z-1 + y-1*z + x-1*z + z-1 + 2*y-1 + 2*x-1 + 2*x-1*y-1*z + 2*x-1*y-1 + x-1*y-2*z + x-2*y-1*z + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2689
Image of polytope 2689 PALP id: 2689
grdb id: 60034
Integer points: [ 1 0 0 1 0 0 0 -1 -1 -2 -2 -1 0 -1 0 -1]
[ 0 1 0 -1 1 0 -1 1 -1 0 -1 0 -1 -1 0 0]
[ 0 0 1 0 -1 -1 1 0 0 1 1 0 0 1 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + y*z-1 + x*y-1 + x-1*y + y-1*z + 2*x-1*z + z-1 + 2*y-1 + 3*x-1 + 2*x-1*y-1*z + x-2*z + x-1*y-1 + x-2*y-1*z
52 rank 2, number 52 x + y + z + y*z-1 + x*y-1 + x-1*y + y-1*z + 2*x-1*z + z-1 + 2*y-1 + 2*x-1 + 2*x-1*y-1*z + x-2*z + x-1*y-1 + x-2*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2690
Image of polytope 2690 PALP id: 2690
grdb id: 59974
Integer points: [ 1 0 0 1 1 -1 0 1 0 -2 -1 0 -1 0 0 -1]
[ 0 1 0 0 -1 0 -1 -1 -1 1 0 -1 0 0 0 1]
[ 0 0 1 -1 0 1 1 -1 -1 0 -1 0 0 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*z-1 + x*y-1 + 2*x-1*y + y-1*z + x-1*z + x*y-1*z-1 + 2*z-1 + 2*y-1 + 2*x-1 + x-2*y + y-1*z-1 + x-1*z-1
31 rank 3, number 3 x + y + z + x*z-1 + x*y-1 + 2*x-1*y + y-1*z + x-1*z + x*y-1*z-1 + 2*z-1 + 2*y-1 + 3*x-1 + x-2*y + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2691
Image of polytope 2691 PALP id: 2691
grdb id: 60018
Integer points: [ 1 0 1 -1 0 -1 -1 0 -1 0 -1 -1 -1 -1 0 0]
[ 0 1 -1 1 0 1 0 -1 0 -2 -2 -1 0 -1 -1 0]
[ 0 0 0 0 1 1 -1 -1 1 -1 -1 0 0 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y*z + x*y-1 + x-1*y + x-1*z + 2*y-1 + 3*x-1 + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1
146 ? x + y + z + x-1*y*z + x*y-1 + x-1*y + x-1*z + 3*y-1 + 3*x-1 + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2692
Image of polytope 2692 PALP id: 2692
grdb id: 59993
Integer points: [ 1 0 1 0 0 0 -1 -1 0 -2 -2 0 -1 -1 0 -1]
[ 0 1 -1 0 0 -1 0 1 -1 1 1 -1 0 0 0 1]
[ 0 0 0 1 -1 1 1 -1 -1 0 -1 0 -1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + x*y-1 + 2*x-1*y + y-1*z + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-2*y + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 2693
Image of polytope 2693 PALP id: 2693
grdb id: 59484
Integer points: [ 1 0 0 0 0 -1 0 -1 -1 -1 -1 -1 0 -1 -1 0]
[ 0 1 0 0 -1 1 -1 0 1 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 1 0 -1 1 -1 1 -1 0 0 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y + y-1*z + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2694
Image of polytope 2694 PALP id: 2694
grdb id: 59490
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -2 -2 -2 -1 -1 0 -1]
[ 0 1 0 0 -1 -1 0 0 -1 -1 -1 -1 0 -1 0 -1]
[ 0 0 1 -1 0 -1 -1 1 1 1 -1 0 0 0 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*z + z-1 + y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 3*x-1*y-1 + x-2*y-1*z + 2*x-1*y-1*z-1 + 2*x-2*y-1 + x-2*y-1*z-1
67 ? x + y + z + x-1*z + z-1 + y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 3*x-1*y-1 + x-2*y-1*z + 2*x-1*y-1*z-1 + 2*x-2*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2695
Image of polytope 2695 PALP id: 2695
grdb id: 59329
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -1 0 1 -1 -1 -2 -2 0 -1 0 -1 0]
[ 0 0 1 -1 1 -1 -1 1 -1 1 0 -1 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + y*z-1 + y-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + 2*x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2696
Image of polytope 2696 PALP id: 2696
grdb id: 12518
Integer points: [ 1 0 0 1 -1 0 0 -1 0 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 1 0 -1 0 -1 0 -1 -1 -1 0 -1 0]
[ 0 0 1 0 0 -1 -1 -1 1 1 -1 1 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*y-1 + x-1*y + y-1*z + x-1*z + z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
146 ? x + y + z + x*y-1 + x-1*y + y-1*z + x-1*z + z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
94 ? x + y + z + x*y-1 + x-1*y + y-1*z + x-1*z + z-1 + 3*y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
146 ? x + y + z + x*y-1 + x-1*y + y-1*z + x-1*z + z-1 + 3*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 6 Lattice Minkowski decompositions of facet 3
Image of facet 23 2 Lattice Minkowski decompositions of facet 23
Polytope 2697
Image of polytope 2697 PALP id: 2697
grdb id: 12519
Integer points: [ 1 0 0 -1 1 -1 1 0 1 -1 0 -1 -1 0 0 0]
[ 0 1 0 1 -1 1 -1 0 -2 0 -2 -1 0 -1 -1 0]
[ 0 0 1 1 0 0 -1 -1 -1 -1 -1 -1 0 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y*z + x*y-1 + x-1*y + x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + x*y-2*z-1 + 3*y-1*z-1 + x-1*z-1 + y-2*z-1 + x-1*y-1*z-1
13 rank 2, number 12 x + y + z + x-1*y*z + x*y-1 + x-1*y + x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1 + y-2*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2698
Image of polytope 2698 PALP id: 2698
grdb id: 12465
Integer points: [ 1 0 0 0 0 1 1 -1 -1 -1 -1 1 0 0 0 -1]
[ 0 1 0 1 -1 0 -1 1 0 1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 1 -1 0 0 1 -1 1 -1 0 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*z-1 + y*z-1 + x*y-1 + x-1*y + y-1*z + x-1*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 3 6 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2699
Image of polytope 2699 PALP id: 2699
grdb id: 12508
Integer points: [ 1 0 1 0 1 -1 -1 0 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 -1 0 -1 1 1 0 0 0 -1 -1 0 -1 -1 0]
[ 0 0 0 1 -1 1 0 -1 1 -1 0 -1 0 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + x-1*y*z + x*y-1 + x-1*y + x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 3*x-1 + 2*y-1*z-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
52 rank 2, number 52 x + y + z + x-1*y*z + x*y-1 + x-1*y + x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + 2*y-1*z-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2700
Image of polytope 2700 PALP id: 2700
grdb id: 12510
Integer points: [ 1 0 0 1 0 -1 1 0 -1 -1 -1 0 0 -1 0 0]
[ 0 1 0 0 1 1 -1 0 0 1 -1 -2 -1 0 0 -1]
[ 0 0 1 -1 -1 0 0 -1 1 -1 1 1 0 0 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*z-1 + y*z-1 + x*y-1 + x-1*y + 2*y-1*z + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + y-2*z + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2701
Image of polytope 2701 PALP id: 2701
grdb id: 12361
Integer points: [ 1 0 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 1 -1 -1 0 0 1 1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 1 0 -1 1 0 -1 1 -1 0 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + y*z-1 + x-1*y + y-1*z + x-1*z + z-1 + x-1*y*z-1 + y-1 + 3*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2702
Image of polytope 2702 PALP id: 2702
grdb id: 1515
Integer points: [ 1 0 0 -1 0 1 -1 0 -1 1 1 -1 0 0 0 0]
[ 0 1 0 1 1 -1 1 -1 0 0 -1 0 -1 -1 0 0]
[ 0 0 1 1 -1 0 0 1 1 -1 -1 0 -1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + x*z-1 + y*z-1 + x*y-1 + x-1*y + y-1*z + x-1*z + x*y-1*z-1 + 2*z-1 + 2*y-1 + x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 7 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Polytope 2703
Image of polytope 2703 PALP id: 2703
grdb id: 1514
Integer points: [ 1 0 0 1 0 -1 0 0 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 1 1 -1 0 0 1 0 -1 -1 0 -1 0]
[ 0 0 1 0 -1 0 1 -1 1 -1 -1 1 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + y*z-1 + x*y-1 + x-1*y + y-1*z + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
39 ? x + y + z + y*z-1 + x*y-1 + x-1*y + y-1*z + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 6 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Polytope 2704
Image of polytope 2704 PALP id: 2704
grdb id: 545568
Integer points: [ 1 0 0 -1 -4 -2 -3 -1 -2 -3 -1 -2 0 -1 0 -1 0]
[ 0 1 1 0 -3 -1 -2 0 -1 -2 0 -1 1 0 0 -1 0]
[ 0 0 2 2 -4 0 -2 1 -1 -3 0 -2 1 -1 1 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 14 1 none
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Polytope 2705
Image of polytope 2705 PALP id: 2705
grdb id: 545569
Integer points: [ 1 0 0 2 -4 1 0 -1 -2 1 0 -1 -2 -3 1 0 -1]
[ 0 1 0 -4 2 -2 -1 0 1 -3 -2 -1 0 1 -1 0 1]
[ 0 0 1 -1 -1 0 0 0 0 -1 -1 -1 -1 -1 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 168 1 Lattice Minkowski decompositions of facet 168
Image of facet 4 2 none
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Polytope 2706
Image of polytope 2706 PALP id: 2706
grdb id: 545552
Integer points: [ 1 0 0 -5 -1 -2 -3 -4 -1 -2 -3 0 -1 0 -1 -2 0]
[ 0 1 1 -4 0 -1 -2 -3 0 -1 -2 1 0 0 -1 -2 0]
[ 0 0 2 -2 2 1 0 -1 1 0 -1 1 0 1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 3 irreducible and admissible
Image of facet 169 1 none
Polytope 2707
Image of polytope 2707 PALP id: 2707
grdb id: 545553
Integer points: [ 1 1 0 -2 -5 -3 -4 -1 -2 -3 -1 -2 0 -1 -2 0 1]
[ 0 2 0 -2 -2 -2 -2 -1 -1 -1 0 0 1 -1 -1 0 1]
[ 0 0 1 1 -2 0 -1 1 0 -1 0 -1 0 0 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 170 1 none
Image of facet 14 1 none
Polytope 2708
Image of polytope 2708 PALP id: 2708
grdb id: 545567
Integer points: [ 1 0 0 -2 -6 -3 -4 -5 -1 -2 -3 -4 -1 -2 -1 -2 0]
[ 0 1 0 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 1 1 -3 0 -1 -2 1 0 -1 -2 0 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 123 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Polytope 2709
Image of polytope 2709 PALP id: 2709
grdb id: 545573
Integer points: [ 1 0 1 0 -6 -1 -2 -3 -4 -5 0 -1 -2 -3 1 0 -1]
[ 0 1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0]
[ 0 0 2 2 -4 1 0 -1 -2 -3 1 0 -1 -2 1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 171 1 Lattice Minkowski decompositions of facet 171
Image of facet 4 1 none
Image of facet 53 1 irreducible and admissible
Polytope 2710
Image of polytope 2710 PALP id: 2710
grdb id: 530438
Integer points: [ 1 0 0 -1 1 -1 0 0 -1 0 -1 -1 1 0 0 0 0]
[ 0 1 1 0 -2 0 -1 -1 0 -1 0 0 -1 0 0 0 1]
[ 0 0 2 2 -2 -2 0 -1 1 -2 0 -1 -1 1 0 -1 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
11 rank 2, number 6 y*z2 + 2*y*z + x + y + 2*z + x-1*z2 + 4*x-1*z + 2*x*y-1*z-1 + 2*z-1 + 2*y-1 + 6*x-1 + 4*y-1*z-1 + 4*x-1*z-1 + x*y-2*z-2 + 2*y-1*z-2 + x-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Polytope 2711
Image of polytope 2711 PALP id: 2711
grdb id: 530436
Integer points: [ 1 0 0 0 -2 -2 -2 -2 -2 -1 -1 -1 0 -1 -1 -1 0]
[ 0 1 0 -2 -3 1 0 -1 -2 0 -1 -2 -1 1 0 -1 0]
[ 0 0 1 -1 -2 2 1 0 -1 1 0 -1 0 1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 172 1 none
Polytope 2712
Image of polytope 2712 PALP id: 2712
grdb id: 530437
Integer points: [ 1 0 0 -2 2 -2 -2 -1 -1 -1 0 0 1 1 -1 0 1]
[ 0 1 0 2 -4 0 1 1 0 -1 -1 -2 -2 -3 1 0 -1]
[ 0 0 1 1 -1 -1 0 1 0 -1 0 -1 0 -1 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 4 2 none
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 2713
Image of polytope 2713 PALP id: 2713
grdb id: 530452
Integer points: [ 1 0 0 1 1 -4 -2 -1 0 1 -3 -2 -1 0 -1 0 1]
[ 0 1 0 -1 -3 2 1 0 -1 -2 1 0 -1 -2 1 0 -1]
[ 0 0 1 1 -1 -1 0 0 0 0 -1 -1 -1 -1 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Image of facet 58 1 Lattice Minkowski decompositions of facet 58
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 4 2 none
Polytope 2714
Image of polytope 2714 PALP id: 2714
grdb id: 530444
Integer points: [ 1 0 0 2 -3 -1 -2 -2 -1 0 -1 0 1 1 -1 0 1]
[ 0 1 0 -4 3 -1 1 2 0 -2 1 -1 -3 -2 1 0 -1]
[ 0 0 1 -1 1 -1 0 1 0 -1 1 0 -1 0 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 4 2 none
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Polytope 2715
Image of polytope 2715 PALP id: 2715
grdb id: 530443
Integer points: [ 1 0 1 -3 2 -4 0 -1 -2 1 0 -1 -2 -3 1 0 -1]
[ 0 1 0 0 -1 -1 0 0 0 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 2 -2 3 -3 1 0 -1 2 1 0 -1 -2 1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 53 1 irreducible and admissible
Image of facet 173 1 Lattice Minkowski decompositions of facet 173
Image of facet 6 2 none
Image of facet 13 1 irreducible and admissible
Polytope 2716
Image of polytope 2716 PALP id: 2716
grdb id: 530446
Integer points: [ 1 1 0 -2 0 -2 -1 -1 0 -2 -1 0 -1 0 1 0 1]
[ 0 3 0 -2 -2 -4 -2 -3 -1 -3 -1 1 -2 0 2 -1 1]
[ 0 0 1 -1 1 1 1 1 1 0 0 0 0 0 0 0 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 37 2 none
Polytope 2717
Image of polytope 2717 PALP id: 2717
grdb id: 529877
Integer points: [ 1 0 0 -2 -3 -3 -3 -3 -2 -2 -2 -1 -1 -1 -1 -1 0]
[ 0 1 0 1 0 -3 -1 -2 0 -1 -2 1 0 -1 0 -1 0]
[ 0 0 1 -2 -2 1 -1 0 -1 0 1 -1 0 1 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 14 1 none
Image of facet 174 1 Lattice Minkowski decompositions of facet 174
Image of facet 9 1 irreducible and admissible
Polytope 2718
Image of polytope 2718 PALP id: 2718
grdb id: 529901
Integer points: [ 1 0 0 1 -3 0 0 0 -1 -1 -1 -2 -2 1 0 0 -1]
[ 0 1 0 -2 0 -3 -2 -1 -2 -1 0 -1 0 -1 -1 0 0]
[ 0 0 1 -2 1 -2 -1 0 -1 0 1 0 1 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 9 1 irreducible and admissible
Image of facet 42 1 none
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2719
Image of polytope 2719 PALP id: 2719
grdb id: 529908
Integer points: [ 1 0 0 -3 -3 -1 -3 -2 -2 -2 -1 -1 0 -1 -1 0 0]
[ 0 1 1 -2 -2 0 -2 -1 -1 -1 0 0 1 -1 -1 0 0]
[ 0 0 2 -2 0 2 -1 1 0 -1 1 0 1 0 -1 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
68 ? y*z2 + 2*y*z + x + y + 2*z + x-1*z2 + 2*x-1*z + x-1 + 2*x-1*y-1 + 2*x-2*y-1*z + 2*x-1*y-1*z-1 + 4*x-2*y-1 + 2*x-2*y-1*z-1 + x-3*y-2 + 2*x-3*y-2*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 3 irreducible and admissible
Image of facet 175 1 Lattice Minkowski decompositions of facet 175
Polytope 2720
Image of polytope 2720 PALP id: 2720
grdb id: 529997
Integer points: [ 1 0 0 -1 -1 -3 -2 -1 -2 -1 -2 -1 0 -1 0 0 0]
[ 0 1 1 -2 0 -2 -1 0 -2 -1 -1 0 1 -1 0 -1 0]
[ 0 0 2 -2 2 0 0 0 -1 -1 1 1 1 0 0 -1 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 14 1 none
Polytope 2721
Image of polytope 2721 PALP id: 2721
grdb id: 529907
Integer points: [ 1 0 0 -1 -1 -3 -1 0 -2 -1 -2 -1 -2 0 0 -1 0]
[ 0 1 1 0 0 -2 0 1 -1 0 -1 0 -1 0 0 -1 0]
[ 0 0 2 -2 2 -2 1 1 0 0 -1 -1 -2 1 0 -1 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 y*z2 + 2*y*z + x + y + 2*z + x-1*z2 + 2*x-1*z + 2*z-1 + 3*x-1 + 2*x-1*z-1 + x-1*z-2 + 2*x-1*y-1*z-1 + 2*x-2*y-1 + 2*x-2*y-1*z-1 + 2*x-2*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 3 irreducible and admissible
Image of facet 176 1 Lattice Minkowski decompositions of facet 176
Polytope 2722
Image of polytope 2722 PALP id: 2722
grdb id: 530429
Integer points: [ 1 0 1 -3 -2 -3 -3 -2 -2 -1 -1 -1 0 -1 -1 0 1]
[ 0 1 0 0 1 -2 -1 0 -1 1 0 -1 0 0 -1 0 0]
[ 0 0 2 -2 -2 0 -1 -1 0 -1 0 1 1 -1 0 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 3 irreducible and admissible
Image of facet 177 1 none
Polytope 2723
Image of polytope 2723 PALP id: 2723
grdb id: 529956
Integer points: [ 1 0 1 -2 -1 -3 0 -1 -2 -1 0 -1 -2 1 0 -1 0]
[ 0 1 0 1 -2 0 0 0 0 1 -1 -1 -1 0 0 0 -1]
[ 0 0 2 -2 0 -2 1 0 -1 -1 1 0 -1 1 0 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x*z2 + 2*x*z + x + y + 4*z + 2*y-1*z + 2*x-1*y*z-1 + 2*y-1 + 6*x-1 + 2*x-1*z-1 + 4*x-1*y-1 + x-2*y*z-2 + 4*x-2*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 2724
Image of polytope 2724 PALP id: 2724
grdb id: 530002
Integer points: [ 1 0 1 -2 1 0 1 0 0 1 0 -1 1 0 -1 0 -1]
[ 0 1 0 0 -2 -2 -1 -1 0 -1 -1 -1 0 0 0 0 0]
[ 0 0 2 -1 -2 -3 -1 -2 -1 0 -1 -2 1 0 -1 1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 9 1 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 14 1 none
Polytope 2725
Image of polytope 2725 PALP id: 2725
grdb id: 529962
Integer points: [ 1 1 0 0 -3 -3 -2 -1 -3 -2 -1 0 -2 -1 -1 0 1]
[ 0 2 0 2 -1 -3 -2 -1 -2 -1 0 1 0 1 -1 0 1]
[ 0 0 1 -1 -1 1 1 1 0 0 0 0 -1 -1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 178 1 Lattice Minkowski decompositions of facet 178
Image of facet 4 1 none
Image of facet 9 2 irreducible and admissible
Polytope 2726
Image of polytope 2726 PALP id: 2726
grdb id: 529845
Integer points: [ 1 0 0 -2 -1 -4 -3 -2 -3 -2 -1 -1 -2 -1 0 -1 0]
[ 0 1 0 0 -2 -2 -2 -2 -1 -1 -1 0 -1 -1 -1 0 0]
[ 0 0 1 1 -2 1 0 -1 1 0 -1 0 1 0 -1 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 102 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2727
Image of polytope 2727 PALP id: 2727
grdb id: 529930
Integer points: [ 1 0 0 -2 0 -4 -1 -2 -3 -1 -2 -3 0 -1 -2 0 -1]
[ 0 1 0 0 -2 -4 -1 -2 -3 0 -1 -2 -1 -2 -3 0 -1]
[ 0 0 1 -1 1 1 1 1 1 0 0 0 1 1 1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
69 ? x + y + z + 2*y-1*z + 3*x-1 + y-2*z + 4*x-1*y-1*z + 2*x-1*y-1 + 4*x-1*y-2*z + x-2*z-1 + 4*x-2*y-1 + 6*x-2*y-2*z + 2*x-2*y-3*z + 2*x-3*y-2 + 4*x-3*y-3*z + x-4*y-4*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 2728
Image of polytope 2728 PALP id: 2728
grdb id: 529927
Integer points: [ 1 0 0 0 -2 -4 -1 -2 -3 -1 -2 -3 0 -1 -2 0 -1]
[ 0 1 0 -2 0 -4 -1 -2 -3 0 -1 -2 -1 -2 -3 0 -1]
[ 0 0 1 -1 -1 -3 0 -1 -2 0 -1 -2 0 -1 -2 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + 2*y-1 + 2*x-1 + 4*x-1*y-1 + y-2*z-1 + 3*x-1*y-1*z-1 + x-2*z-1 + 4*x-1*y-2*z-1 + 4*x-2*y-1*z-1 + 6*x-2*y-2*z-1 + 2*x-2*y-3*z-2 + 2*x-3*y-2*z-2 + 4*x-3*y-3*z-2 + x-4*y-4*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 32 2 Lattice Minkowski decompositions of facet 32
Polytope 2729
Image of polytope 2729 PALP id: 2729
grdb id: 529925
Integer points: [ 1 0 0 0 -2 -4 -3 -2 -1 -2 -1 0 -3 -2 -1 -1 0]
[ 0 1 0 -2 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 0 1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + 2*y-1 + 2*x-1 + 4*x-1*y-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-2*z-1 + 2*x-2*y-1 + 4*x-1*y-2*z-1 + 4*x-2*y-1*z-1 + 6*x-2*y-2*z-1 + 2*x-3*y-1*z-1 + 4*x-3*y-2*z-1 + x-4*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 32 2 Lattice Minkowski decompositions of facet 32
Polytope 2730
Image of polytope 2730 PALP id: 2730
grdb id: 529994
Integer points: [ 1 1 -1 0 -2 1 1 0 -1 0 -1 1 1 0 0 -1 0]
[ 0 2 -2 0 -2 4 3 1 -1 2 0 1 2 0 1 -1 -1]
[ 0 0 0 1 1 -2 -1 0 1 -1 0 0 -1 0 -1 0 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 14 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2731
Image of polytope 2731 PALP id: 2731
grdb id: 530179
Integer points: [ 1 0 0 -3 -1 -3 -3 -3 -3 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 0 -2 -1 -2 -2 -2 -2 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 1 -1 2 3 2 1 0 2 1 0 1 0 1 0 0]
Degree: 46
Hilbert function: 1 + 26 t + 120 t2 + 329 t3 + 699 t4 + 1276 t5 + 2106 t6 + 3235 t7 + 4709 t8 + 6574 t9 + 8876 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 64 1 none
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 121 1 none
Polytope 2732
Image of polytope 2732 PALP id: 2732
grdb id: 529833
Integer points: [ 1 0 0 -3 -1 -3 -2 -3 -2 -1 -3 -2 -1 -1 0 -1 0]
[ 0 1 0 -1 -2 -4 -3 -3 -2 -1 -2 -1 0 -2 -1 -1 0]
[ 0 0 1 -1 2 2 2 1 1 1 0 0 0 1 1 0 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 179 1 none
Image of facet 14 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2733
Image of polytope 2733 PALP id: 2733
grdb id: 529945
Integer points: [ 1 0 0 0 -3 -4 -1 -2 -3 0 -1 -2 0 -1 -2 0 -1]
[ 0 1 -1 1 0 1 1 1 1 0 0 0 1 1 1 0 0]
[ 0 0 0 2 -2 -2 1 0 -1 1 0 -1 1 0 -1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 y*z2 + 2*y*z + x + y + 2*z + 4*x-1*y*z + 4*x-1*y + y-1 + 4*x-1 + 6*x-2*y + 2*x-1*z-1 + 2*x-2*y*z-1 + 3*x-2*z-1 + 4*x-3*y*z-1 + x-3*z-2 + x-4*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 3 irreducible and admissible
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2734
Image of polytope 2734 PALP id: 2734
grdb id: 529946
Integer points: [ 1 0 1 -2 0 -4 -1 0 -2 -1 -3 -2 -1 -3 1 0 -1]
[ 0 1 0 1 -1 -1 -1 0 -1 0 -1 0 1 0 0 0 0]
[ 0 0 2 -2 2 -2 1 1 0 0 -1 -1 -1 -2 1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 180 1 Lattice Minkowski decompositions of facet 180
Image of facet 13 1 irreducible and admissible
Image of facet 4 1 none
Polytope 2735
Image of polytope 2735 PALP id: 2735
grdb id: 530386
Integer points: [ 1 0 0 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0]
[ 0 1 0 2 1 -4 0 -1 -2 -3 1 0 -1 -2 1 0 -1]
[ 0 0 1 -2 -2 3 -1 0 1 2 -1 0 1 2 -1 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 43 1 irreducible and admissible
Image of facet 4 1 none
Image of facet 181 1 Lattice Minkowski decompositions of facet 181
Polytope 2736
Image of polytope 2736 PALP id: 2736
grdb id: 530204
Integer points: [ 1 0 0 -2 -5 -1 -2 -3 -4 -1 -2 -3 -1 0 -1 -2 0]
[ 0 1 0 0 -2 -2 -2 -2 -2 -1 -1 -1 0 -1 -1 -1 0]
[ 0 0 1 -1 -2 2 1 0 -1 1 0 -1 0 1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 182 1 none
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 2737
Image of polytope 2737 PALP id: 2737
grdb id: 530243
Integer points: [ 1 0 1 -3 -5 1 0 -1 -2 -3 -4 0 -1 -2 1 0 -1]
[ 0 1 0 0 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 0 2 -2 -3 3 2 1 0 -1 -2 1 0 -1 1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
75 ? x*z2 + x*y-1*z3 + 2*x*z + x + y + 5*z + 6*y-1*z2 + 8*x-1 + 15*x-1*y-1*z + 2*x-1*z-1 + 5*x-2*z-1 + 20*x-2*y-1 + x-3*z-2 + 15*x-3*y-1*z-1 + 6*x-4*y-1*z-2 + x-5*y-1*z-3
24 ? x*z2 + x*y-1*z3 + 2*x*z + x + y + 4*z + 6*y-1*z2 + 6*x-1 + 15*x-1*y-1*z + 2*x-1*z-1 + 4*x-2*z-1 + 20*x-2*y-1 + x-3*z-2 + 15*x-3*y-1*z-1 + 6*x-4*y-1*z-2 + x-5*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 53 1 irreducible and admissible
Image of facet 183 1 Lattice Minkowski decompositions of facet 183
Polytope 2738
Image of polytope 2738 PALP id: 2738
grdb id: 529973
Integer points: [ 1 0 0 -2 -4 -6 -3 -4 -5 -1 -2 -3 -1 -2 -3 0 -1]
[ 0 1 0 -1 -4 -5 -2 -3 -4 -1 -2 -3 0 -1 -2 0 -1]
[ 0 0 1 0 -3 -4 -1 -2 -3 0 -1 -2 0 -1 -2 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 134 1 Lattice Minkowski decompositions of facet 134
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 8 1 none
Image of facet 13 1 irreducible and admissible
Polytope 2739
Image of polytope 2739 PALP id: 2739
grdb id: 530174
Integer points: [ 1 0 0 -1 -2 -6 -3 -4 -5 -2 -3 -4 -1 -2 -1 -2 0]
[ 0 1 0 0 -1 -5 -2 -3 -4 -1 -2 -3 0 -1 -1 -2 0]
[ 0 0 1 1 1 -3 0 -1 -2 0 -1 -2 0 -1 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 148 1 none
Image of facet 64 1 none
Polytope 2740
Image of polytope 2740 PALP id: 2740
grdb id: 529838
Integer points: [ 1 0 0 -1 -5 -7 -5 -3 -6 -4 -2 -3 -1 -3 -1 -2 0]
[ 0 1 0 -1 -2 -4 -3 -2 -3 -2 -1 -1 0 -2 -1 -1 0]
[ 0 0 1 1 -2 -2 -1 0 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 184 1 Lattice Minkowski decompositions of facet 184
Image of facet 14 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2741
Image of polytope 2741 PALP id: 2741
grdb id: 530395
Integer points: [ 1 0 -1 0 -3 -5 -1 -2 -3 -4 -1 -2 -1 -2 -3 0 -1]
[ 0 1 -1 0 4 5 1 2 3 4 2 3 0 1 2 0 1]
[ 0 0 0 1 -3 -4 0 -1 -2 -3 -1 -2 0 -1 -2 0 -1]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 8 1 none
Image of facet 146 1 Lattice Minkowski decompositions of facet 146
Image of facet 9 1 irreducible and admissible
Image of facet 73 1 none
Polytope 2742
Image of polytope 2742 PALP id: 2742
grdb id: 529800
Integer points: [ 1 0 1 -5 3 -6 -2 0 2 -3 -1 1 -4 -2 1 -2 0]
[ 0 1 0 -2 1 -2 -1 0 1 -1 0 1 -1 0 0 -1 0]
[ 0 0 2 -2 3 -3 0 1 2 -1 0 1 -2 -1 1 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x3*y*z3 + 3*x2*y*z2 + 3*x*y*z + x*z2 + 2*x*z + x + y + 5*z + 7*x-1 + 3*x-2*z-1 + 2*x-2*y-1 + 2*x-2*y-1*z-1 + 5*x-3*y-1*z-1 + 3*x-4*y-1*z-2 + x-5*y-2*z-2 + x-6*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 174 1 Lattice Minkowski decompositions of facet 174
Image of facet 9 2 irreducible and admissible
Polytope 2743
Image of polytope 2743 PALP id: 2743
grdb id: 529809
Integer points: [ 1 0 1 0 -5 -6 -4 -2 -3 -1 -2 0 -3 -1 -2 0 1]
[ 0 1 -2 0 2 3 2 1 1 0 0 -1 2 1 1 0 -1]
[ 0 0 0 1 -2 -2 -1 0 -1 0 -1 0 -1 0 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 104 1 none
Image of facet 14 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2744
Image of polytope 2744 PALP id: 2744
grdb id: 529929
Integer points: [ 1 0 0 -2 -2 -8 -2 -4 -6 -1 -3 -5 -1 -3 -5 0 -2]
[ 0 1 0 0 -2 -4 -1 -2 -3 0 -1 -2 -1 -2 -3 0 -1]
[ 0 0 1 -1 -1 -3 0 -1 -2 0 -1 -2 0 -1 -2 0 -1]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 80 1 none
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 2745
Image of polytope 2745 PALP id: 2745
grdb id: 529101
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 1 -2 0 0 0 0 0 -1 -1 -1 1 0 0 0 -1]
[ 0 0 2 -2 2 -2 1 0 -1 0 -1 -2 1 1 0 -1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 y*z2 + 2*y*z + x + y + 2*z + x-1*z2 + 4*x-1*z + 2*z-1 + 6*x-1 + 2*y-1*z-1 + 4*x-1*z-1 + 2*x-1*y-1 + x-1*z-2 + 4*x-1*y-1*z-1 + 2*x-1*y-1*z-2 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 3 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 2746
Image of polytope 2746 PALP id: 2746
grdb id: 528912
Integer points: [ 1 0 0 -1 -1 -4 -1 -1 -2 -2 -2 -3 -3 0 -1 -1 -2]
[ 0 1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 1 -1 2 2 0 1 0 1 2 1 2 0 0 1 1]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 14 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2747
Image of polytope 2747 PALP id: 2747
grdb id: 474432
Integer points: [ 1 0 0 0 -2 -1 -2 -2 -2 -1 -1 -1 0 -1 -1 0 0]
[ 0 1 0 -2 2 -2 -1 0 1 -1 0 1 -1 0 1 -1 0]
[ 0 0 1 -1 1 -2 -2 -1 0 -1 0 1 0 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 14 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2748
Image of polytope 2748 PALP id: 2748
grdb id: 474431
Integer points: [ 1 0 0 -1 -2 0 -2 -2 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 1 0 1 1 -3 -1 0 -2 -1 0 -2 -1 0 1 -1 0]
[ 0 0 1 1 0 -2 -2 -1 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + x-1*y*z + 2*x-1*y + 3*y-1 + 4*x-1 + x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + 3*y-2*z-1 + 5*x-1*y-1*z-1 + 2*x-2*z-1 + y-3*z-2 + 2*x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 9 1 irreducible and admissible
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 2749
Image of polytope 2749 PALP id: 2749
grdb id: 474442
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -2 2 2 -3 -1 0 1 -2 -1 0 1 -1 0 1]
[ 0 0 1 2 -2 -3 2 1 0 -1 1 0 -1 -2 1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 43 1 irreducible and admissible
Image of facet 157 1 Lattice Minkowski decompositions of facet 157
Image of facet 6 2 none
Polytope 2750
Image of polytope 2750 PALP id: 2750
grdb id: 474445
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 0 -1 -1 -1 0 0 0]
[ 0 1 1 -1 0 -1 0 0 0 0 1 -1 -1 -1 0 0 0]
[ 0 0 2 1 2 -3 -2 1 0 -1 1 0 -1 -2 1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 13 1 irreducible and admissible
Image of facet 6 2 none
Image of facet 134 1 Lattice Minkowski decompositions of facet 134
Polytope 2751
Image of polytope 2751 PALP id: 2751
grdb id: 474437
Integer points: [ 1 0 0 0 -1 -2 -4 -3 -2 -3 -2 -1 -1 -2 -1 -1 0]
[ 0 1 -1 0 1 -1 1 1 1 0 0 0 -1 1 1 0 0]
[ 0 0 0 1 1 -2 -2 -1 0 -2 -1 0 -1 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 14 1 none
Polytope 2752
Image of polytope 2752 PALP id: 2752
grdb id: 474446
Integer points: [ 1 -1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0]
[ 0 0 1 1 -2 0 -2 -1 -1 0 -1 0 -1 0 1 0 1]
[ 0 0 0 3 -3 2 -2 0 -1 1 -1 1 -2 0 2 -1 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 y*z3 + x*z2 + 3*y*z2 + 2*x*z + 3*y*z + x + y + z + 2*x*y-1 + 2*x*y-1*z-1 + 3*z-1 + x-1 + y-1*z-1 + x*y-2*z-2 + 3*y-1*z-2 + y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 2 irreducible and admissible
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 48 1 Lattice Minkowski decompositions of facet 48
Polytope 2753
Image of polytope 2753 PALP id: 2753
grdb id: 474441
Integer points: [ 1 0 1 1 -2 -2 0 -1 -1 0 -1 0 -1 0 1 0 1]
[ 0 1 1 3 -3 -1 3 1 0 2 -1 1 -2 0 2 -1 1]
[ 0 0 2 3 -3 -2 2 0 -1 1 -1 1 -2 0 2 -1 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
51 rank 2, number 7 x*y3*z3 + 3*x*y2*z2 + y3*z2 + x*y*z2 + 3*x*y*z + 2*y2*z + y*z + x + y + 2*x-1*y + 3*y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1*z-1 + 3*x-1*y-2*z-2 + x-2*y-1*z-2 + x-2*y-3*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 2 irreducible and admissible
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 47 1 Lattice Minkowski decompositions of facet 47
Polytope 2754
Image of polytope 2754 PALP id: 2754
grdb id: 474444
Integer points: [ 1 0 2 -3 -1 -3 1 -2 -1 0 -2 -1 0 1 -1 0 1]
[ 0 1 2 -2 -1 -2 2 -1 0 1 -1 0 0 1 -1 0 1]
[ 0 0 3 -3 0 -2 2 -1 0 1 -2 -1 1 2 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 9 2 irreducible and admissible
Image of facet 90 2 Lattice Minkowski decompositions of facet 90
Image of facet 6 2 none
Polytope 2755
Image of polytope 2755 PALP id: 2755
grdb id: 474429
Integer points: [ 1 1 -1 0 1 -3 1 -1 1 -1 1 0 -2 0 0 -1 1]
[ 0 2 -2 0 0 -3 3 -1 1 0 2 -1 -2 0 1 -1 1]
[ 0 0 0 1 -1 1 -1 0 -1 0 -1 0 1 0 0 1 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x*y3*z-1 + x*y2 + 3*x*y2*z-1 + 2*x*y + 3*x*y*z-1 + x + 3*y + z + x*z-1 + 2*y-1 + 2*x-1 + 3*x-1*y-1*z + 3*x-1*y-1 + x-1*y-2 + 3*x-2*y-2*z + x-3*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Polytope 2756
Image of polytope 2756 PALP id: 2756
grdb id: 474373
Integer points: [ 1 0 -1 1 0 -2 -4 -1 -3 -2 -1 0 -3 -2 -1 0 1]
[ 0 1 -1 0 1 1 -1 1 0 0 0 0 -1 -1 0 0 0]
[ 0 0 0 2 1 -1 -3 0 -2 -1 0 1 -2 -1 -1 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 1 none
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 158 1 Lattice Minkowski decompositions of facet 158
Image of facet 9 1 irreducible and admissible
Polytope 2757
Image of polytope 2757 PALP id: 2757
grdb id: 474447
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0]
[ 0 1 1 -1 -1 -2 -2 -2 -1 -1 -1 -1 0 0 0 1 1]
[ 0 0 3 0 -3 -4 -2 -3 -1 -2 -1 -2 1 0 -1 2 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 2 none
Image of facet 9 1 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2758
Image of polytope 2758 PALP id: 2758
grdb id: 471968
Integer points: [ 1 0 1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 -1 0 2 -1 -1 -1 -1 0 0 0 1 1 -1 -1 0]
[ 0 0 0 1 -1 -1 2 1 0 1 0 -1 0 -1 1 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 14 1 none
Polytope 2759
Image of polytope 2759 PALP id: 2759
grdb id: 473302
Integer points: [ 1 0 0 -2 1 -2 -1 0 -1 0 -2 -1 0 1 -1 0 -1]
[ 0 1 0 1 -2 -1 -2 -2 -1 -1 0 0 -1 -1 0 0 1]
[ 0 0 1 0 0 -2 -2 -1 -1 0 -1 0 -1 0 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + 2*x*y-1 + 2*x-1*y + x*y-2 + y-1 + 2*x-1 + x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + 2*y-2*z-1 + 3*x-1*y-1*z-1 + 2*x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
52 rank 2, number 52 x + y + z + 2*x*y-1 + 2*x-1*y + x*y-2 + 2*y-1 + x-1 + x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + 2*y-2*z-1 + 3*x-1*y-1*z-1 + 2*x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 112 1 Lattice Minkowski decompositions of facet 112
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 2760
Image of polytope 2760 PALP id: 2760
grdb id: 472027
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 -1 -2 -2 0 -1 0 -1 -2 -1 -2 0 -1 -1]
[ 0 0 1 1 1 -2 1 0 -1 1 0 -1 1 0 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y*z + y-1*z + 3*x-1*z + 3*y-1 + 3*x-1 + 3*x-1*y-1*z + 2*y-1*z-1 + 6*x-1*y-1 + x-1*y-2*z + 3*x-1*y-1*z-1 + 3*x-1*y-2 + 3*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Polytope 2761
Image of polytope 2761 PALP id: 2761
grdb id: 473110
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 -1 0 0]
[ 0 1 0 -1 -2 0 2 1 0 1 0 -1 1 0 -1 0 -1]
[ 0 0 1 1 0 -2 -2 -1 0 -2 -1 0 -1 0 -1 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + 2*y*z-1 + x-1*y2*z-2 + 2*z-1 + 3*x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + 2*x-1*y*z-2 + 4*x-1*z-1 + 2*x-1*y-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Polytope 2762
Image of polytope 2762 PALP id: 2762
grdb id: 473300
Integer points: [ 1 0 0 0 -1 -2 -2 -2 -1 -1 -1 0 -1 -1 0 0 0]
[ 0 1 -1 1 -2 1 -1 0 1 0 -1 0 1 0 1 0 -1]
[ 0 0 0 2 -2 0 -2 -1 1 0 -1 1 0 -1 1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 y*z2 + 2*y*z + x + y + 2*z + 2*x-1*y*z + 2*x-1*y + y-1 + 4*x-1 + x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1*z-1 + 2*x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
31 rank 3, number 3 y*z2 + 2*y*z + x + y + 2*z + 2*x-1*y*z + 2*x-1*y + y-1 + 5*x-1 + x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + 4*x-1*y-1*z-1 + 2*x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 3 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Polytope 2763
Image of polytope 2763 PALP id: 2763
grdb id: 472749
Integer points: [ 1 0 0 0 0 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0]
[ 0 0 0 1 -1 -2 2 1 0 -1 1 0 -1 1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 80 1 none
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 2764
Image of polytope 2764 PALP id: 2764
grdb id: 473336
Integer points: [ 1 1 0 -1 -1 -2 1 1 0 -1 1 0 1 0 0 -1 0]
[ 0 2 0 0 -2 -2 0 1 -1 -1 0 0 1 1 -1 -1 0]
[ 0 0 1 0 0 1 -2 0 0 1 -1 0 -1 0 -1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x*y2 + 2*x*y + 2*x*y*z-1 + x + 2*y + z + 2*x*z-1 + x*z-2 + 2*z-1 + 2*y-1 + x-1 + 2*x-1*y-1*z + 2*y-1*z-1 + 2*x-1*y-1 + x-1*y-2 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 3 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2765
Image of polytope 2765 PALP id: 2765
grdb id: 472143
Integer points: [ 1 0 0 -1 -2 -3 -3 -3 -3 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 0 1 1 0 -3 -1 -2 0 -1 -2 0 -1 0 -1 0]
[ 0 0 1 0 -1 -2 -2 -2 -2 -1 -1 -1 0 0 -1 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Image of facet 153 1 Lattice Minkowski decompositions of facet 153
Polytope 2766
Image of polytope 2766 PALP id: 2766
grdb id: 473062
Integer points: [ 1 0 0 -1 -1 -3 -3 -2 -1 -3 -2 -1 -2 -1 0 -1 0]
[ 0 1 0 1 -2 0 -2 0 0 -1 -1 -1 -2 0 0 -1 -1]
[ 0 0 1 -1 0 -2 -2 -1 0 -2 -1 0 -1 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
25 ? x + y + z + x-1*y*z-1 + 2*y-1 + 3*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2 + 4*x-2*y-1*z-1 + x-3*z-2 + 2*x-2*y-2*z-1 + 2*x-3*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Polytope 2767
Image of polytope 2767 PALP id: 2767
grdb id: 472633
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 1 -1 -3 0 1 0 -1 -2 0 -1 -2 0 -1]
[ 0 0 1 -1 1 1 -1 1 0 0 0 0 -1 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 13 1 irreducible and admissible
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 2768
Image of polytope 2768 PALP id: 2768
grdb id: 472138
Integer points: [ 1 0 0 0 -1 -3 -3 -2 -1 -3 -2 -1 -3 -2 -1 0 -1]
[ 0 1 0 1 1 -2 1 1 1 0 0 0 -1 -1 0 0 -1]
[ 0 0 1 -1 -2 0 -3 -2 -1 -2 -1 0 -1 0 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 124 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2769
Image of polytope 2769 PALP id: 2769
grdb id: 473155
Integer points: [ 1 0 0 0 -1 -1 -3 -2 -1 -2 -1 -2 -1 -1 0 0 0]
[ 0 1 0 1 -2 0 -2 -1 0 -2 -1 -1 0 -1 0 -1 0]
[ 0 0 1 1 0 -2 -2 -1 0 -1 0 -2 -1 -1 0 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 y*z + x + y + z + 2*z-1 + 2*y-1 + 3*x-1 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*z-2 + 4*x-1*y-1*z-1 + x-1*y-2 + 3*x-2*y-1*z-1 + 2*x-2*y-1*z-2 + 2*x-2*y-2*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Polytope 2770
Image of polytope 2770 PALP id: 2770
grdb id: 472067
Integer points: [ 1 0 0 1 1 0 -3 0 0 -1 -1 -1 -2 -2 0 0 -1]
[ 0 1 0 -1 -2 -3 0 -2 -1 -2 -1 0 -1 0 -1 0 0]
[ 0 0 1 0 -1 -2 -2 -1 0 -2 -1 0 -2 -1 -1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 66 1 none
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Polytope 2771
Image of polytope 2771 PALP id: 2771
grdb id: 472026
Integer points: [ 1 0 1 0 1 -3 0 0 -1 0 -1 -2 -1 -2 0 0 -1]
[ 0 1 -1 0 -2 0 -3 -1 0 -2 -1 0 -2 -1 0 -1 0]
[ 0 0 0 1 -1 1 -2 0 1 -1 0 1 -1 0 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Image of facet 153 1 Lattice Minkowski decompositions of facet 153
Polytope 2772
Image of polytope 2772 PALP id: 2772
grdb id: 473102
Integer points: [ 1 0 0 1 -2 -1 -2 0 -1 -2 0 -1 0 -1 1 0 -1]
[ 0 1 0 0 0 -2 -2 -1 -1 -1 0 0 -1 -1 0 0 0]
[ 0 0 1 -2 1 2 3 0 1 2 -1 0 1 2 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + 2*x*z-1 + 2*y-1*z + 2*x-1*z + 2*x-1*y-1*z2 + x*z-2 + 3*z-1 + 2*y-1 + 3*x-1 + 4*x-1*y-1*z + x-2*z + x-1*y-2*z2 + 2*x-2*y-1*z2 + x-2*y-2*z3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2773
Image of polytope 2773 PALP id: 2773
grdb id: 471922
Integer points: [ 1 0 0 -2 -1 0 -3 -1 0 -1 -2 0 -1 -2 0 -1 0]
[ 0 1 0 2 -2 -3 2 1 -1 0 1 -2 -1 0 0 1 -1]
[ 0 0 1 -1 0 1 -2 0 1 0 -1 1 0 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + 2*x-1*y + 3*y-1*z + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 6*x-1 + 3*y-2*z + 4*x-2*y*z-1 + 5*x-1*y-1 + y-3*z + x-3*y2*z-2 + 2*x-2*z-1 + x-1*y-2
52 rank 2, number 52 x + y + z + 2*x-1*y + 3*y-1*z + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 5*x-1 + 3*y-2*z + 3*x-2*y*z-1 + 4*x-1*y-1 + y-3*z + x-3*y2*z-2 + 2*x-2*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 155 1 Lattice Minkowski decompositions of facet 155
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2774
Image of polytope 2774 PALP id: 2774
grdb id: 472129
Integer points: [ 1 0 0 -1 -3 -2 -3 -3 -2 -1 -3 -2 -1 -2 -1 -1 0]
[ 0 1 0 0 -2 -1 -2 -2 -1 0 -2 -1 0 -1 -1 -1 0]
[ 0 0 1 -1 -1 2 2 1 1 1 0 0 0 -1 1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 155 1 Lattice Minkowski decompositions of facet 155
Image of facet 14 1 none
Polytope 2775
Image of polytope 2775 PALP id: 2775
grdb id: 472376
Integer points: [ 1 0 0 -1 -3 -1 -3 -2 -3 -2 -1 -2 -1 -1 0 -1 0]
[ 0 1 0 1 0 -2 -2 -2 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 -1 -2 2 0 1 -1 0 1 -1 0 0 1 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + 2*y-1*z + x-1*y*z-1 + 5*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 2*x-1*y-1 + 3*x-2*z-1 + 4*x-2*y-1 + 2*x-2*y-2*z + x-3*z-2 + 2*x-3*y-1*z-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 185 1 Lattice Minkowski decompositions of facet 185
Polytope 2776
Image of polytope 2776 PALP id: 2776
grdb id: 473967
Integer points: [ 1 0 0 -1 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 0 0 0]
[ 0 1 0 2 -2 -3 2 -2 -1 0 1 -1 0 1 -1 0 1]
[ 0 0 1 -2 2 2 -3 1 0 -1 -2 1 0 -1 1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
75 ? x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 5*x-1*y*z-1 + 8*x-1 + 5*x-1*y-1*z + x-1*y-2*z2 + x-2*y2*z-3 + 5*x-2*y*z-2 + 10*x-2*z-1 + 10*x-2*y-1 + 5*x-2*y-2*z + x-2*y-3*z2
24 ? x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 4*x-1*y*z-1 + 6*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + x-2*y2*z-3 + 5*x-2*y*z-2 + 10*x-2*z-1 + 10*x-2*y-1 + 5*x-2*y-2*z + x-2*y-3*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 4 irreducible and admissible
Image of facet 186 1 Lattice Minkowski decompositions of facet 186
Image of facet 43 1 irreducible and admissible
Polytope 2777
Image of polytope 2777 PALP id: 2777
grdb id: 472341
Integer points: [ 1 0 0 -1 -1 -2 -2 0 -1 -1 -1 -2 -2 -2 0 0 0]
[ 0 1 1 0 0 -1 -1 1 0 0 0 -1 -1 -1 0 0 0]
[ 0 0 2 -2 2 1 -3 1 -1 0 1 -2 -1 0 -1 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
75 ? y*z2 + 2*y*z + x + y + 2*z + x-1*z2 + 5*x-1*z + 2*z-1 + 8*x-1 + 5*x-1*z-1 + x-2*y-1*z + x-1*z-2 + 4*x-2*y-1 + 6*x-2*y-1*z-1 + 4*x-2*y-1*z-2 + x-2*y-1*z-3
24 ? y*z2 + 2*y*z + x + y + 2*z + x-1*z2 + 4*x-1*z + 2*z-1 + 6*x-1 + 4*x-1*z-1 + x-2*y-1*z + x-1*z-2 + 4*x-2*y-1 + 6*x-2*y-1*z-1 + 4*x-2*y-1*z-2 + x-2*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 5 irreducible and admissible
Image of facet 187 1 Lattice Minkowski decompositions of facet 187
Image of facet 13 1 irreducible and admissible
Polytope 2778
Image of polytope 2778 PALP id: 2778
grdb id: 474160
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 -1 -1 -1 -1]
[ 0 1 0 0 -1 2 -3 -2 -1 0 1 -1 0 -2 -1 0 1]
[ 0 0 1 1 1 -1 -1 0 0 0 0 0 0 -1 -1 -1 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 43 1 irreducible and admissible
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Polytope 2779
Image of polytope 2779 PALP id: 2779
grdb id: 473198
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 2 -1 -3 0 1 -2 -1 0 1 -2 -1 -1 0]
[ 0 0 1 -1 -1 2 2 1 0 2 1 0 -1 1 0 1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 8 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Polytope 2780
Image of polytope 2780 PALP id: 2780
grdb id: 473340
Integer points: [ 1 0 0 0 -1 -2 -2 -1 0 -1 -2 -1 0 -1 0 -1 0]
[ 0 1 -1 1 -2 -1 -3 0 0 -1 -2 -2 1 0 0 -1 -1]
[ 0 0 0 2 -2 0 -2 1 1 0 -1 -1 1 0 0 -1 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 y*z2 + 2*y*z + x + y + 2*z + 2*x-1*z + y-1 + 2*x-1 + 2*y-1*z-1 + 4*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + 2*x-1*y-2*z-1 + x-1*y-2*z-2 + 2*x-2*y-2*z-1 + x-2*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 3 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2781
Image of polytope 2781 PALP id: 2781
grdb id: 472391
Integer points: [ 1 0 0 -2 -1 -3 -3 -2 -3 -2 -1 -2 -1 -1 0 -1 0]
[ 0 1 0 0 -2 -2 -4 -3 -3 -2 -1 -1 0 -2 -1 -1 0]
[ 0 0 1 -1 0 -2 -2 -1 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
29 rank 2, number 23 x + y + z + 2*y-1 + 2*x-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 2*x-2*y-1*z-1 + 3*x-2*y-2*z-1 + 2*x-2*y-3*z-1 + x-3*y-2*z-2 + 2*x-3*y-3*z-2 + x-3*y-4*z-2
122 ? x + y + z + 2*y-1 + 2*x-1 + 4*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 4*x-2*y-1*z-1 + 6*x-2*y-2*z-1 + 2*x-2*y-3*z-1 + x-3*y-2*z-2 + 2*x-3*y-3*z-2 + x-3*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 135 1 Lattice Minkowski decompositions of facet 135
Polytope 2782
Image of polytope 2782 PALP id: 2782
grdb id: 472851
Integer points: [ 1 0 0 -2 1 0 1 1 0 0 -1 -1 1 1 0 0 -1]
[ 0 1 0 1 -2 -3 -4 -3 -1 -2 0 -1 -1 -2 0 -1 1]
[ 0 0 1 0 0 -2 -2 -1 0 -1 0 -1 0 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 105 1 none
Polytope 2783
Image of polytope 2783 PALP id: 2783
grdb id: 473103
Integer points: [ 1 0 0 0 -2 -1 -2 0 -1 -1 -1 -2 -2 0 0 -1 -1]
[ 0 1 0 -2 -1 -2 -4 -1 -3 -2 -1 -3 -2 -1 0 -1 0]
[ 0 0 1 -1 0 -2 -3 0 -2 -1 0 -2 -1 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + 2*y-1 + 2*x-1 + 2*y-1*z-1 + 2*x-1*y-1 + y-2*z-1 + 3*x-1*y-1*z-1 + x-2*y-1 + 4*x-1*y-2*z-1 + x-1*y-2*z-2 + 3*x-2*y-2*z-1 + 2*x-1*y-3*z-2 + 3*x-2*y-3*z-2 + x-2*y-4*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2784
Image of polytope 2784 PALP id: 2784
grdb id: 473149
Integer points: [ 1 0 0 0 -1 -2 -4 -3 -2 -2 -1 -3 -2 -1 -1 0 -1]
[ 0 1 -1 0 -1 -1 -1 -1 -1 0 0 -1 -1 -1 0 0 -1]
[ 0 0 0 1 1 -2 -2 -1 0 -1 0 -2 -1 0 -1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + y-1 + 3*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + 3*x-2*y-1 + 4*x-2*y-1*z-1 + x-2*y-1*z-2 + 3*x-3*y-1*z-1 + 2*x-3*y-1*z-2 + x-4*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Polytope 2785
Image of polytope 2785 PALP id: 2785
grdb id: 473158
Integer points: [ 1 0 0 0 -1 -2 -4 -3 -2 -2 -1 -3 -2 -1 -1 0 -1]
[ 0 1 -1 0 0 -1 -3 -2 -1 -2 -1 -2 -1 0 -1 0 0]
[ 0 0 0 1 1 -2 -2 -1 0 -1 0 -2 -1 0 -1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + x-1*z + y-1 + 2*x-1 + 2*x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*y-1 + 4*x-2*y-1*z-1 + x-2*y-1*z-2 + 2*x-2*y-2*z-1 + 3*x-3*y-2*z-1 + 2*x-3*y-2*z-2 + x-4*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2786
Image of polytope 2786 PALP id: 2786
grdb id: 472577
Integer points: [ 1 0 0 0 0 -3 -4 -3 -2 -1 -2 -1 -2 -1 0 -1 0]
[ 0 1 0 -1 -1 0 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
[ 0 0 1 -1 1 -2 -3 -2 -1 0 -1 0 -2 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + y-1*z + 2*y-1 + 3*x-1 + y-1*z-1 + 3*x-1*z-1 + 4*x-1*y-1 + 4*x-1*y-1*z-1 + 3*x-2*z-1 + 6*x-2*y-1*z-1 + 2*x-2*y-1*z-2 + x-3*z-2 + 4*x-3*y-1*z-2 + x-4*y-1*z-3
38 ? x + y + z + y-1*z + 2*y-1 + 3*x-1 + y-1*z-1 + 2*x-1*z-1 + 4*x-1*y-1 + 4*x-1*y-1*z-1 + 3*x-2*z-1 + 6*x-2*y-1*z-1 + 2*x-2*y-1*z-2 + x-3*z-2 + 4*x-3*y-1*z-2 + x-4*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 9 1 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2787
Image of polytope 2787 PALP id: 2787
grdb id: 472149
Integer points: [ 1 0 0 -2 -3 -1 -3 -3 -2 -3 -2 -1 -2 -1 -1 -1 0]
[ 0 1 0 -1 -2 -1 -2 -2 -1 -2 -1 0 -1 0 -1 -1 0]
[ 0 0 1 -1 0 2 3 1 0 2 1 0 2 1 0 1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 124 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2788
Image of polytope 2788 PALP id: 2788
grdb id: 472024
Integer points: [ 1 0 0 -1 -3 -1 -3 -3 -3 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 0 -1 -2 -1 -2 -2 -2 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 1 -1 0 2 3 1 2 0 1 2 0 1 0 1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
65 ? x + y + z + 3*x-1*z + x-1*y-1*z2 + 3*x-1 + 4*x-1*y-1*z + 3*x-2*y-1*z2 + 3*x-1*y-1 + 6*x-2*y-1*z + x-3*y-2*z3 + x-1*y-1*z-1 + 3*x-2*y-1 + 3*x-3*y-2*z2 + 3*x-3*y-2*z + x-3*y-2
47 ? x + y + z + 3*x-1*z + x-1*y-1*z2 + 3*x-1 + 2*x-1*y-1*z + 3*x-2*y-1*z2 + 2*x-1*y-1 + 6*x-2*y-1*z + x-3*y-2*z3 + x-1*y-1*z-1 + 3*x-2*y-1 + 3*x-3*y-2*z2 + 3*x-3*y-2*z + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Polytope 2789
Image of polytope 2789 PALP id: 2789
grdb id: 472064
Integer points: [ 1 0 0 -1 -3 -1 -3 -3 -3 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 0 0 -2 -1 -2 -2 -2 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 1 -1 0 2 3 2 1 2 1 0 1 0 1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? x + y + z + 3*x-1*z + x-1*y-1*z2 + 2*x-1 + 3*x-1*y-1*z + 3*x-2*y-1*z2 + x-1*z-1 + 2*x-1*y-1 + 5*x-2*y-1*z + x-3*y-2*z3 + 2*x-2*y-1 + 3*x-3*y-2*z2 + 3*x-3*y-2*z + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 132 1 Lattice Minkowski decompositions of facet 132
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2790
Image of polytope 2790 PALP id: 2790
grdb id: 473334
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0]
[ 0 1 1 -2 1 -1 1 0 0 1 -1 0 -1 0 1 0 1]
[ 0 0 3 -3 2 -2 0 0 -1 1 -1 1 -2 0 2 -1 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
97 ? y*z3 + 3*y*z2 + 3*y*z + x-1*y*z2 + x + y + 3*z + 2*x-1*y*z + x-1*y + 3*z-1 + 2*x-1 + 3*y-1*z-1 + 2*x-1*z-1 + 3*y-1*z-2 + x-1*y-1*z-2 + y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 3 irreducible and admissible
Image of facet 44 3 Lattice Minkowski decompositions of facet 44
Polytope 2791
Image of polytope 2791 PALP id: 2791
grdb id: 472855
Integer points: [ 1 0 1 -3 -2 -3 1 -2 -1 -2 -1 0 -1 0 -1 0 1]
[ 0 1 2 -2 -1 -2 2 -1 0 -1 0 1 0 1 -1 0 1]
[ 0 0 3 -3 0 -2 2 -2 -1 -1 0 1 1 2 -1 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
24 ? x*y2*z3 + x*y2*z2 + 2*x*y*z + 3*y*z2 + 4*y*z + x + y + 3*x-1*z + 6*x-1 + 3*x-1*z-1 + 2*x-1*y-1*z-1 + x-2*y-1 + 4*x-2*y-1*z-1 + 3*x-2*y-1*z-2 + x-3*y-2*z-2 + x-3*y-2*z-3
75 ? x*y2*z3 + x*y2*z2 + 2*x*y*z + 3*y*z2 + 5*y*z + x + y + 3*x-1*z + 8*x-1 + 3*x-1*z-1 + 2*x-1*y-1*z-1 + x-2*y-1 + 5*x-2*y-1*z-1 + 3*x-2*y-1*z-2 + x-3*y-2*z-2 + x-3*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 188 1 Lattice Minkowski decompositions of facet 188
Image of facet 9 2 irreducible and admissible
Polytope 2792
Image of polytope 2792 PALP id: 2792
grdb id: 472378
Integer points: [ 1 0 0 -2 -3 -1 -3 -2 -3 -2 -1 -2 -1 -1 0 -1 0]
[ 0 1 0 0 -2 -2 -4 -3 -3 -2 -1 -1 0 -2 -1 -1 0]
[ 0 0 1 -1 0 2 2 2 1 1 1 0 0 1 1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
63 ? x + y + z + 2*y-1*z + 2*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*y-1 + 2*x-1*y-2*z + x-2*z-1 + 2*x-2*y-1 + 3*x-2*y-2*z + 2*x-2*y-3*z2 + x-3*y-2 + 2*x-3*y-3*z + x-3*y-4*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 189 1 Lattice Minkowski decompositions of facet 189
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 2793
Image of polytope 2793 PALP id: 2793
grdb id: 473274
Integer points: [ 1 0 0 -1 -3 -1 -3 -2 -1 -3 -2 -1 -1 0 -2 -1 0]
[ 0 1 0 0 -2 -2 -4 -1 0 -3 -2 -1 -1 0 -3 -2 -1]
[ 0 0 1 -1 0 2 2 0 0 1 1 1 0 0 2 1 1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + 2*y-1*z + 3*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-2*z + 3*x-2*y-1 + 5*x-2*y-2*z + 2*x-2*y-3*z2 + x-3*y-2 + 2*x-3*y-3*z + x-3*y-4*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 2794
Image of polytope 2794 PALP id: 2794
grdb id: 473140
Integer points: [ 1 0 0 0 -1 -2 -4 -3 -2 -3 -2 -1 -1 -2 -1 -1 0]
[ 0 1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 0 1 -1 2 2 1 0 2 1 0 1 1 0 1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 14 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Polytope 2795
Image of polytope 2795 PALP id: 2795
grdb id: 472576
Integer points: [ 1 0 0 0 0 -3 -4 -3 -2 -1 -2 -1 0 -2 -1 -1 0]
[ 0 1 0 -1 -2 2 2 1 0 -1 1 0 -1 1 0 1 0]
[ 0 0 1 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 8 1 none
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Polytope 2796
Image of polytope 2796 PALP id: 2796
grdb id: 473037
Integer points: [ 1 0 0 -1 -3 -3 -5 -4 -4 -3 -2 -2 -1 -2 -1 -1 0]
[ 0 1 0 1 0 -2 -2 -2 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 -1 -2 0 -2 -1 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
103 ? x + y + z + x-1*y*z-1 + 3*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + 5*x-2*z-1 + 2*x-2*y-1 + 2*x-2*y-1*z-1 + x-3*z-2 + 5*x-3*y-1*z-1 + x-3*y-2 + 2*x-4*y-1*z-2 + 2*x-4*y-2*z-1 + x-5*y-2*z-2
28 rank 2, number 25 x + y + z + x-1*y*z-1 + 2*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-2*z-1 + x-2*y-1 + 2*x-2*y-1*z-1 + x-3*z-2 + 3*x-3*y-1*z-1 + x-3*y-2 + 2*x-4*y-1*z-2 + 2*x-4*y-2*z-1 + x-5*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 190 1 Lattice Minkowski decompositions of facet 190
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 2797
Image of polytope 2797 PALP id: 2797
grdb id: 472610
Integer points: [ 1 0 0 -1 -1 -3 -5 -4 -3 -2 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 -1 -1 0 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
[ 0 0 1 -1 1 -2 -3 -2 -1 0 -1 0 -2 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + 3*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + 3*x-2*z-1 + 4*x-2*y-1 + 4*x-2*y-1*z-1 + x-3*z-2 + 6*x-3*y-1*z-1 + 2*x-3*y-1*z-2 + 4*x-4*y-1*z-2 + x-5*y-1*z-3
122 ? x + y + z + 4*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + 4*x-2*z-1 + 4*x-2*y-1 + 4*x-2*y-1*z-1 + x-3*z-2 + 6*x-3*y-1*z-1 + 2*x-3*y-1*z-2 + 4*x-4*y-1*z-2 + x-5*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 93 1 Lattice Minkowski decompositions of facet 93
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 2798
Image of polytope 2798 PALP id: 2798
grdb id: 472556
Integer points: [ 1 0 0 -1 -1 -3 -5 -4 -3 -2 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 0 0 -3 -4 -3 -2 -1 -2 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 1 -2 -3 -2 -1 0 -1 0 -2 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 8 1 none
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 80 1 none
Image of facet 9 1 irreducible and admissible
Polytope 2799
Image of polytope 2799 PALP id: 2799
grdb id: 472671
Integer points: [ 1 0 0 -1 -1 -3 -5 -4 -3 -2 -3 -2 -1 -2 -1 -1 0]
[ 0 1 0 0 0 -3 -4 -3 -2 -1 -2 -1 0 -2 -1 -1 0]
[ 0 0 1 -1 1 1 1 1 1 1 0 0 0 1 1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 8 1 none
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Image of facet 9 1 irreducible and admissible
Polytope 2800
Image of polytope 2800 PALP id: 2800
grdb id: 473154
Integer points: [ 1 0 0 -1 -1 -2 -5 -4 -3 -3 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 -1 -1 0 -3 -2 -1 -2 -1 0 -2 -1 0 -1 0]
[ 0 0 1 -1 1 1 1 1 1 0 0 0 1 1 1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
69 ? x + y + z + 2*x-1*z + 3*x-1 + x-1*y-1*z + x-2*z + 2*x-1*y-1 + 4*x-2*y-1*z + x-1*y-1*z-1 + 3*x-2*y-1 + 3*x-3*y-1*z + 2*x-3*y-2*z + 2*x-3*y-2 + 3*x-4*y-2*z + x-5*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 56 1 Lattice Minkowski decompositions of facet 56
Polytope 2801
Image of polytope 2801 PALP id: 2801
grdb id: 471870
Integer points: [ 1 0 0 0 -2 -4 -5 -1 -3 -2 -1 -4 -3 -2 -1 0 -2]
[ 0 1 0 -1 -2 -1 -2 -1 -2 -1 0 -2 -1 0 -1 0 -1]
[ 0 0 1 1 1 -2 -2 1 0 0 0 -1 -1 -1 0 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
147 ? x + y + z + y-1*z + 4*x-1 + 2*x-1*y-1*z + 3*x-1*y-1 + 2*x-2*z-1 + 6*x-2*y-1 + x-2*y-2*z + 2*x-2*y-1*z-1 + 5*x-3*y-1*z-1 + 3*x-3*y-2 + x-4*y-1*z-2 + 3*x-4*y-2*z-1 + x-5*y-2*z-2
112 rank 3, number 15 x + y + z + y-1*z + 3*x-1 + 2*x-1*y-1*z + 3*x-1*y-1 + 2*x-2*z-1 + 5*x-2*y-1 + x-2*y-2*z + 2*x-2*y-1*z-1 + 4*x-3*y-1*z-1 + 3*x-3*y-2 + x-4*y-1*z-2 + 3*x-4*y-2*z-1 + x-5*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 155 1 Lattice Minkowski decompositions of facet 155
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2802
Image of polytope 2802 PALP id: 2802
grdb id: 473257
Integer points: [ 1 0 0 1 -2 -3 -4 -1 0 -3 -2 -1 -1 0 1 -2 -1]
[ 0 1 0 -2 1 2 3 0 -1 2 1 0 1 0 -1 2 1]
[ 0 0 1 0 0 -2 -2 0 0 -1 -1 -1 0 0 0 -1 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + z + 2*x*y-1 + 2*x-1*y + 2*x-1*y*z-1 + 2*x-2*y2*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + 2*x-1*z-1 + 4*x-2*y*z-1 + 2*x-3*y2*z-1 + x-3*y2*z-2 + x-4*y3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2803
Image of polytope 2803 PALP id: 2803
grdb id: 471958
Integer points: [ 1 0 0 0 -1 -4 -6 -4 -2 -5 -3 -1 -2 -3 -1 -2 0]
[ 0 1 -1 0 -2 -3 -3 -2 -1 -3 -2 -1 -2 -1 0 -1 0]
[ 0 0 0 1 -1 -2 -2 -1 0 -2 -1 0 -1 -1 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 138 1 Lattice Minkowski decompositions of facet 138
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Polytope 2804
Image of polytope 2804 PALP id: 2804
grdb id: 473141
Integer points: [ 1 0 0 0 -1 -4 -6 -4 -2 -5 -3 -1 -2 -3 -1 -2 0]
[ 0 1 -1 0 0 -1 -3 -2 -1 -2 -1 0 0 -2 -1 -1 0]
[ 0 0 0 1 -1 -2 -2 -1 0 -2 -1 0 -1 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 14 1 none
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Polytope 2805
Image of polytope 2805 PALP id: 2805
grdb id: 472675
Integer points: [ 1 0 0 0 -2 -5 -8 -6 -4 -2 -3 -1 -5 -3 -1 -2 0]
[ 0 1 -1 0 2 2 4 3 2 1 1 0 3 2 1 1 0]
[ 0 0 0 1 -1 -2 -3 -2 -1 0 -1 0 -2 -1 0 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 80 1 none
Image of facet 64 1 none
Polytope 2806
Image of polytope 2806 PALP id: 2806
grdb id: 470079
Integer points: [ 1 0 0 -2 1 0 1 0 -1 1 0 -1 1 0 -1 1 0]
[ 0 1 0 1 -2 -1 -2 -1 0 -2 -1 0 -1 0 1 -1 0]
[ 0 0 1 0 0 -2 -2 0 0 -1 -1 -1 0 0 0 -1 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? x + y + z + 2*x*y-1 + 2*x-1*y + 2*x*y-1*z-1 + 2*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + 2*x*y-2*z-1 + 4*y-1*z-1 + 2*x-1*z-1 + x*y-2*z-2 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2807
Image of polytope 2807 PALP id: 2807
grdb id: 469775
Integer points: [ 1 0 0 0 0 -2 -2 -1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 1 0 1 -2 0 1 0 1 -1 0 1 -1 0 1 -1 0]
[ 0 0 1 -2 1 1 0 1 0 1 0 -1 1 0 -1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 x + y + z + 2*y*z-1 + 2*x-1*y + 2*y-1*z + 2*x-1*z + y*z-2 + 3*z-1 + 2*x-1*y*z-1 + 3*y-1 + 4*x-1 + x-2*y + y-2*z + 2*x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2808
Image of polytope 2808 PALP id: 2808
grdb id: 469891
Integer points: [ 1 0 0 0 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 2 -1 2 0 1 0 1 2 -1 0 1 0 1]
[ 0 0 0 1 1 -2 1 -1 0 -1 0 1 -1 0 1 0 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 y2*z + 2*y*z + 2*x-1*y2*z + x + y + z + 2*x-1*y*z + x-2*y2*z + 4*x-1*y + y-1 + 4*x-1 + 3*x-2*y + 2*x-1*z-1 + 2*x-1*y-1*z-1 + 3*x-2*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2809
Image of polytope 2809 PALP id: 2809
grdb id: 468913
Integer points: [ 1 0 0 0 0 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0]
[ 0 0 1 -1 0 2 -2 -1 0 1 -1 0 1 -1 0 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
3 ? x + y + z + 2*x-1*z + z-1 + y-1 + 4*x-1 + 2*x-1*y-1*z + x-2*y-1*z2 + 2*x-1*z-1 + 4*x-1*y-1 + 4*x-2*y-1*z + 2*x-1*y-1*z-1 + 6*x-2*y-1 + 4*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 32 2 Lattice Minkowski decompositions of facet 32
Polytope 2810
Image of polytope 2810 PALP id: 2810
grdb id: 470080
Integer points: [ 1 0 0 0 -1 -3 -3 -2 -1 -3 -2 -1 -2 -1 0 -1 0]
[ 0 1 0 -1 -2 0 -2 0 0 -1 -1 -1 -2 0 0 -1 -1]
[ 0 0 1 1 0 -2 -2 -1 0 -2 -1 0 -1 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + y-1*z + 2*y-1 + 3*x-1 + 2*x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2 + 5*x-2*y-1*z-1 + x-3*z-2 + 2*x-2*y-2*z-1 + 2*x-3*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Polytope 2811
Image of polytope 2811 PALP id: 2811
grdb id: 469940
Integer points: [ 1 0 0 0 -1 -2 -4 -3 -2 -3 -2 -1 -1 -2 -1 -1 0]
[ 0 1 -1 0 0 -3 -3 -2 -1 -3 -2 -1 -2 -1 0 -1 0]
[ 0 0 0 1 1 -2 -2 -1 0 -2 -1 0 -1 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 14 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2812
Image of polytope 2812 PALP id: 2812
grdb id: 468782
Integer points: [ 1 0 0 0 0 -3 -4 -1 -2 -3 0 -1 -2 -1 -2 0 -1]
[ 0 1 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 1 -1 1 1 1 1 1 1 0 0 0 1 1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 8 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Polytope 2813
Image of polytope 2813 PALP id: 2813
grdb id: 467882
Integer points: [ 1 0 0 0 -1 -3 -3 -1 -2 -1 -2 -3 -2 -3 0 -1 -1]
[ 0 1 -1 0 2 0 3 0 0 1 1 1 2 2 0 0 1]
[ 0 0 0 1 -1 -2 -2 0 -1 0 -1 -2 -1 -2 0 -1 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + x-1*y2*z-1 + 3*x-1*y + 3*x-1*y*z-1 + 3*x-2*y2*z-1 + y-1 + 3*x-1 + x-3*y3*z-2 + 2*x-1*z-1 + 6*x-2*y*z-1 + 3*x-3*y2*z-2 + 3*x-2*z-1 + 3*x-3*y*z-2 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Polytope 2814
Image of polytope 2814 PALP id: 2814
grdb id: 468224
Integer points: [ 1 0 0 0 0 -2 -3 -1 -2 0 -1 -2 0 -1 -1 0 -1]
[ 0 1 -1 0 -3 3 3 1 2 -1 0 1 -2 -1 2 0 1]
[ 0 0 0 1 1 -2 -2 0 -1 1 0 -1 1 0 -1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
56 rank 2, number 11 x + y + z + 2*x-1*y2*z-1 + 3*x-1*y + 3*y-1*z + x-2*y3*z-2 + 2*x-1*y*z-1 + 3*x-2*y2*z-1 + y-1 + 6*x-1 + 3*y-2*z + x-3*y3*z-2 + 3*x-2*y*z-1 + 3*x-1*y-1 + y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 9 1 irreducible and admissible
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Polytope 2815
Image of polytope 2815 PALP id: 2815
grdb id: 355617
Integer points: [ 1 0 0 -1 1 -1 -1 -3 -2 -2 -1 0 0 -2 -1 -1 0]
[ 0 1 0 1 -1 1 -1 1 1 0 0 0 -1 1 1 0 0]
[ 0 0 1 1 -1 -1 1 1 0 1 0 -1 0 1 0 1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
23 ? x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + 2*x-2*y*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + 2*x-2*y + x-1*y-1*z + 2*x-2*z + x-3*y*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Polytope 2816
Image of polytope 2816 PALP id: 2816
grdb id: 355616
Integer points: [ 1 1 -1 -1 0 0 2 -2 0 -1 0 1 -1 0 1 0 0]
[ 0 2 -2 0 0 -2 3 -1 1 0 1 2 -1 0 1 -1 -1]
[ 0 0 0 0 1 1 -1 -1 0 -1 -1 -1 0 0 0 1 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
22 ? x2*y3*z-1 + x*y2 + 4*x*y2*z-1 + 3*x*y + x + 2*y + z + 6*y*z-1 + 2*y-1*z + 2*y-1 + x-1 + y-2*z + 4*x-1*z-1 + 3*x-1*y-1 + x-1*y-2 + x-2*y-1*z-1
7 rank 1, V12 x2*y3*z-1 + x*y2 + 4*x*y2*z-1 + 2*x*y + x + 2*y + z + 6*y*z-1 + 2*y-1*z + 2*y-1 + x-1 + y-2*z + 4*x-1*z-1 + 3*x-1*y-1 + x-1*y-2 + x-2*y-1*z-1
11 rank 2, number 6 x2*y3*z-1 + x*y2 + 4*x*y2*z-1 + 2*x*y + x + 2*y + z + 6*y*z-1 + 2*y-1*z + 2*y-1 + x-1 + y-2*z + 4*x-1*z-1 + 2*x-1*y-1 + x-1*y-2 + x-2*y-1*z-1
7 rank 1, V12 x2*y3*z-1 + x*y2 + 4*x*y2*z-1 + 3*x*y + x + 2*y + z + 6*y*z-1 + 2*y-1*z + 2*y-1 + x-1 + y-2*z + 4*x-1*z-1 + 2*x-1*y-1 + x-1*y-2 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 59 2 Lattice Minkowski decompositions of facet 59
Image of facet 23 2 Lattice Minkowski decompositions of facet 23
Polytope 2817
Image of polytope 2817 PALP id: 2817
grdb id: 355615
Integer points: [ 1 1 0 0 -1 -1 -1 -1 -1 -1 -1 0 0 0 1 -1 -1]
[ 0 2 0 1 -3 0 -1 0 0 -1 -2 1 0 -1 1 -1 -2]
[ 0 0 1 1 -1 -1 1 1 0 0 0 0 0 0 0 -1 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 2 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Polytope 2818
Image of polytope 2818 PALP id: 2818
grdb id: 355607
Integer points: [ 1 1 0 -2 0 -2 -2 -4 -1 -3 -2 -1 0 -3 -1 0 1]
[ 0 2 0 -2 1 -1 -1 -3 0 -2 -1 0 1 -2 -1 0 1]
[ 0 0 1 -1 1 -1 1 -1 1 0 0 0 0 -1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
24 ? x*y2 + 2*x*y + y*z + x + 4*y + z + 2*x-1*z + 6*x-1 + 2*x-1*y-1 + x-2*y-1*z + 4*x-2*y-1 + x-2*y-1*z-1 + x-2*y-2*z-1 + 2*x-3*y-2 + 2*x-3*y-2*z-1 + x-4*y-3*z-1
75 ? x*y2 + 2*x*y + y*z + x + 4*y + z + 2*x-1*z + 6*x-1 + 3*x-1*y-1 + x-2*y-1*z + 4*x-2*y-1 + x-2*y-1*z-1 + x-2*y-2*z-1 + 2*x-3*y-2 + 2*x-3*y-2*z-1 + x-4*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 140 1 Lattice Minkowski decompositions of facet 140
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2819
Image of polytope 2819 PALP id: 2819
grdb id: 354967
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 -1 1 0 -2 1 0 0 0 -1 -1 0 0 -1]
[ 0 0 1 1 1 -1 -2 0 0 1 0 -1 0 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
24 ? x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 6*x-1 + x-1*y-1*z + 4*x-1*z-1 + 4*x-1*y-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
13 rank 2, number 12 x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 135 1 Lattice Minkowski decompositions of facet 135
Polytope 2820
Image of polytope 2820 PALP id: 2820
grdb id: 355397
Integer points: [ 1 0 0 -1 -1 0 -1 -1 -1 -1 0 -1 -1 -1 0 0 0]
[ 0 1 0 1 -1 -1 -2 -2 0 -1 0 0 -1 -2 0 -1 -1]
[ 0 0 1 1 1 -2 0 -2 0 -1 -1 1 0 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + x-1*y*z + 2*x-1*z + 2*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + 2*y-1*z-1 + 4*x-1*y-1 + y-1*z-2 + 3*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2821
Image of polytope 2821 PALP id: 2821
grdb id: 355506
Integer points: [ 1 0 0 0 1 -2 0 -2 0 -1 -1 -1 -2 0 0 -1 -1]
[ 0 1 0 0 -1 0 -2 -2 -1 -2 -1 0 -1 -1 0 -1 0]
[ 0 0 1 -1 -1 1 -1 -1 0 -1 0 1 0 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + 2*x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + x-2*z + 2*y-1*z-1 + 4*x-1*y-1 + y-2*z-1 + 2*x-1*y-1*z-1 + 2*x-2*y-1 + 2*x-1*y-2*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2822
Image of polytope 2822 PALP id: 2822
grdb id: 355387
Integer points: [ 1 0 0 0 -1 -1 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -2 2 -1 2 1 0 1 0 -1 1 0 0 -1]
[ 0 0 1 -1 0 -1 -1 -1 -1 -1 0 0 0 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
128 ? x + y + z + y*z-1 + x-1*y2*z-1 + 2*x-1*y + 3*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 3*x-1 + 2*x-1*z-1 + 3*x-2*y*z-1 + 3*x-1*y-1 + 3*x-2*z-1 + x-1*y-2 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 56 1 Lattice Minkowski decompositions of facet 56
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2823
Image of polytope 2823 PALP id: 2823
grdb id: 355511
Integer points: [ 1 0 0 0 -1 -1 0 2 0 -1 -1 1 1 0 0 0 1]
[ 0 1 0 0 2 -1 -2 -2 -1 0 1 -2 -1 -1 0 1 -1]
[ 0 0 1 -1 2 -1 -1 -1 0 0 1 -1 0 -1 0 1 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x-1*y2*z2 + 2*y*z + x + y + z + 3*x-1*y*z + 2*x*y-1 + x2*y-2*z-1 + 2*x*y-1*z-1 + z-1 + 2*y-1 + 3*x-1 + 2*x*y-2*z-1 + 2*y-1*z-1 + y-2*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2824
Image of polytope 2824 PALP id: 2824
grdb id: 355442
Integer points: [ 1 0 0 1 -1 -2 0 -2 -1 -2 -1 0 -1 0 -1 0 1]
[ 0 1 0 -2 1 2 -2 0 -1 1 0 -1 0 -1 1 0 -1]
[ 0 0 1 0 -1 -1 1 1 1 0 0 0 1 1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + z + 2*x*y-1 + 2*x-1*y + 2*y-1*z + 2*x-1*z + x-1*y*z-1 + x-2*y2*z-1 + x*y-2 + 3*y-1 + 3*x-1 + 2*x-2*y + y-2*z + 2*x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2825
Image of polytope 2825 PALP id: 2825
grdb id: 354996
Integer points: [ 1 0 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 1 -1 -2 -3 0 -1 -2 0 -1 -2 -1 0 -1]
[ 0 0 1 -1 1 -1 1 1 1 1 1 0 0 0 1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + x-1*y*z + 2*y-1*z + 4*x-1*z + z-1 + 2*y-1 + 2*x-1 + y-2*z + 6*x-1*y-1*z + 4*x-1*y-1 + 4*x-1*y-2*z + x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-3*z
17 rank 1, V22 x + y + z + x-1*y*z + 2*y-1*z + 4*x-1*z + z-1 + 3*y-1 + 2*x-1 + y-2*z + 6*x-1*y-1*z + 4*x-1*y-1 + 4*x-1*y-2*z + x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2826
Image of polytope 2826 PALP id: 2826
grdb id: 354817
Integer points: [ 1 0 1 0 -1 0 -2 -2 -2 -2 -1 -1 -1 0 -1 -1 0]
[ 0 1 -1 0 1 -2 0 -3 -1 -2 0 -1 -2 -1 0 -1 0]
[ 0 0 0 1 1 -1 1 -2 0 -1 1 0 -1 0 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
100 ? x + y + z + x-1*y*z + x*y-1 + 2*x-1*z + 4*y-1 + 3*x-1 + x-2*z + 5*x-1*y-1 + y-2*z-1 + 2*x-1*y-1*z-1 + 3*x-2*y-1 + 3*x-1*y-2*z-1 + 3*x-2*y-2*z-1 + x-2*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 138 1 Lattice Minkowski decompositions of facet 138
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2827
Image of polytope 2827 PALP id: 2827
grdb id: 355343
Integer points: [ 1 0 0 0 -1 -2 -1 -2 -1 -1 -1 0 0 -2 -2 -1 -1]
[ 0 1 -1 0 -1 0 2 3 0 1 2 0 1 1 2 0 1]
[ 0 0 0 1 1 1 -2 -2 1 0 -1 0 -1 0 -1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + 2*y*z-1 + 2*x-1*y2*z-1 + 4*x-1*y + 2*x-1*z + x-1*y2*z-2 + x-2*y3*z-2 + 3*x-1*y*z-1 + 3*x-2*y2*z-1 + y-1 + 4*x-1 + 3*x-2*y + x-1*y-1*z + x-2*z
60 rank 2, number 18 x + y + z + 2*y*z-1 + 2*x-1*y2*z-1 + 4*x-1*y + 2*x-1*z + x-1*y2*z-2 + x-2*y3*z-2 + 2*x-1*y*z-1 + 3*x-2*y2*z-1 + y-1 + 2*x-1 + 3*x-2*y + x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2828
Image of polytope 2828 PALP id: 2828
grdb id: 355133
Integer points: [ 1 0 0 -2 -2 1 -3 1 -1 0 -1 -2 0 -1 1 0 -1]
[ 0 1 0 0 2 -2 2 -3 1 -1 0 1 -2 -1 -1 0 1]
[ 0 0 1 -1 -1 2 -2 2 0 1 0 -1 1 0 1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
109 ? x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*x-1*y + 5*y-1*z + x*y-3*z2 + 2*x-1*y*z-1 + x-2*y2*z-1 + 7*x-1 + 3*y-2*z + 4*x-2*y*z-1 + 3*x-1*y-1 + x-3*y2*z-2 + x-2*z-1
39 ? x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*x-1*y + 3*y-1*z + x*y-3*z2 + 2*x-1*y*z-1 + x-2*y2*z-1 + 4*x-1 + 3*y-2*z + 3*x-2*y*z-1 + 3*x-1*y-1 + x-3*y2*z-2 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 166 1 Lattice Minkowski decompositions of facet 166
Image of facet 9 1 irreducible and admissible
Polytope 2829
Image of polytope 2829 PALP id: 2829
grdb id: 355346
Integer points: [ 1 0 0 -1 -1 -1 0 -1 -1 -1 0 0 -1 -1 0 0 0]
[ 0 1 0 1 2 2 -3 -2 0 -1 -1 -2 1 0 0 -1 1]
[ 0 0 1 0 -1 -2 1 0 0 0 1 1 -1 -1 0 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + 2*y*z-1 + x-1*y2*z-1 + x-1*y + 3*y-1*z + x-1*y2*z-2 + 3*x-1*y*z-1 + 2*y-1 + 3*x-1 + 3*y-2*z + 2*x-1*z-1 + 3*x-1*y-1 + y-3*z + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2830
Image of polytope 2830 PALP id: 2830
grdb id: 355485
Integer points: [ 1 0 0 -1 -1 -1 0 -1 -1 -1 -1 0 0 -1 0 0 0]
[ 0 1 0 2 0 2 -3 -2 1 0 -1 -1 -2 1 1 0 -1]
[ 0 0 1 1 -1 2 -2 -2 1 0 -1 0 -1 0 1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x-1*y2*z2 + 2*y*z + x-1*y2*z + x + y + z + 4*x-1*y*z + 2*x-1*y + 3*y-1 + 6*x-1 + y-1*z-1 + x-1*z-1 + 3*y-2*z-1 + 4*x-1*y-1*z-1 + y-3*z-2 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 9 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Polytope 2831
Image of polytope 2831 PALP id: 2831
grdb id: 355341
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 2 -3 2 -2 1 0 -1 1 0 -1 -2 1 0 -1]
[ 0 0 1 1 -2 2 -1 2 1 0 1 0 0 -1 1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x-1*y2*z2 + 2*y*z + x-1*y2*z + x-1*y*z2 + x + y + z + 3*x-1*y*z + 3*x-1*z + 3*y-1 + 2*x-1 + 2*y-1*z-1 + 3*x-1*y-1 + 3*y-2*z-1 + x-1*y-2*z-1 + y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2832
Image of polytope 2832 PALP id: 2832
grdb id: 354990
Integer points: [ 1 0 0 1 0 -1 1 -3 -2 -1 0 -1 0 1 -2 -1 0]
[ 0 1 0 -2 -1 0 -2 2 1 0 -1 1 0 -1 1 0 -1]
[ 0 0 1 0 1 1 -1 -1 0 0 0 0 0 0 -1 -1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 8 1 none
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Polytope 2833
Image of polytope 2833 PALP id: 2833
grdb id: 355007
Integer points: [ 1 0 1 -2 0 -1 -3 -3 -2 -1 -3 -2 -1 0 -1 0 1]
[ 0 1 0 -1 1 1 -1 1 1 1 0 0 0 0 0 0 0]
[ 0 0 2 -1 1 -1 -2 -2 -1 0 -2 -1 0 1 -1 0 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 141 1 Lattice Minkowski decompositions of facet 141
Polytope 2834
Image of polytope 2834 PALP id: 2834
grdb id: 355498
Integer points: [ 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 0 -3 -2 -4 0 -1 -1 -2 -3 0 -1 -1 -2]
[ 0 0 1 1 1 -2 -2 -3 0 -1 0 -1 -2 0 -1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
35 rank 2, number 15 x + y + z + x-1*y*z + x-1*z + 3*y-1 + 3*x-1 + y-1*z-1 + 4*x-1*y-1 + 3*y-2*z-1 + 3*x-1*y-1*z-1 + 6*x-1*y-2*z-1 + y-3*z-2 + x-1*y-2*z-2 + 4*x-1*y-3*z-2 + x-1*y-4*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 90 2 Lattice Minkowski decompositions of facet 90
Polytope 2835
Image of polytope 2835 PALP id: 2835
grdb id: 355384
Integer points: [ 1 0 0 -1 0 -1 -2 -4 -3 -2 -1 -1 0 -3 -2 -2 -1]
[ 0 1 0 0 -1 0 -1 -3 -2 -1 0 -1 0 -2 -1 -2 -1]
[ 0 0 1 -1 -1 1 1 -1 0 0 0 0 0 -1 -1 -1 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 14 1 none
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2836
Image of polytope 2836 PALP id: 2836
grdb id: 355386
Integer points: [ 1 0 1 0 -1 -2 -1 -4 -3 -2 -2 -1 0 -3 -2 -1 0]
[ 0 1 -1 0 -1 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 0 0 1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
159 ? x + y + z + x*y-1 + 3*y-1 + 2*x-1 + 3*x-1*y-1 + x-1*y-1*z-1 + x-2*z-1 + 2*x-2*y-1 + x-1*y-2*z-1 + 3*x-2*y-1*z-1 + 3*x-2*y-2*z-1 + 2*x-3*y-1*z-1 + 3*x-3*y-2*z-1 + x-4*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 56 1 Lattice Minkowski decompositions of facet 56
Polytope 2837
Image of polytope 2837 PALP id: 2837
grdb id: 355353
Integer points: [ 1 0 0 -1 2 -2 3 2 1 0 2 1 0 -1 1 0 -1]
[ 0 1 0 0 -1 1 -3 -3 -2 -1 -2 -1 -1 0 -1 0 1]
[ 0 0 1 1 -1 0 -2 -2 -1 0 -1 0 -1 0 -1 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 14 1 none
Polytope 2838
Image of polytope 2838 PALP id: 2838
grdb id: 355345
Integer points: [ 1 0 1 0 -1 -1 -3 -4 -2 -3 0 -1 -2 -2 1 0 -1]
[ 0 1 -2 0 0 -1 2 2 0 1 -1 0 1 1 -1 0 1]
[ 0 0 0 1 -1 -1 -1 -1 -1 -1 0 0 0 -1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 56 1 Lattice Minkowski decompositions of facet 56
Image of facet 8 1 none
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2839
Image of polytope 2839 PALP id: 2839
grdb id: 353935
Integer points: [ 1 0 0 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 -1 -1 1 -1 -1 0 0 0 1 -1 -1 0 0]
[ 0 0 1 1 -1 1 -1 -1 0 -1 0 1 0 -1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + x-1*y-1*z + 2*y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 2840
Image of polytope 2840 PALP id: 2840
grdb id: 353396
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 0 -1 0 -2 -2 -2 -1 -1 -1 0 -1 -1 0 0]
[ 0 0 1 0 1 -2 0 -2 -1 -2 -1 0 -1 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + 2*z-1 + 2*y-1 + x-1 + x-1*y-1*z + 2*y-1*z-1 + 2*x-1*z-1 + 4*x-1*y-1 + x-1*z-2 + 5*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-1*z-2 + 2*x-1*y-2*z-1 + x-1*y-2*z-2
38 ? x + y + z + 2*z-1 + 2*y-1 + x-1 + x-1*y-1*z + 2*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + x-1*z-2 + 4*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-1*z-2 + 2*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2841
Image of polytope 2841 PALP id: 2841
grdb id: 353944
Integer points: [ 1 0 0 0 -1 0 -2 -2 -1 -2 -1 -1 0 -1 0 -1 0]
[ 0 1 0 0 1 -2 0 -2 -1 -1 0 -2 -1 -1 0 0 -1]
[ 0 0 1 -1 -1 1 -1 1 1 0 0 1 1 0 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + 2*y-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + y-2*z + 2*x-1*y-1*z + 2*x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-2*z + x-2*z-1 + 2*x-2*y-1 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2842
Image of polytope 2842 PALP id: 2842
grdb id: 353023
Integer points: [ 1 0 0 0 0 -1 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 -1 0 -1 -1 -1 -1 0 0 -1 -1 -1 0 -1]
[ 0 0 1 -1 1 1 1 -2 0 -1 0 -1 1 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + y-1*z + x-1*z + 2*y-1 + 3*x-1 + 2*x-1*y-1*z + y-1*z-1 + 2*x-1*z-1 + 4*x-1*y-1 + x-2*y-1*z + 2*x-1*y-1*z-1 + 3*x-2*y-1 + 3*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2843
Image of polytope 2843 PALP id: 2843
grdb id: 353483
Integer points: [ 1 0 0 0 1 0 -2 -2 -1 -1 0 -2 -1 0 -1 0 -1]
[ 0 1 0 0 -1 -2 0 -2 -2 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 0 1 -1 1 1 1 1 0 0 0 0 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*y-1 + 2*y-1*z + z-1 + 3*y-1 + 2*x-1 + y-2*z + 2*x-1*y-1*z + 2*x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-2*z + x-2*z-1 + 2*x-2*y-1 + x-2*y-2*z
146 ? x + y + z + x*y-1 + 2*y-1*z + z-1 + 4*y-1 + 2*x-1 + y-2*z + 2*x-1*y-1*z + 2*x-1*z-1 + 5*x-1*y-1 + 2*x-1*y-2*z + x-2*z-1 + 2*x-2*y-1 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2844
Image of polytope 2844 PALP id: 2844
grdb id: 351081
Integer points: [ 1 0 0 -1 -1 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -1 -2 2 -2 1 0 -1 1 0 -1 0 0 -1]
[ 0 0 1 -1 -1 0 -1 -1 -1 -1 -1 0 0 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
85 rank 3, number 8 x + y + z + 2*x-1*y + x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 4*x-1 + 2*x-1*z-1 + 4*x-2*y*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + 6*x-2*z-1 + x-1*y-2 + 4*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Polytope 2845
Image of polytope 2845 PALP id: 2845
grdb id: 352896
Integer points: [ 1 0 0 0 0 -2 -1 -2 -2 -2 -1 -1 -1 0 -1 -1 0]
[ 0 1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 1 -1 2 2 1 0 1 0 -1 0 1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 14 1 none
Polytope 2846
Image of polytope 2846 PALP id: 2846
grdb id: 353942
Integer points: [ 1 0 1 0 0 -2 0 -2 -1 -2 -1 0 -1 -1 0 -1 0]
[ 0 1 -1 0 0 2 -2 0 -1 1 0 -1 1 0 -1 1 0]
[ 0 0 0 1 -1 1 -1 1 0 1 0 -1 0 1 0 1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + 2*x-1*y*z + x-2*y2*z + x*y-1 + 2*x-1*y + 2*x-1*z + 2*x-2*y*z + z-1 + 2*y-1 + 4*x-1 + x-2*z + 2*y-1*z-1 + 2*x-1*y-1 + y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 2847
Image of polytope 2847 PALP id: 2847
grdb id: 349759
Integer points: [ 1 0 0 -1 -1 -1 -3 -3 -2 -3 -2 -1 -3 -2 -1 0 -1]
[ 0 1 0 0 0 -1 -2 -2 -1 -2 -1 0 -2 -1 -1 0 -1]
[ 0 0 1 -1 1 1 -2 1 1 0 0 0 -1 -1 0 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? x + y + z + x-1*z + 4*x-1 + x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + 2*x-2*y-1*z + 2*x-1*y-1*z-1 + 5*x-2*y-1 + 3*x-2*y-1*z-1 + x-3*y-2*z + 3*x-3*y-2 + 3*x-3*y-2*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 138 1 Lattice Minkowski decompositions of facet 138
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2848
Image of polytope 2848 PALP id: 2848
grdb id: 352650
Integer points: [ 1 0 0 -1 0 -2 -1 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -1 0 -2 -3 -1 -2 0 -1 -2 0 -1 0 -1]
[ 0 0 1 -1 1 -1 -1 -1 -1 -1 0 0 0 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 8 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2849
Image of polytope 2849 PALP id: 2849
grdb id: 352819
Integer points: [ 1 0 0 -1 0 0 -1 -3 -1 -2 -1 -2 0 -1 -2 0 -1]
[ 0 1 0 1 -1 -2 -3 -3 -1 -2 0 -1 -1 -2 -3 0 -1]
[ 0 0 1 0 -1 -1 -2 -2 0 -1 0 -1 0 -1 -2 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 14 1 none
Polytope 2850
Image of polytope 2850 PALP id: 2850
grdb id: 352406
Integer points: [ 1 0 0 0 -2 -2 -3 -3 -1 -2 -1 -3 -2 -1 -1 0 -1]
[ 0 1 0 1 -2 1 -2 0 1 0 0 -1 -1 -1 0 0 -1]
[ 0 0 1 1 -1 -1 -2 -2 0 -1 0 -2 -1 0 -1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? y*z + x + y + z + 2*x-1*y + 4*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 4*x-2*z-1 + 4*x-2*y-1*z-1 + x-3*z-2 + x-2*y-2*z-1 + 2*x-3*y-1*z-2 + x-3*y-2*z-2
67 ? y*z + x + y + z + 2*x-1*y + 5*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 5*x-2*z-1 + 5*x-2*y-1*z-1 + x-3*z-2 + x-2*y-2*z-1 + 2*x-3*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 164 1 Lattice Minkowski decompositions of facet 164
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2851
Image of polytope 2851 PALP id: 2851
grdb id: 352703
Integer points: [ 1 0 0 0 -1 -2 0 -3 -1 -2 0 -1 0 -1 -2 0 -1]
[ 0 1 0 0 1 1 -2 1 -1 0 -1 0 -1 0 1 0 1]
[ 0 0 1 -1 -1 0 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + 2*x-1*y + z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-2*y + 2*y-1*z-1 + 4*x-1*z-1 + 2*x-2*y*z-1 + y-2*z-1 + 3*x-1*y-1*z-1 + 3*x-2*z-1 + x-3*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2852
Image of polytope 2852 PALP id: 2852
grdb id: 349178
Integer points: [ 1 0 0 0 -1 -1 -3 -3 -2 -1 -2 -1 -2 -1 -1 0 0]
[ 0 1 0 1 1 -2 0 1 1 1 0 0 -1 -1 0 0 -1]
[ 0 0 1 1 -1 0 -2 -2 -1 0 -1 0 -1 0 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 136 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2853
Image of polytope 2853 PALP id: 2853
grdb id: 352835
Integer points: [ 1 0 0 0 -1 -1 0 -3 -1 -2 0 -1 -2 -1 -2 0 -1]
[ 0 1 0 -1 0 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 0 1 -1 -1 1 -1 -1 -1 -1 0 0 0 -1 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*z + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1 + 4*x-1*y-1 + y-2*z-1 + 3*x-1*y-1*z-1 + 2*x-2*y-1 + 3*x-1*y-2*z-1 + 2*x-2*y-1*z-1 + 3*x-2*y-2*z-1 + x-3*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2854
Image of polytope 2854 PALP id: 2854
grdb id: 352704
Integer points: [ 1 0 0 0 -1 0 -2 -3 -2 -1 0 -2 -1 -1 0 -1 0]
[ 0 1 0 0 1 -2 1 1 1 0 -1 0 -1 1 0 0 -1]
[ 0 0 1 -1 0 1 -2 -2 -1 0 1 -1 0 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y + 2*y-1*z + z-1 + 2*x-1*y*z-1 + 2*y-1 + 4*x-1 + y-2*z + 3*x-1*z-1 + 2*x-2*y*z-1 + 3*x-1*y-1 + x-2*y*z-2 + 3*x-2*z-1 + x-3*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2855
Image of polytope 2855 PALP id: 2855
grdb id: 353919
Integer points: [ 1 0 0 0 -1 0 -2 -2 -1 -2 -1 0 -1 -1 0 -1 0]
[ 0 1 0 0 1 -2 0 -2 0 -1 -1 -1 -2 0 0 -1 -1]
[ 0 0 1 -1 0 -1 -1 -3 0 -2 -1 0 -2 -1 0 -2 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y + z-1 + 2*y-1 + 2*x-1 + 2*y-1*z-1 + 3*x-1*z-1 + y-2*z-1 + 4*x-1*y-1*z-1 + x-2*z-1 + 2*x-1*y-1*z-2 + 2*x-1*y-2*z-2 + 2*x-2*y-1*z-2 + x-2*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2856
Image of polytope 2856 PALP id: 2856
grdb id: 352916
Integer points: [ 1 0 0 0 0 -2 -1 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 0 1 -2 -2 -1 0 -1 0 -1 0 1 -1 0]
[ 0 0 1 0 -1 0 -2 -3 -2 -1 -1 0 -2 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 66 1 none
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2857
Image of polytope 2857 PALP id: 2857
grdb id: 352810
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 -2 -1 2 -2 -3 0 1 -2 -1 0 -1 0 1 -1]
[ 0 0 1 1 1 -2 0 1 0 -1 1 0 -1 1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 3*x-1*y*z-1 + 2*y-1 + 3*x-1 + y-2*z + x-1*y-1*z + 2*x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-2*z + x-1*y-2 + x-1*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2858
Image of polytope 2858 PALP id: 2858
grdb id: 352783
Integer points: [ 1 0 0 0 0 -1 -2 -3 -2 -1 0 -2 -1 0 -1 0 -1]
[ 0 1 0 1 -1 -2 -1 -2 -2 -1 0 -1 0 -1 -1 0 0]
[ 0 0 1 -1 -1 0 2 2 1 0 -1 1 0 0 1 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + y*z-1 + 2*x-1*z + 2*z-1 + 2*y-1 + 3*x-1 + 3*x-1*y-1*z + x-2*y-1*z2 + y-1*z-1 + 4*x-1*y-1 + 3*x-2*y-1*z + x-1*y-2 + 2*x-2*y-2*z + x-3*y-2*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2859
Image of polytope 2859 PALP id: 2859
grdb id: 353579
Integer points: [ 1 0 -1 0 -1 -1 -3 -3 -2 -3 -2 -1 -2 -1 0 -1 0]
[ 0 1 0 0 0 -2 -2 -4 -3 -3 -2 -1 -1 -2 -1 -1 0]
[ 0 0 0 1 -1 0 -2 -2 -1 -2 -1 0 -1 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + 2*y-1 + x-1 + x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 2*x-2*y-1*z-1 + 4*x-2*y-2*z-1 + 2*x-2*y-3*z-1 + x-3*y-2*z-2 + 2*x-3*y-3*z-2 + x-3*y-4*z-2
77 ? x + y + z + 2*y-1 + x-1 + x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 2*x-2*y-1*z-1 + 5*x-2*y-2*z-1 + 2*x-2*y-3*z-1 + x-3*y-2*z-2 + 2*x-3*y-3*z-2 + x-3*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2860
Image of polytope 2860 PALP id: 2860
grdb id: 349672
Integer points: [ 1 0 -1 0 -1 0 -3 -3 -2 -1 -2 -1 -2 -1 -1 0 0]
[ 0 1 1 0 -1 -1 -3 -4 -3 -2 -2 -1 -1 0 -2 -1 0]
[ 0 0 0 1 -1 1 -2 -2 -1 0 -1 0 -1 0 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 136 1 none
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Polytope 2861
Image of polytope 2861 PALP id: 2861
grdb id: 351073
Integer points: [ 1 0 -1 0 1 -2 1 0 0 0 0 -1 -1 -1 1 0 0]
[ 0 1 1 0 -1 0 -3 -4 -1 -2 -3 0 -1 -2 -2 0 -1]
[ 0 0 0 1 1 -1 1 1 1 1 1 0 0 0 1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Polytope 2862
Image of polytope 2862 PALP id: 2862
grdb id: 351060
Integer points: [ 1 0 0 -1 0 -2 -2 -4 -1 -2 -3 -1 -1 -2 -3 0 -1]
[ 0 1 -1 1 0 0 -3 -4 -1 -2 -3 -2 0 -1 -2 0 -1]
[ 0 0 0 0 1 -1 -2 -3 0 -1 -2 -1 0 -1 -2 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 80 1 none
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2863
Image of polytope 2863 PALP id: 2863
grdb id: 351062
Integer points: [ 1 0 0 -1 0 -2 -2 -4 -1 -2 -3 -1 -2 -3 -1 0 -1]
[ 0 1 0 0 1 -1 -2 -3 0 -1 -2 0 -1 -2 -1 0 -1]
[ 0 0 1 -1 1 -1 1 1 1 1 1 0 0 0 1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 8 1 none
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Polytope 2864
Image of polytope 2864 PALP id: 2864
grdb id: 352837
Integer points: [ 1 0 0 -1 0 -1 -2 -4 -2 -3 -1 -2 -1 -2 -3 0 -1]
[ 0 1 0 0 -1 0 -1 -3 -1 -2 -1 -2 0 -1 -2 0 -1]
[ 0 0 1 -1 1 1 -1 1 1 1 1 1 0 0 0 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + y-1*z + x-1*z + 3*x-1 + 3*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + 3*x-2*y-1*z + 4*x-2*y-1 + 2*x-2*y-2*z + x-2*y-1*z-1 + 3*x-3*y-2*z + 2*x-3*y-2 + x-4*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 2865
Image of polytope 2865 PALP id: 2865
grdb id: 352782
Integer points: [ 1 0 0 0 -1 -2 -2 -4 -1 -3 -2 -1 -3 -2 -1 0 -1]
[ 0 1 -1 0 1 -1 -2 -2 -1 -2 -1 0 -1 0 -1 0 0]
[ 0 0 0 1 0 -2 -1 -3 0 -2 -1 0 -2 -1 -1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + x-1*y + y-1 + 2*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*z-1 + 4*x-2*y-1*z-1 + x-2*y-1*z-2 + x-2*y-2*z-1 + 3*x-3*y-1*z-2 + 2*x-3*y-2*z-2 + x-4*y-2*z-3
80 ? x + y + z + x-1*y + y-1 + 2*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + 3*x-2*z-1 + 4*x-2*y-1*z-1 + x-2*y-1*z-2 + x-2*y-2*z-1 + 3*x-3*y-1*z-2 + 2*x-3*y-2*z-2 + x-4*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2866
Image of polytope 2866 PALP id: 2866
grdb id: 352685
Integer points: [ 1 0 0 0 -1 -2 -2 -4 -2 -3 -1 -2 -3 -1 -1 0 -1]
[ 0 1 0 -1 1 1 -1 1 1 1 0 0 0 -1 1 0 0]
[ 0 0 1 1 0 -2 -1 -3 -1 -2 0 -1 -2 0 -1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 8 1 none
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 2867
Image of polytope 2867 PALP id: 2867
grdb id: 353915
Integer points: [ 1 0 0 0 -1 -1 -1 -3 -2 -1 -2 0 -1 0 -2 -1 0]
[ 0 1 0 0 0 -2 -2 -4 -3 -1 -2 -1 -2 0 -3 -1 -1]
[ 0 0 1 -1 0 0 -2 -2 -1 0 -1 0 -1 0 -2 -1 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + z-1 + 2*y-1 + x-1 + 2*y-1*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2 + 4*x-1*y-2*z-1 + x-1*y-2*z-2 + 2*x-2*y-2*z-1 + 2*x-2*y-3*z-1 + 2*x-2*y-3*z-2 + x-3*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2868
Image of polytope 2868 PALP id: 2868
grdb id: 353584
Integer points: [ 1 0 0 0 0 -2 -2 -4 -1 -3 -2 -1 -3 -1 0 -2 -1]
[ 0 1 -1 0 -1 1 -1 1 -1 0 0 0 1 0 0 1 1]
[ 0 0 0 1 -1 0 -2 -2 -1 -2 -1 0 -1 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + 2*x-1*y + y-1 + 3*x-1 + x-2*y + y-1*z-1 + 3*x-1*z-1 + 2*x-2*y*z-1 + 2*x-1*y-1*z-1 + 4*x-2*z-1 + 2*x-3*y*z-1 + x-2*y-1*z-2 + 2*x-3*z-2 + x-4*y*z-2
67 ? x + y + z + 2*x-1*y + y-1 + 4*x-1 + x-2*y + y-1*z-1 + 3*x-1*z-1 + 2*x-2*y*z-1 + 2*x-1*y-1*z-1 + 5*x-2*z-1 + 2*x-3*y*z-1 + x-2*y-1*z-2 + 2*x-3*z-2 + x-4*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2869
Image of polytope 2869 PALP id: 2869
grdb id: 353583
Integer points: [ 1 0 0 0 0 -2 -2 -4 -1 -3 -2 -1 -1 0 -3 -2 -1]
[ 0 1 -1 0 1 1 1 1 1 1 1 1 0 0 1 0 0]
[ 0 0 0 1 -1 0 -2 -2 0 -1 -1 -1 0 0 -2 -1 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
80 ? x + y + z + y*z-1 + 2*x-1*y + 4*x-1*y*z-1 + y-1 + 2*x-1 + x-2*y + 2*x-1*z-1 + 5*x-2*y*z-1 + x-2*y*z-2 + 2*x-2*z-1 + 2*x-3*y*z-1 + 2*x-3*y*z-2 + x-4*y*z-2
107 rank 3, number 11 x + y + z + y*z-1 + 2*x-1*y + 3*x-1*y*z-1 + y-1 + 2*x-1 + x-2*y + 2*x-1*z-1 + 4*x-2*y*z-1 + x-2*y*z-2 + 2*x-2*z-1 + 2*x-3*y*z-1 + 2*x-3*y*z-2 + x-4*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2870
Image of polytope 2870 PALP id: 2870
grdb id: 353914
Integer points: [ 1 0 0 0 0 -2 -2 -4 -2 -3 -1 -3 -1 -2 0 -1 -1]
[ 0 1 0 0 -1 0 -2 -2 -1 -1 0 -2 -1 -1 0 0 -1]
[ 0 0 1 -1 0 1 1 1 0 1 0 1 0 1 0 1 1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + 2*x-1*z + z-1 + y-1 + 2*x-1 + 2*x-1*y-1*z + x-2*z + 2*x-1*y-1 + 4*x-2*y-1*z + 2*x-2*y-1 + x-2*y-2*z + 2*x-3*y-1*z + 2*x-3*y-2*z + x-4*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Polytope 2871
Image of polytope 2871 PALP id: 2871
grdb id: 352657
Integer points: [ 1 0 0 1 -1 0 -3 -4 -2 -3 -1 -2 0 -1 -2 0 -1]
[ 0 1 0 -1 -1 -1 0 -1 -1 -1 0 0 -1 -1 -1 0 0]
[ 0 0 1 0 0 -1 -2 -3 -1 -2 0 -1 0 -1 -2 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x*y-1 + 2*y-1 + 3*x-1 + y-1*z-1 + 3*x-1*z-1 + x-1*y-1 + 4*x-1*y-1*z-1 + 3*x-2*z-1 + 3*x-2*y-1*z-1 + 2*x-2*y-1*z-2 + x-3*z-2 + 3*x-3*y-1*z-2 + x-4*y-1*z-3
38 ? x + y + z + x*y-1 + 2*y-1 + 3*x-1 + y-1*z-1 + 2*x-1*z-1 + x-1*y-1 + 4*x-1*y-1*z-1 + 3*x-2*z-1 + 3*x-2*y-1*z-1 + 2*x-2*y-1*z-2 + x-3*z-2 + 3*x-3*y-1*z-2 + x-4*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 9 1 irreducible and admissible
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2872
Image of polytope 2872 PALP id: 2872
grdb id: 351015
Integer points: [ 1 0 0 -1 -2 0 -3 -4 -1 -2 -3 -1 0 -1 -2 0 -1]
[ 0 1 0 -1 -1 2 -2 -2 1 0 -1 0 1 0 -1 0 -1]
[ 0 0 1 0 -2 1 -2 -3 0 -1 -2 -1 1 0 -1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? y2*z + 2*y*z + x + y + z + 4*x-1*y + 5*x-1 + 2*x-1*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + 6*x-2*z-1 + 4*x-2*y-1*z-1 + x-2*y-1*z-2 + 4*x-3*y-1*z-2 + x-3*y-2*z-2 + x-4*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Polytope 2873
Image of polytope 2873 PALP id: 2873
grdb id: 352836
Integer points: [ 1 0 0 0 -1 -1 -2 -4 -2 -3 -1 -2 -1 -2 -3 0 -1]
[ 0 1 -1 0 -1 1 2 2 0 1 0 1 0 1 2 0 1]
[ 0 0 0 1 -1 -1 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + 2*x-1*y + x-1*y*z-1 + x-2*y2*z-1 + y-1 + 3*x-1 + 2*x-2*y + 2*x-1*z-1 + 4*x-2*y*z-1 + 2*x-3*y2*z-1 + x-1*y-1*z-1 + 3*x-2*z-1 + 3*x-3*y*z-1 + x-4*y2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2874
Image of polytope 2874 PALP id: 2874
grdb id: 349717
Integer points: [ 1 0 0 -1 -1 -2 -4 -5 -3 -4 -2 -3 -1 -2 -1 -2 0]
[ 0 1 0 -1 0 -1 -3 -4 -2 -3 -1 -2 0 -1 -1 -2 0]
[ 0 0 1 -1 1 1 -2 -2 0 -1 0 -1 0 -1 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 136 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2875
Image of polytope 2875 PALP id: 2875
grdb id: 352732
Integer points: [ 1 0 0 0 -2 -1 -3 -5 -3 -4 -1 -2 -3 -1 -2 0 -1]
[ 0 1 -1 0 -1 -2 -2 -4 -2 -3 -1 -2 -3 0 -1 0 -1]
[ 0 0 0 1 0 -1 -2 -3 -1 -2 0 -1 -2 0 -1 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + y-1 + 2*x-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + x-1*y-2*z-1 + 3*x-2*y-1*z-1 + 4*x-2*y-2*z-1 + 3*x-3*y-2*z-1 + x-3*y-2*z-2 + 2*x-3*y-3*z-2 + 3*x-4*y-3*z-2 + x-5*y-4*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2876
Image of polytope 2876 PALP id: 2876
grdb id: 350427
Integer points: [ 1 0 0 0 -1 -3 -3 -5 -2 -3 -4 -1 -2 -1 -2 0 -1]
[ 0 1 0 -1 -1 0 -1 -1 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 1 1 -2 -2 -3 0 -1 -2 0 -1 0 -1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + y-1*z + 3*x-1 + x-1*y-1*z + 2*x-1*z-1 + 3*x-1*y-1 + 3*x-2*z-1 + 4*x-2*y-1 + 3*x-2*y-1*z-1 + x-3*z-2 + 6*x-3*y-1*z-1 + x-3*y-1*z-2 + 4*x-4*y-1*z-2 + x-5*y-1*z-3
144 rank 3, number 12 x + y + z + y-1*z + 4*x-1 + x-1*y-1*z + 2*x-1*z-1 + 3*x-1*y-1 + 4*x-2*z-1 + 4*x-2*y-1 + 3*x-2*y-1*z-1 + x-3*z-2 + 6*x-3*y-1*z-1 + x-3*y-1*z-2 + 4*x-4*y-1*z-2 + x-5*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 93 1 Lattice Minkowski decompositions of facet 93
Polytope 2877
Image of polytope 2877 PALP id: 2877
grdb id: 352788
Integer points: [ 1 0 0 0 -1 -2 -3 -5 -3 -4 -1 -2 -1 -2 -3 0 -1]
[ 0 1 -1 0 1 1 0 1 1 1 0 0 1 1 1 0 0]
[ 0 0 0 1 -1 0 -2 -3 -1 -2 0 -1 0 -1 -2 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? x + y + z + 2*x-1*y + x-1*y*z-1 + y-1 + 3*x-1 + x-2*y + 2*x-1*z-1 + 4*x-2*y*z-1 + 4*x-2*z-1 + 3*x-3*y*z-1 + 2*x-3*y*z-2 + x-3*z-2 + 3*x-4*y*z-2 + x-5*y*z-3
50 ? x + y + z + 2*x-1*y + x-1*y*z-1 + y-1 + 2*x-1 + x-2*y + 2*x-1*z-1 + 4*x-2*y*z-1 + 2*x-2*z-1 + 3*x-3*y*z-1 + 2*x-3*y*z-2 + x-3*z-2 + 3*x-4*y*z-2 + x-5*y*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2878
Image of polytope 2878 PALP id: 2878
grdb id: 345920
Integer points: [ 1 0 0 -1 0 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -1 -2 1 -2 -1 0 -1 0 -2 -1 0 -1 0]
[ 0 0 1 0 -1 -1 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y + 2*y-1 + 3*x-1 + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + y-2*z-1 + 4*x-1*y-1*z-1 + 3*x-2*z-1 + 2*x-1*y-2*z-1 + 3*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2879
Image of polytope 2879 PALP id: 2879
grdb id: 347831
Integer points: [ 1 0 0 0 -1 0 -2 -2 -1 -2 -1 -1 0 -1 0 -1 0]
[ 0 1 0 0 1 -2 0 -2 -1 -1 0 -2 -1 -1 0 0 -1]
[ 0 0 1 -1 0 -1 -1 -1 0 -1 0 -1 0 -1 0 -1 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*y + z-1 + 2*y-1 + 2*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + y-2*z-1 + 4*x-1*y-1*z-1 + x-2*z-1 + 2*x-1*y-2*z-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2880
Image of polytope 2880 PALP id: 2880
grdb id: 342527
Integer points: [ 1 0 0 0 -1 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 2 -2 2 -1 0 1 -1 0 1 0 1 0]
[ 0 0 0 1 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y2*z-1 + 2*x-1*y + 3*x-1*y*z-1 + x-2*y2*z-1 + y-1 + 4*x-1 + 3*x-1*z-1 + 4*x-2*y*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + 6*x-2*z-1 + 4*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 9 1 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2881
Image of polytope 2881 PALP id: 2881
grdb id: 347781
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 0 0 -2 -2 -1 0 -1 -2 -1 0 -1 0 -1]
[ 0 0 1 -1 0 -2 2 0 -1 -1 0 1 1 -1 0 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + y*z-1 + 2*y-1*z + 2*z-1 + 2*y-1 + x-1 + 2*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-2*z + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 2882
Image of polytope 2882 PALP id: 2882
grdb id: 346002
Integer points: [ 1 0 0 0 -1 -1 0 -3 -2 -1 -2 -1 -2 -1 0 -1 0]
[ 0 1 -1 0 0 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 0 0 1 -1 1 1 1 1 1 0 0 1 1 1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + 2*y-1*z + x-1*z + y-1 + 2*x-1 + y-2*z + 4*x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-2*z + 2*x-2*y-1*z + 2*x-2*y-1 + 3*x-2*y-2*z + x-3*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2883
Image of polytope 2883 PALP id: 2883
grdb id: 345957
Integer points: [ 1 0 0 0 0 -2 -1 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 0 -2 -3 -1 -2 0 -1 0 -1 -2 0 -1]
[ 0 0 1 -1 1 1 0 1 1 1 0 0 1 1 1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + y-1*z + 2*x-1*z + z-1 + 2*y-1 + 2*x-1 + 4*x-1*y-1*z + x-2*z + 3*x-1*y-1 + 2*x-1*y-2*z + 3*x-2*y-1*z + x-1*y-2 + 3*x-2*y-2*z + x-2*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2884
Image of polytope 2884 PALP id: 2884
grdb id: 186756
Integer points: [ 1 0 0 -1 1 0 0 -2 -2 -1 -2 -1 0 -1 -1 0 1]
[ 0 1 0 1 -2 -1 -1 1 1 0 1 0 -1 0 1 0 -1]
[ 0 0 1 1 0 -1 1 -1 1 1 0 0 0 -1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 1 none
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Polytope 2885
Image of polytope 2885 PALP id: 2885
grdb id: 186731
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 0 2 -2 1 2 0 1 0 -1 1 1 0 -1]
[ 0 0 1 0 -1 2 -2 2 1 1 1 0 -1 0 1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x-1*y2*z2 + 2*y*z + x-1*y2*z + x-1*y*z2 + x + y + z + 2*x-1*y*z + 2*x-1*y + 2*x-1*z + 3*x-1 + 2*y-1*z-1 + x-1*z-1 + x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2*z-2
101 ? x-1*y2*z2 + 2*y*z + x-1*y2*z + x-1*y*z2 + x + y + z + 5*x-1*y*z + 2*x-1*y + 2*x-1*z + 6*x-1 + 2*y-1*z-1 + x-1*z-1 + x-1*y-1 + 4*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 147 1 Lattice Minkowski decompositions of facet 147
Polytope 2886
Image of polytope 2886 PALP id: 2886
grdb id: 186785
Integer points: [ 1 0 0 1 1 0 0 -1 -1 0 0 -1 -1 -1 0 0 0]
[ 0 1 0 -1 0 -2 1 -2 2 0 -1 1 0 -1 1 0 -1]
[ 0 0 1 0 -1 1 -2 2 -2 -1 0 -1 0 1 -1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
26 rank 2, number 8 x + y + z + x*z-1 + y*z-1 + x*y-1 + y-1*z + y*z-2 + x-1*y2*z-2 + 3*z-1 + 4*x-1*y*z-1 + 3*y-1 + 6*x-1 + y-2*z + 4*x-1*y-1*z + x-1*y-2*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 10 2 Lattice Minkowski decompositions of facet 10
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Polytope 2887
Image of polytope 2887 PALP id: 2887
grdb id: 186783
Integer points: [ 1 0 1 -1 0 -1 -1 0 -1 -1 -1 -1 0 0 0 0 1]
[ 0 1 0 0 -1 -1 1 1 1 1 0 0 0 1 0 0 0]
[ 0 0 2 -2 0 -1 -1 2 1 0 -1 0 -1 1 0 1 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 x*z2 + y*z2 + 2*x*z + 2*y*z + x + y + 3*z + x-1*y*z + 2*x-1*y + 2*z-1 + x-1*y*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + x-1*z-2 + x-1*y-1*z-1
20 rank 1, V16 x*z2 + y*z2 + 2*x*z + 2*y*z + x + y + 2*z + x-1*y*z + 2*x-1*y + 2*z-1 + x-1*y*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + x-1*z-2 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2888
Image of polytope 2888 PALP id: 2888
grdb id: 186782
Integer points: [ 1 1 -1 0 1 0 -2 0 -2 -1 -1 0 -1 -1 0 1 0]
[ 0 2 -2 0 2 1 -2 1 -1 0 0 1 -1 -1 0 1 -1]
[ 0 0 0 1 -1 -1 1 1 1 0 1 0 0 1 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 1 none
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2889
Image of polytope 2889 PALP id: 2889
grdb id: 186748
Integer points: [ 1 0 0 0 -2 0 -2 1 -3 -1 0 -1 -2 -1 1 0 -1]
[ 0 1 -1 0 2 -2 0 -2 2 -1 -1 0 1 1 -1 0 1]
[ 0 0 0 1 -1 1 -1 2 -2 0 1 0 -1 0 1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
75 ? x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*x-1*y + 4*y-1*z + 2*x-1*y*z-1 + x-2*y2*z-1 + y-1 + 7*x-1 + y-2*z + 4*x-2*y*z-1 + 2*x-1*y-1 + x-3*y2*z-2 + x-2*z-1
13 rank 2, number 12 x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*x-1*y + 2*y-1*z + 2*x-1*y*z-1 + x-2*y2*z-1 + y-1 + 2*x-1 + y-2*z + 2*x-2*y*z-1 + 2*x-1*y-1 + x-3*y2*z-2 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 144 1 Lattice Minkowski decompositions of facet 144
Image of facet 1 2 irreducible and admissible
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Polytope 2890
Image of polytope 2890 PALP id: 2890
grdb id: 186772
Integer points: [ 1 0 0 0 0 1 -2 -2 -3 -1 -2 -1 0 -1 0 1 -1]
[ 0 1 0 0 -1 -2 1 2 2 0 1 0 -1 1 0 -1 1]
[ 0 0 1 -1 0 2 -2 -1 -2 -1 -1 0 1 -1 0 1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*x-1*y + 4*y-1*z + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + y-1 + 6*x-1 + 2*x-1*z-1 + 4*x-2*y*z-1 + x-2*y*z-2 + x-3*y2*z-2
40 rank 2, number 10 x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*x-1*y + 4*y-1*z + z-1 + 3*x-1*y*z-1 + x-2*y2*z-1 + y-1 + 6*x-1 + 2*x-1*z-1 + 4*x-2*y*z-1 + x-2*y*z-2 + x-3*y2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 59 2 Lattice Minkowski decompositions of facet 59
Polytope 2891
Image of polytope 2891 PALP id: 2891
grdb id: 185547
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 1 0 -2 -1 -2 0 0 -1 -1 -2 0 -1 -1]
[ 0 0 1 0 1 -1 0 1 -2 1 0 0 -1 -1 0 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + x-1*y*z + x-1*y + 2*x-1*z + 2*y-1 + 3*x-1 + x-1*y-1*z + 2*y-1*z-1 + x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + x-1*y-2*z-2
128 ? x + y + z + x-1*y*z + x-1*y + 2*x-1*z + 2*y-1 + 3*x-1 + x-1*y-1*z + 2*y-1*z-1 + x-1*z-1 + 4*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 143 1 Lattice Minkowski decompositions of facet 143
Polytope 2892
Image of polytope 2892 PALP id: 2892
grdb id: 186241
Integer points: [ 1 0 0 -1 -1 1 -1 0 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 0 -1 -1 -1 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 0 1 -1 1 -2 -2 0 -1 0 -1 0 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y + x-1*z + x*y-1*z-1 + 2*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + 3*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + y-1*z-2 + 3*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Polytope 2893
Image of polytope 2893 PALP id: 2893
grdb id: 186627
Integer points: [ 1 0 0 -1 1 -1 1 0 -1 0 0 -1 1 0 0 -1 -1]
[ 0 1 0 1 -1 1 -2 -2 -1 -1 0 0 -1 -1 0 0 1]
[ 0 0 1 1 -1 -1 0 1 1 0 -1 0 0 1 0 1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + 2*y-1*z + 2*x-1*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + x*y-2 + 3*y-1 + 2*x-1 + y-2*z + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2894
Image of polytope 2894 PALP id: 2894
grdb id: 186242
Integer points: [ 1 0 0 0 -1 -1 -1 -2 -2 -2 -2 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 1 -2 1 -2 -1 0 -1 0 -1 0 -1 0]
[ 0 0 1 -1 0 -1 0 -1 -1 -1 -1 0 0 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + 3*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2 + 3*x-2*y-1*z-1 + x-2*y-2*z-1
100 ? x + y + z + x-1*y + z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + 3*x-1*z-1 + x-2*y*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2 + 3*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2895
Image of polytope 2895 PALP id: 2895
grdb id: 186614
Integer points: [ 1 0 0 0 -1 -1 1 0 -1 -1 -1 -1 0 0 0 0 1]
[ 0 1 0 1 1 1 -2 -2 -1 0 0 1 -1 0 -1 0 -1]
[ 0 0 1 -1 1 -1 0 -1 -1 -1 0 0 -1 -1 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + x-1*y*z + y*z-1 + 2*x*y-1 + 2*x-1*y + 3*z-1 + x-1*y*z-1 + x*y-2 + 2*y-1 + 2*x-1 + 3*y-1*z-1 + 2*x-1*z-1 + y-2*z-1 + x-1*y-1*z-1
20 rank 1, V16 x + y + z + x-1*y*z + y*z-1 + 2*x*y-1 + 2*x-1*y + 3*z-1 + x-1*y*z-1 + x*y-2 + 3*y-1 + 2*x-1 + 3*y-1*z-1 + 2*x-1*z-1 + y-2*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Polytope 2896
Image of polytope 2896 PALP id: 2896
grdb id: 186640
Integer points: [ 1 0 0 0 -1 1 0 -2 -2 -1 0 -1 0 -1 1 0 -1]
[ 0 1 0 1 1 -2 -1 1 1 0 -1 0 0 1 -1 0 1]
[ 0 0 1 -1 1 0 -1 0 -1 -1 0 0 -1 -1 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y*z + y*z-1 + 2*x*y-1 + 2*x-1*y + 2*z-1 + 2*x-1*y*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1
40 rank 2, number 10 x + y + z + x-1*y*z + y*z-1 + 2*x*y-1 + 3*x-1*y + 2*z-1 + 2*x-1*y*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2897
Image of polytope 2897 PALP id: 2897
grdb id: 186448
Integer points: [ 1 0 0 0 1 -2 1 0 -2 -1 0 -1 0 -1 1 0 -1]
[ 0 1 0 0 -1 1 -2 -2 0 -1 -1 0 -1 0 -1 0 1]
[ 0 0 1 -1 -1 0 0 1 1 1 0 0 1 1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? x + y + z + 2*x*y-1 + 2*x-1*y + 2*y-1*z + 2*x-1*z + x*y-1*z-1 + z-1 + x*y-2 + 4*y-1 + 3*x-1 + x-2*y + y-2*z + 2*x-1*y-1*z + x-2*z
10 rank 1, V18 x + y + z + 2*x*y-1 + 2*x-1*y + 2*y-1*z + 2*x-1*z + x*y-1*z-1 + z-1 + x*y-2 + 2*y-1 + 2*x-1 + x-2*y + y-2*z + 2*x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2898
Image of polytope 2898 PALP id: 2898
grdb id: 186626
Integer points: [ 1 0 0 0 1 0 -1 -2 -2 -1 0 -1 0 0 -1 -1 0]
[ 0 1 0 0 1 -2 1 1 0 1 1 0 0 -1 0 -1 -1]
[ 0 0 1 -1 -1 1 0 -1 -1 -1 -1 0 0 1 -1 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x*y*z-1 + x + y + z + 3*y*z-1 + x-1*y + 2*y-1*z + z-1 + 3*x-1*y*z-1 + 2*y-1 + 3*x-1 + y-2*z + 2*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2899
Image of polytope 2899 PALP id: 2899
grdb id: 186540
Integer points: [ 1 0 0 1 -1 -2 1 0 1 0 0 -1 1 0 -1 0 -1]
[ 0 1 0 -1 0 1 -2 -1 -2 -1 -1 0 -1 0 0 0 1]
[ 0 0 1 0 1 0 -1 -2 -2 0 -1 0 -1 0 -1 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
56 rank 2, number 11 x + y + z + x*y-1 + 2*x-1*y + x-1*z + 2*x*y-1*z-1 + 2*z-1 + 2*y-1 + x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + 2*x-1*z-1 + x*y-2*z-2 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 71 1 Lattice Minkowski decompositions of facet 71
Polytope 2900
Image of polytope 2900 PALP id: 2900
grdb id: 186305
Integer points: [ 1 0 0 1 -1 0 -2 -2 0 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 0 1 -1 1 1 -1 1 0 0 0 0 0 -1 -1]
[ 0 0 1 -1 1 1 1 0 -2 0 1 0 -1 0 -1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + x-1*y*z + x*z-1 + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + 2*z-1 + 3*y-1 + 4*x-1 + x-2*y + 3*y-1*z-1 + 2*x-1*z-1 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 2901
Image of polytope 2901 PALP id: 2901
grdb id: 186252
Integer points: [ 1 0 0 1 -1 1 -2 0 -2 -1 0 -1 0 -1 -1 0 0]
[ 0 1 0 -1 1 0 1 -2 0 0 0 -1 -1 1 0 0 -1]
[ 0 0 1 -1 1 -1 0 -1 -1 -1 -1 -1 -1 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + x*z-1 + 2*x-1*y + x*y-1*z-1 + 3*z-1 + 2*y-1 + 3*x-1 + x-2*y + 3*y-1*z-1 + 3*x-1*z-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2902
Image of polytope 2902 PALP id: 2902
grdb id: 186306
Integer points: [ 1 0 0 1 -1 1 0 -2 0 0 0 1 -1 -1 0 0 -1]
[ 0 1 0 -1 0 -1 -1 1 -1 -1 -1 -1 0 0 0 0 1]
[ 0 0 1 1 1 -1 1 0 -2 0 -1 0 0 -1 0 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + x*y-1*z + z + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + x*y-1*z-1 + 2*z-1 + 3*y-1 + 3*x-1 + x-2*y + 3*y-1*z-1 + 2*x-1*z-1 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2903
Image of polytope 2903 PALP id: 2903
grdb id: 186477
Integer points: [ 1 0 1 0 -1 -2 0 -1 -2 -2 -1 -1 0 -1 -1 0 0]
[ 0 1 -1 0 1 1 -2 -2 -1 0 0 -1 -1 1 0 0 -1]
[ 0 0 0 1 1 0 -1 -2 -2 -1 0 -1 0 0 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + x-1*y*z + x*y-1 + 2*x-1*y + 2*y-1 + 4*x-1 + x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + y-2*z-1 + 4*x-1*y-1*z-1 + 2*x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
52 rank 2, number 52 x + y + z + x-1*y*z + x*y-1 + 2*x-1*y + 2*y-1 + 3*x-1 + x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + y-2*z-1 + 3*x-1*y-1*z-1 + 2*x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 96 1 Lattice Minkowski decompositions of facet 96
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2904
Image of polytope 2904 PALP id: 2904
grdb id: 185509
Integer points: [ 1 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 -1 0 -2 2 -2 2 -1 1 0 1 0 -1 1 0 -1]
[ 0 0 0 1 1 -2 2 -1 2 0 1 -1 0 1 -1 0 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + 2*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + x-1*y2*z-2 + 3*x-1*y*z-1 + 3*x-1 + 2*x-1*y-1*z + x-1*y-2*z2 + x-1*y-1 + x-1*y-2*z
127 ? x + y + z + 2*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + x-1*y2*z-2 + 4*x-1*y*z-1 + 6*x-1 + 5*x-1*y-1*z + x-1*y-2*z2 + x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 145 1 Lattice Minkowski decompositions of facet 145
Polytope 2905
Image of polytope 2905 PALP id: 2905
grdb id: 186059
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 -1 -2 2 -1 2 1 0 1 0 -1 1 0 -1]
[ 0 0 1 -1 0 2 -2 2 -1 0 1 -1 0 1 -1 0 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
91 ? x + y + z + 2*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + x-1*y2*z-2 + 4*x-1*y*z-1 + 7*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + x-1*z-1 + x-1*y-1
17 rank 1, V22 x + y + z + 2*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + x-1*y2*z-2 + 2*x-1*y*z-1 + 2*x-1 + 2*x-1*y-1*z + x-1*y-2*z2 + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 142 1 Lattice Minkowski decompositions of facet 142
Polytope 2906
Image of polytope 2906 PALP id: 2906
grdb id: 186665
Integer points: [ 1 0 0 -1 0 -1 -1 0 -1 -1 -1 0 0 -1 0 0 0]
[ 0 1 0 1 1 1 -1 -2 -2 0 -1 0 -1 0 1 0 -1]
[ 0 0 1 0 -2 -1 2 1 2 0 1 -1 0 1 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + 2*y*z-1 + x-1*y + y-1*z + 2*x-1*z + x-1*y-1*z2 + y*z-2 + 3*z-1 + x-1*y*z-1 + 3*y-1 + 3*x-1 + y-2*z + 3*x-1*y-1*z + x-1*y-2*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2907
Image of polytope 2907 PALP id: 2907
grdb id: 186304
Integer points: [ 1 0 0 0 0 0 -1 -2 -2 -2 -2 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 1 -2 1 0 -1 0 -1 1 0 -1 0]
[ 0 0 1 -1 0 1 2 -1 2 1 0 1 0 1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 66 1 none
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Polytope 2908
Image of polytope 2908 PALP id: 2908
grdb id: 186239
Integer points: [ 1 0 1 0 -1 0 -2 -1 -2 -2 -2 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 1 -1 2 -1 -1 1 0 1 0 -1 0 0 -1]
[ 0 0 0 1 -1 1 -1 -1 -1 -1 -1 0 0 0 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2909
Image of polytope 2909 PALP id: 2909
grdb id: 186653
Integer points: [ 1 0 1 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 -1 0 2 -2 0 0 -2 -1 -1 0 1 1 -1 -1 0]
[ 0 0 0 1 -1 1 -1 1 1 0 1 0 -1 0 0 1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 8 1 none
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2910
Image of polytope 2910 PALP id: 2910
grdb id: 186253
Integer points: [ 1 0 1 0 0 1 -2 -1 -2 0 -1 0 -1 -2 0 -1 -1]
[ 0 1 -1 0 0 -1 1 -1 -1 -1 -1 -1 0 0 0 0 1]
[ 0 0 0 1 -1 -1 0 2 2 0 1 1 0 1 0 1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*y-1 + 2*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + x*y-1*z-1 + z-1 + 3*y-1 + 3*x-1 + x-2*y + 3*x-1*y-1*z + 2*x-2*z + x-2*y-1*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2911
Image of polytope 2911 PALP id: 2911
grdb id: 186035
Integer points: [ 1 0 0 -1 -2 1 1 -2 1 0 -1 0 -1 0 1 0 -1]
[ 0 1 0 0 1 -2 -2 0 -3 -2 -1 -1 0 -1 -1 0 1]
[ 0 0 1 -1 0 0 -1 -1 -1 -1 -1 0 0 -1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
109 ? x + y + z + 2*x*y-1 + 2*x-1*y + x*y-2 + 4*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1 + x*y-3*z-1 + 3*y-2*z-1 + 3*x-1*y-1*z-1 + x-2*z-1
39 ? x + y + z + 2*x*y-1 + 2*x-1*y + x*y-2 + 2*y-1 + 2*x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1 + x*y-3*z-1 + 3*y-2*z-1 + 3*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Polytope 2912
Image of polytope 2912 PALP id: 2912
grdb id: 186243
Integer points: [ 1 0 0 -1 0 -1 -2 -1 -2 -2 -2 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -1 0 0 -2 -3 -2 -1 -1 0 -2 -1 -1 0]
[ 0 0 1 0 -1 -1 -1 0 -1 -1 -1 0 0 -1 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + x-2*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 3*x-2*y-1*z-1 + 3*x-2*y-2*z-1 + x-2*y-3*z-1
143 ? x + y + z + x-1*y + 2*y-1 + 3*x-1 + y-1*z-1 + x-1*z-1 + 4*x-1*y-1 + 3*x-1*y-1*z-1 + x-2*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 3*x-2*y-1*z-1 + 3*x-2*y-2*z-1 + x-2*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2913
Image of polytope 2913 PALP id: 2913
grdb id: 186612
Integer points: [ 1 0 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 1 -1 -2 -1 -3 0 -2 -1 0 -2 -1 0 -1]
[ 0 0 1 -1 -1 1 1 -1 1 -1 0 0 0 1 0 0 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + 2*y-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + y-2*z + x-1*y-1*z + 2*x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-2*z + x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-3*z
17 rank 1, V22 x + y + z + 2*y-1*z + z-1 + x-1*y*z-1 + 3*y-1 + 2*x-1 + y-2*z + x-1*y-1*z + 2*x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-2*z + x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2914
Image of polytope 2914 PALP id: 2914
grdb id: 186299
Integer points: [ 1 0 0 0 0 0 -1 -1 -3 -2 -1 -2 -1 -2 -1 -1 0]
[ 0 1 0 0 -1 1 1 -1 1 1 1 1 1 0 0 0 0]
[ 0 0 1 -1 0 1 -1 1 1 1 1 0 0 1 1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? y*z + x + y + z + 3*x-1*y*z + 3*x-1*y + 3*x-1*z + 3*x-2*y*z + z-1 + x-1*y*z-1 + y-1 + 3*x-1 + 2*x-2*y + x-1*y-1*z + 2*x-2*z + x-3*y*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2915
Image of polytope 2915 PALP id: 2915
grdb id: 186256
Integer points: [ 1 0 0 0 1 -1 0 -2 -3 -1 -2 -1 -2 0 -1 0 -1]
[ 0 1 0 0 -1 1 -1 -1 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 -1 1 0 1 -2 -2 0 -1 0 -1 0 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + x*y-1*z + z + x-1*y + y-1*z + z-1 + 3*y-1 + 3*x-1 + 2*x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + 2*x-2*z-1 + 3*x-2*y-1*z-1 + x-2*y-1*z-2 + x-3*y-1*z-2
52 rank 2, number 52 x + y + x*y-1*z + z + x-1*y + y-1*z + z-1 + 3*y-1 + 3*x-1 + 3*x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + 2*x-2*z-1 + 3*x-2*y-1*z-1 + x-2*y-1*z-2 + x-3*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2916
Image of polytope 2916 PALP id: 2916
grdb id: 186255
Integer points: [ 1 0 0 0 1 0 -1 -2 -3 -2 -1 -2 -1 -1 0 -1 0]
[ 0 1 0 0 -1 -1 1 -1 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 -1 0 -1 -1 0 -1 -1 -1 -1 -1 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*y-1 + z-1 + x-1*y*z-1 + 3*y-1 + 2*x-1 + y-1*z-1 + 3*x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1 + 3*x-2*y-1*z-1 + x-3*y-1*z-1
146 ? x + y + z + x*y-1 + z-1 + x-1*y*z-1 + 3*y-1 + 3*x-1 + y-1*z-1 + 3*x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1 + 3*x-2*y-1*z-1 + x-3*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 9 1 irreducible and admissible
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2917
Image of polytope 2917 PALP id: 2917
grdb id: 186249
Integer points: [ 1 0 1 -1 0 -1 -1 -1 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 1 -1 1 0 0 0 -2 -3 -2 -1 -2 -1 -1 0 -1 0]
[ 0 0 0 0 1 -1 1 -2 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 66 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2918
Image of polytope 2918 PALP id: 2918
grdb id: 186279
Integer points: [ 1 0 1 -1 0 -1 1 0 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 1 -1 1 0 0 -2 -3 -3 -2 -1 -2 -1 -1 0 -1 0]
[ 0 0 0 0 1 1 -1 -2 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2919
Image of polytope 2919 PALP id: 2919
grdb id: 186187
Integer points: [ 1 0 1 0 -1 0 -1 -1 -3 -2 -1 0 -1 0 -2 -2 -1]
[ 0 1 -1 0 1 -1 -1 -1 -1 -1 -1 -1 0 0 -1 0 0]
[ 0 0 0 1 -1 1 -1 1 -1 0 0 0 0 0 -1 -1 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*y-1 + y-1*z + x-1*y*z-1 + 3*y-1 + 3*x-1 + x-1*y-1*z + 2*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + 2*x-2*z-1 + 2*x-2*y-1 + 2*x-2*y-1*z-1 + x-3*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2920
Image of polytope 2920 PALP id: 2920
grdb id: 186479
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 -1 0 2 0 -2 2 3 -1 0 1 1 2 -1 0 1]
[ 0 0 0 1 1 -1 -2 2 2 -1 0 1 0 1 -1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x-1*y3*z2 + y2*z + x-1*y2*z2 + y*z + 3*x-1*y2*z + x + y + z + 4*x-1*y*z + 3*x-1*y + y-1 + 6*x-1 + 2*y-1*z-1 + x-1*z-1 + 4*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Polytope 2921
Image of polytope 2921 PALP id: 2921
grdb id: 186624
Integer points: [ 1 0 1 0 0 0 -1 -2 -2 -1 -1 0 0 0 -1 -1 0]
[ 0 1 -1 0 0 -2 2 2 3 1 2 -1 0 1 0 1 -1]
[ 0 0 0 1 -1 1 -2 -1 -2 0 -1 1 0 -1 0 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + 2*y*z-1 + 2*x-1*y2*z-1 + x*y-1 + 2*x-1*y + 2*y-1*z + x-1*y2*z-2 + x-2*y3*z-2 + z-1 + 3*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 2*x-1 + y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2922
Image of polytope 2922 PALP id: 2922
grdb id: 186663
Integer points: [ 1 0 0 0 1 0 -2 -2 -3 -1 -2 0 -1 -1 1 0 -1]
[ 0 1 0 0 -2 -1 1 2 2 0 1 -1 0 1 -1 0 1]
[ 0 0 1 -1 0 -1 0 -1 -1 -1 -1 0 0 -1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + 2*x*y-1 + x-1*y + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + y-1*z-1 + 3*x-1*z-1 + 3*x-2*y*z-1 + x-3*y2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2923
Image of polytope 2923 PALP id: 2923
grdb id: 186637
Integer points: [ 1 0 1 0 -2 1 -1 1 -3 0 -1 -2 -1 0 1 0 -1]
[ 0 1 -1 0 2 -2 0 -2 2 -1 0 1 1 -1 -1 0 1]
[ 0 0 0 1 -1 1 -1 2 -2 1 0 -1 0 0 1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 x + y + 2*x*y-1*z + z + x*y-2*z2 + x*y-1 + 2*x-1*y + x*y-2*z + 4*y-1*z + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 6*x-1 + x-1*z-1 + 4*x-2*y*z-1 + x-3*y2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 59 2 Lattice Minkowski decompositions of facet 59
Polytope 2924
Image of polytope 2924 PALP id: 2924
grdb id: 181703
Integer points: [ 1 0 -1 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 1 0 0 1 -1 -2 -2 0 -1 0 -1 -2 -1 0 -1]
[ 0 0 0 1 -1 1 1 -1 1 1 1 0 0 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 8 1 none
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 2925
Image of polytope 2925 PALP id: 2925
grdb id: 181838
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 -1 -1]
[ 0 1 0 1 -1 1 0 -2 -2 -1 -2 -1 0 -1 0 -1 0]
[ 0 0 1 0 1 -1 1 1 -1 1 0 0 0 0 0 -1 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 2926
Image of polytope 2926 PALP id: 2926
grdb id: 184688
Integer points: [ 1 0 0 -1 1 -2 1 1 -2 0 -1 0 -1 0 1 -1 0]
[ 0 1 0 -1 0 0 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 0 1 1 -2 1 -1 -2 1 0 0 -1 1 0 -1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? x + y + z + 2*x*z-1 + 2*x-1*z + x*z-2 + x*y-1*z-1 + 3*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + x-2*z + x*y-1*z-2 + 3*y-1*z-1 + 3*x-1*y-1 + x-2*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2927
Image of polytope 2927 PALP id: 2927
grdb id: 184657
Integer points: [ 1 0 0 -1 1 1 -2 1 -1 0 -1 0 0 1 -1 0 1]
[ 0 1 0 1 0 -2 1 -2 0 -1 0 -1 0 -1 1 0 -1]
[ 0 0 1 1 -1 0 0 -1 -1 -1 0 0 -1 -1 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 x + y + z + x-1*y*z + x*z-1 + 2*x*y-1 + 2*x-1*y + 2*x*y-1*z-1 + 2*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2928
Image of polytope 2928 PALP id: 2928
grdb id: 181714
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 1 -1 1 -2 -2 0 -1 1 0 -1 0 0 -1]
[ 0 0 1 1 -1 -1 1 0 1 1 1 0 0 0 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + x-1*y*z + 2*x-1*y + y-1*z + 3*x-1*z + x-1*y*z-1 + 2*y-1 + 5*x-1 + 3*x-1*y-1*z + 2*x-1*z-1 + 4*x-1*y-1 + x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 2929
Image of polytope 2929 PALP id: 2929
grdb id: 181660
Integer points: [ 1 0 0 0 -1 -1 -1 0 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 1 0 -1 1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 1 1 0 1 1 -2 -2 0 -1 0 -1 0 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + x-1*y + y-1*z + x-1*z + 2*z-1 + 3*y-1 + 3*x-1 + x-1*y-1*z + 3*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + y-1*z-2 + 3*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2930
Image of polytope 2930 PALP id: 2930
grdb id: 181753
Integer points: [ 1 0 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 1 1 -1 -1 -1 0 0 0 -1 -1 0 0 -1]
[ 0 0 1 0 1 0 -2 1 -2 1 0 -1 0 -1 0 -1 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y*z + x-1*y + 2*x-1*z + 2*z-1 + y-1 + 4*x-1 + x-1*y-1*z + 2*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + y-1*z-2 + 3*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2931
Image of polytope 2931 PALP id: 2931
grdb id: 183533
Integer points: [ 1 0 0 0 -1 0 -2 -1 -2 -2 -1 -1 0 -1 -1 0 0]
[ 0 1 0 -1 0 -1 1 0 1 1 0 0 -1 1 1 0 0]
[ 0 0 1 1 1 -1 0 -2 -2 -1 0 -1 0 0 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + 2*x-1*y + y-1*z + x-1*z + 2*z-1 + 2*x-1*y*z-1 + 2*y-1 + 3*x-1 + x-2*y + y-1*z-1 + 3*x-1*z-1 + 2*x-2*y*z-1 + x-1*z-2 + x-2*y*z-2
39 ? x + y + z + 2*x-1*y + y-1*z + x-1*z + 2*z-1 + 2*x-1*y*z-1 + 2*y-1 + 4*x-1 + x-2*y + y-1*z-1 + 4*x-1*z-1 + 2*x-2*y*z-1 + x-1*z-2 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 96 1 Lattice Minkowski decompositions of facet 96
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2932
Image of polytope 2932 PALP id: 2932
grdb id: 181709
Integer points: [ 1 0 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 1 -1 -2 -1 -2 -1 0 -2 -1 0 -1 0 -1]
[ 0 0 1 -1 0 1 0 -2 -2 0 0 -1 -1 -1 0 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y + y-1*z + z-1 + 2*y-1 + 3*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + 4*x-1*y-1*z-1 + x-1*y-2 + x-1*y-1*z-2 + 2*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 2933
Image of polytope 2933 PALP id: 2933
grdb id: 181894
Integer points: [ 1 0 0 0 0 0 -1 -2 -2 -2 -2 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 1 -1 -1 -1 -1 -1 0 0 0 -1 -1 0]
[ 0 0 1 -1 0 1 1 1 -2 0 -1 1 0 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 y*z + x + y + z + 2*x-1*z + z-1 + y-1 + 4*x-1 + x-1*y-1*z + 2*x-1*z-1 + 3*x-1*y-1 + x-2*y-1*z + 2*x-1*y-1*z-1 + 3*x-2*y-1 + 3*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 2934
Image of polytope 2934 PALP id: 2934
grdb id: 181682
Integer points: [ 1 0 1 -1 0 -1 -2 -1 -2 -2 -2 -1 -1 -1 -1 0 0]
[ 0 1 -1 1 0 1 1 -2 -2 -1 0 -1 0 -1 0 -1 0]
[ 0 0 0 0 1 -1 -1 -1 -1 -1 -1 0 0 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 8 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2935
Image of polytope 2935 PALP id: 2935
grdb id: 181758
Integer points: [ 1 0 0 0 -1 -1 -1 -2 -2 -2 -2 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 0 2 -2 2 -1 1 0 1 0 -1 1 0 -1]
[ 0 0 1 1 -1 -1 0 -1 -1 -1 -1 0 0 0 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y2*z-1 + 2*x-1*y + y-1*z + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 4*x-1 + x-1*z-1 + 3*x-2*y*z-1 + 3*x-1*y-1 + 3*x-2*z-1 + x-1*y-2 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2936
Image of polytope 2936 PALP id: 2936
grdb id: 181988
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 0 2 -2 -2 -1 -1 -1 0 1 0 1 -1 0]
[ 0 0 0 1 -1 -1 1 2 2 0 1 0 -1 1 0 1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y2*z-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + 2*x-1*y*z-1 + y-1 + 5*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 2937
Image of polytope 2937 PALP id: 2937
grdb id: 181441
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 0 2 -2 -2 -1 -1 -1 0 1 0 1 -1 0]
[ 0 0 1 1 1 -1 1 0 -1 1 0 0 0 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y2*z-1 + 2*x-1*y + y-1*z + x-1*z + 3*x-1*y*z-1 + 2*y-1 + 5*x-1 + 2*x-1*y-1*z + 3*x-1*z-1 + 4*x-1*y-1 + x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 9 1 irreducible and admissible
Polytope 2938
Image of polytope 2938 PALP id: 2938
grdb id: 184165
Integer points: [ 1 0 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 0 -1 0 -1 -1 -1 -1 -1 0 0 -1 0 0]
[ 0 0 1 1 1 -1 -2 2 -2 -1 0 1 -1 0 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + y-1*z + x-1*z + x-1*y-1*z2 + 2*z-1 + 2*y-1 + 3*x-1 + 4*x-1*y-1*z + y-1*z-1 + 3*x-1*z-1 + 6*x-1*y-1 + x-1*z-2 + 4*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 9 1 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2939
Image of polytope 2939 PALP id: 2939
grdb id: 178124
Integer points: [ 1 0 0 0 -1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 0]
[ 0 0 1 -1 0 1 -1 -2 2 -1 0 1 -1 0 1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y + y-1*z + 2*x-1*z + x-1*y-1*z2 + z-1 + 2*y-1 + 4*x-1 + 4*x-1*y-1*z + y-1*z-1 + 2*x-1*z-1 + 6*x-1*y-1 + 4*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 2940
Image of polytope 2940 PALP id: 2940
grdb id: 184644
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 0 -2 -1 2 -2 1 0 1 -1 0 -1 0 1 -1]
[ 0 0 1 -1 1 1 -2 1 -2 0 -1 0 -1 1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + z-1 + 3*x-1*y*z-1 + 2*y-1 + 3*x-1 + y-2*z + x-1*y-1*z + x-1*y*z-2 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2941
Image of polytope 2941 PALP id: 2941
grdb id: 184793
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 -1 2 -1 -2 2 -1 0 1 0 1 -1 0 1]
[ 0 0 1 -1 0 1 -2 -2 2 -1 0 1 -1 0 -1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? x-1*y2*z2 + 2*y*z + x-1*y2*z + x + y + z + 4*x-1*y*z + 3*x-1*y + z-1 + y-1 + 6*x-1 + 2*y-1*z-1 + 3*x-1*z-1 + 4*x-1*y-1*z-1 + x-1*y-1*z-2 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 2942
Image of polytope 2942 PALP id: 2942
grdb id: 181688
Integer points: [ 1 0 -1 0 -1 -1 -1 0 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 1 0 0 -1 0 -2 -3 -2 -1 -2 -1 0 -1 -1 0]
[ 0 0 0 1 -1 -1 1 1 1 1 1 0 0 0 1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2943
Image of polytope 2943 PALP id: 2943
grdb id: 178413
Integer points: [ 1 0 0 -1 -1 -1 -2 -1 -2 -2 -2 -2 -1 -1 -1 0 0]
[ 0 1 0 1 0 -2 1 -2 -3 -2 -1 0 -1 0 -1 -1 0]
[ 0 0 1 0 -1 0 -1 -1 -1 -1 -1 -1 0 0 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
88 ? x + y + z + x-1*y + 2*y-1 + 4*x-1 + x-1*z-1 + x-2*y*z-1 + 4*x-1*y-1 + 2*x-1*y-1*z-1 + 4*x-2*z-1 + x-1*y-2 + x-1*y-2*z-1 + 6*x-2*y-1*z-1 + 4*x-2*y-2*z-1 + x-2*y-3*z-1
67 ? x + y + z + x-1*y + 2*y-1 + 3*x-1 + x-1*z-1 + x-2*y*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + 4*x-2*z-1 + x-1*y-2 + x-1*y-2*z-1 + 6*x-2*y-1*z-1 + 4*x-2*y-2*z-1 + x-2*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 93 1 Lattice Minkowski decompositions of facet 93
Polytope 2944
Image of polytope 2944 PALP id: 2944
grdb id: 179896
Integer points: [ 1 0 0 -1 -1 0 -1 -3 -3 -2 -2 -1 -2 -1 -1 0 0]
[ 0 1 0 0 1 -1 -2 -1 -2 -2 -1 -1 0 0 -1 -1 0]
[ 0 0 1 -1 0 1 0 -2 -2 -1 -1 0 -1 0 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y + y-1*z + 2*y-1 + 2*x-1 + x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + x-1*y-2 + 3*x-2*y-1*z-1 + 2*x-2*y-2*z-1 + x-3*y-1*z-2 + x-3*y-2*z-2
67 ? x + y + z + x-1*y + y-1*z + 2*y-1 + 3*x-1 + x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + x-1*y-2 + 4*x-2*y-1*z-1 + 2*x-2*y-2*z-1 + x-3*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 143 1 Lattice Minkowski decompositions of facet 143
Polytope 2945
Image of polytope 2945 PALP id: 2945
grdb id: 180485
Integer points: [ 1 0 0 -1 -1 0 -1 -3 -3 -2 -1 -2 -1 -2 0 -1 0]
[ 0 1 0 1 1 -1 -2 1 0 1 0 0 -1 -1 0 0 -1]
[ 0 0 1 -1 0 1 0 -2 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*y + y-1*z + x-1*y*z-1 + 2*y-1 + 3*x-1 + 2*x-1*z-1 + 2*x-2*y*z-1 + 3*x-1*y-1 + 4*x-2*z-1 + x-1*y-2 + x-3*y*z-2 + 2*x-2*y-1*z-1 + x-3*z-2
38 ? x + y + z + x-1*y + y-1*z + x-1*y*z-1 + 2*y-1 + 3*x-1 + 2*x-1*z-1 + 2*x-2*y*z-1 + 2*x-1*y-1 + 3*x-2*z-1 + x-1*y-2 + x-3*y*z-2 + 2*x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 143 1 Lattice Minkowski decompositions of facet 143
Polytope 2946
Image of polytope 2946 PALP id: 2946
grdb id: 179890
Integer points: [ 1 0 0 0 -1 -2 -2 -3 -3 -1 -2 -1 -3 -2 -1 0 -1]
[ 0 1 -1 0 1 1 -2 0 -2 -1 -1 0 -1 0 -1 0 0]
[ 0 0 0 1 0 -1 -1 -2 -2 0 -1 0 -2 -1 -1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + x-1*y + y-1 + 3*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*z-1 + 4*x-2*y-1*z-1 + x-3*z-2 + x-2*y-2*z-1 + 2*x-3*y-1*z-2 + x-3*y-2*z-2
107 rank 3, number 11 x + y + z + x-1*y + y-1 + 2*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*z-1 + 3*x-2*y-1*z-1 + x-3*z-2 + x-2*y-2*z-1 + 2*x-3*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 143 1 Lattice Minkowski decompositions of facet 143
Polytope 2947
Image of polytope 2947 PALP id: 2947
grdb id: 181674
Integer points: [ 1 0 0 0 -1 -1 -1 -3 -3 -2 -1 -3 -2 -1 -1 0 -2]
[ 0 1 -1 0 1 0 -2 -1 -3 -2 -1 -2 -1 0 -1 0 0]
[ 0 0 0 1 0 -1 -1 -2 -2 -1 0 -2 -1 0 -1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
80 ? x + y + z + x-1*y + y-1 + 2*x-1 + x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + 2*x-2*z-1 + x-1*y-2*z-1 + 4*x-2*y-1*z-1 + 3*x-2*y-2*z-1 + x-3*y-1*z-2 + 2*x-3*y-2*z-2 + x-3*y-3*z-2
107 rank 3, number 11 x + y + z + x-1*y + y-1 + 2*x-1 + x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + x-1*y-2*z-1 + 4*x-2*y-1*z-1 + 3*x-2*y-2*z-1 + x-3*y-1*z-2 + 2*x-3*y-2*z-2 + x-3*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2948
Image of polytope 2948 PALP id: 2948
grdb id: 181701
Integer points: [ 1 0 0 0 -1 -1 -1 -3 -3 -2 -1 -3 -2 -1 -2 -1 0]
[ 0 1 0 1 -1 0 -1 -2 -2 -1 0 -2 -1 0 -1 -1 0]
[ 0 0 1 1 -1 -1 1 -1 1 1 1 0 0 0 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? y*z + x + y + z + 3*x-1*z + 4*x-1 + x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + 3*x-2*y-1*z + x-1*y-1*z-1 + 5*x-2*y-1 + 2*x-2*y-1*z-1 + x-3*y-2*z + 2*x-3*y-2 + x-3*y-2*z-1
144 rank 3, number 12 y*z + x + y + z + 3*x-1*z + 4*x-1 + x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + 3*x-2*y-1*z + x-1*y-1*z-1 + 5*x-2*y-1 + 2*x-2*y-1*z-1 + x-3*y-2*z + 2*x-3*y-2 + x-3*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2949
Image of polytope 2949 PALP id: 2949
grdb id: 184828
Integer points: [ 1 0 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 0 0 -1 0]
[ 0 1 0 -1 0 0 -1 -2 -2 -1 -2 -1 0 -1 0 -1 0]
[ 0 0 1 0 1 -1 -2 -1 -3 0 -2 -1 0 -1 0 -2 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*z + 2*z-1 + y-1 + 2*x-1 + 3*y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + y-1*z-2 + 4*x-1*y-1*z-1 + 2*x-1*y-1*z-2 + x-1*y-2*z-1 + 2*x-1*y-2*z-2 + x-1*y-2*z-3
38 ? x + y + z + x-1*z + 2*z-1 + y-1 + 2*x-1 + 2*y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + y-1*z-2 + 4*x-1*y-1*z-1 + 2*x-1*y-1*z-2 + x-1*y-2*z-1 + 2*x-1*y-2*z-2 + x-1*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2950
Image of polytope 2950 PALP id: 2950
grdb id: 181644
Integer points: [ 1 0 0 0 0 0 -2 -1 -3 -2 -1 -1 -2 -1 0 -1 0]
[ 0 1 0 0 -1 -1 0 -1 -1 -1 -1 0 -1 -1 -1 0 0]
[ 0 0 1 -1 1 -1 -1 -2 -2 -1 0 0 -2 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + y-1*z + z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + 3*x-1*z-1 + 3*x-1*y-1 + 4*x-1*y-1*z-1 + x-2*z-1 + x-1*y-1*z-2 + 3*x-2*y-1*z-1 + 2*x-2*y-1*z-2 + x-3*y-1*z-2
38 ? x + y + z + y-1*z + z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + 4*x-1*y-1*z-1 + x-2*z-1 + x-1*y-1*z-2 + 3*x-2*y-1*z-1 + 2*x-2*y-1*z-2 + x-3*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2951
Image of polytope 2951 PALP id: 2951
grdb id: 184238
Integer points: [ 1 0 0 0 1 1 -2 -2 -3 -1 0 -2 -1 0 -1 0 -1]
[ 0 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 0 -1 -1 0 -1 0 0 -1 -1 -1 0 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + x*y-1 + x*y-1*z-1 + z-1 + 3*y-1 + x-1 + 4*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + 6*x-1*y-1*z-1 + x-2*z-1 + x-2*y-1 + 4*x-2*y-1*z-1 + x-3*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Polytope 2952
Image of polytope 2952 PALP id: 2952
grdb id: 181692
Integer points: [ 1 0 1 -1 0 1 -2 -2 0 0 0 -1 -1 -1 0 0 -1]
[ 0 1 -1 1 0 -2 0 -1 -3 -1 -2 0 -1 -2 0 -1 0]
[ 0 0 0 0 1 -1 -1 -2 -2 0 -1 0 -1 -2 0 -1 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*y-1 + x-1*y + 3*y-1 + 2*x-1 + x*y-2*z-1 + 3*y-1*z-1 + 2*x-1*z-1 + 3*y-2*z-1 + 4*x-1*y-1*z-1 + x-2*z-1 + y-3*z-2 + 2*x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2953
Image of polytope 2953 PALP id: 2953
grdb id: 181769
Integer points: [ 1 0 1 0 -2 1 0 -2 -3 -1 -2 0 -1 0 -1 0 -1]
[ 0 1 -1 0 1 -2 -2 1 1 -1 0 -1 0 -1 0 0 1]
[ 0 0 0 1 0 -1 -1 -1 -1 -1 -1 0 0 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*y-1 + 2*x-1*y + 2*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + 3*y-1*z-1 + 3*x-1*z-1 + x-2*y*z-1 + y-2*z-1 + 3*x-1*y-1*z-1 + 3*x-2*z-1 + x-3*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2954
Image of polytope 2954 PALP id: 2954
grdb id: 181697
Integer points: [ 1 0 0 0 0 0 -1 -2 -3 -1 -2 0 -1 -2 -1 0 -1]
[ 0 1 0 0 -1 -1 0 2 2 0 1 -1 0 1 1 0 1]
[ 0 0 1 -1 1 -1 1 -1 -1 -1 -1 0 0 0 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + 3*x-1*y + y-1*z + x-1*z + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 4*x-1 + 2*x-2*y + y-1*z-1 + 3*x-1*z-1 + 3*x-2*y*z-1 + x-3*y2*z-1
13 rank 2, number 12 x + y + z + 2*x-1*y + y-1*z + x-1*z + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 4*x-1 + 2*x-2*y + y-1*z-1 + 3*x-1*z-1 + 3*x-2*y*z-1 + x-3*y2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2955
Image of polytope 2955 PALP id: 2955
grdb id: 181632
Integer points: [ 1 0 0 0 -1 -1 -2 -2 -4 -2 -3 -1 -2 -3 -1 0 -1]
[ 0 1 -1 0 -1 1 -1 1 1 1 1 0 0 0 1 0 0]
[ 0 0 0 1 0 0 -1 -2 -3 -1 -2 0 -1 -2 -1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + x-1*y + 2*x-1*y*z-1 + y-1 + 3*x-1 + 2*x-1*z-1 + 3*x-2*y*z-1 + x-1*y-1 + x-2*y*z-2 + 4*x-2*z-1 + 3*x-3*y*z-2 + x-2*y-1*z-1 + 2*x-3*z-2 + x-4*y*z-3
144 rank 3, number 12 x + y + z + x-1*y + 2*x-1*y*z-1 + y-1 + 3*x-1 + 3*x-1*z-1 + 3*x-2*y*z-1 + x-1*y-1 + x-2*y*z-2 + 4*x-2*z-1 + 3*x-3*y*z-2 + x-2*y-1*z-1 + 2*x-3*z-2 + x-4*y*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2956
Image of polytope 2956 PALP id: 2956
grdb id: 181640
Integer points: [ 1 0 0 0 0 -1 -1 -3 -4 -2 -3 -1 -2 -1 -2 0 -1]
[ 0 1 -1 0 -1 0 0 2 3 1 2 1 2 0 1 0 1]
[ 0 0 0 1 1 -1 1 -2 -2 0 -1 0 -1 0 -1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + 3*x-1*y + y-1*z + x-1*z + 2*x-1*y*z-1 + 2*x-2*y2*z-1 + y-1 + 4*x-1 + 3*x-2*y + x-1*z-1 + 4*x-2*y*z-1 + 3*x-3*y2*z-1 + x-3*y2*z-2 + x-4*y3*z-2
46 ? x + y + z + 3*x-1*y + y-1*z + x-1*z + 2*x-1*y*z-1 + 2*x-2*y2*z-1 + y-1 + 3*x-1 + 3*x-2*y + x-1*z-1 + 3*x-2*y*z-1 + 3*x-3*y2*z-1 + x-3*y2*z-2 + x-4*y3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2957
Image of polytope 2957 PALP id: 2957
grdb id: 195631
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 -1 1 1 0 -2 0 -1 1 0 -1 0 -1 0]
[ 0 0 1 -1 1 0 -2 -2 0 0 0 -1 -1 -1 0 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + y*z-1 + x-1*y + y-1*z + 2*z-1 + 2*x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*y*z-2 + 4*x-1*z-1 + 3*x-1*y-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 2958
Image of polytope 2958 PALP id: 2958
grdb id: 195881
Integer points: [ 1 0 0 0 0 0 -1 -2 -2 -2 -2 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 0 -1 -1 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 1 -1 0 1 1 1 -2 0 -1 0 -1 1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + y-1*z + x-1*z + z-1 + y-1 + 3*x-1 + 2*x-1*y-1*z + 2*x-1*z-1 + 4*x-1*y-1 + x-2*y-1*z + 2*x-1*y-1*z-1 + 3*x-2*y-1 + 3*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2959
Image of polytope 2959 PALP id: 2959
grdb id: 194956
Integer points: [ 1 0 0 0 0 -1 -1 -2 -2 -2 -2 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 2 -1 -1 2 1 0 1 0 -1 1 0 0]
[ 0 0 0 1 1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + x-1*y2*z-1 + 2*x-1*y + y-1*z + 3*x-1*y*z-1 + x-2*y2*z-1 + y-1 + 4*x-1 + 3*x-1*z-1 + 3*x-2*y*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + 3*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Polytope 2960
Image of polytope 2960 PALP id: 2960
grdb id: 195976
Integer points: [ 1 0 0 0 0 0 -1 -2 -3 -2 -1 0 -2 -1 -1 0 -1]
[ 0 1 0 0 -1 -1 -1 0 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 -1 1 -1 1 1 0 0 0 1 1 0 0 1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
3 ? x + y + z + y-1*z + 2*x-1*z + z-1 + 2*y-1 + 3*x-1 + 3*x-1*y-1*z + x-2*z + y-1*z-1 + 4*x-1*y-1 + 3*x-2*y-1*z + x-1*y-1*z-1 + 2*x-2*y-1 + x-3*y-1*z
36 rank 3, number 7 x + y + z + y-1*z + 2*x-1*z + z-1 + 2*y-1 + 2*x-1 + 3*x-1*y-1*z + x-2*z + y-1*z-1 + 4*x-1*y-1 + 3*x-2*y-1*z + x-1*y-1*z-1 + 2*x-2*y-1 + x-3*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2961
Image of polytope 2961 PALP id: 2961
grdb id: 639892
Integer points: [ 1 0 0 -2 2 0 0 -1 1 -2 1 1 0 -1 -1 0 -1]
[ 0 1 0 2 -2 0 1 2 -2 1 -1 -1 0 1 1 -1 0]
[ 0 0 1 1 -1 -1 1 1 0 0 -1 0 0 0 1 0 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
26 rank 2, number 8 y*z + x-1*y2*z + x + y + z + 2*x-1*y*z + x-2*y2*z + x*y-1 + x-1*y + x2*y-2*z-1 + 2*x*y-1*z-1 + z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 10 2 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Polytope 2962
Image of polytope 2962 PALP id: 2962
grdb id: 639854
Integer points: [ 1 0 0 -1 0 -1 -2 -2 1 0 -1 0 -1 0 1 -1 0]
[ 0 1 0 1 0 1 1 0 -2 -2 0 -1 -1 0 -1 0 -1]
[ 0 0 1 1 -1 0 1 1 -2 -1 0 -1 0 0 -1 1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
56 rank 2, number 11 x + y + z + x-1*y*z + x-1*y + 2*x-1*z + x-2*y*z + 2*x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + x-2*z + 2*y-1*z-1 + 2*x-1*y-1 + x*y-2*z-2 + y-2*z-1
10 rank 1, V18 x + y + z + x-1*y*z + x-1*y + 2*x-1*z + x-2*y*z + 2*x*y-1*z-1 + z-1 + 2*y-1 + 4*x-1 + x-2*z + 3*y-1*z-1 + 2*x-1*y-1 + x*y-2*z-2 + y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2963
Image of polytope 2963 PALP id: 2963
grdb id: 639872
Integer points: [ 1 0 0 -1 1 -2 1 -1 0 -2 -1 -1 0 -1 0 1 0]
[ 0 1 0 1 -2 1 -2 0 -1 1 0 0 -1 1 0 -1 -1]
[ 0 0 1 1 0 0 -1 -1 1 1 1 0 0 0 0 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
151 ? x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + x*y-2 + 4*y-1 + 4*x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 1 2 irreducible and admissible
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 96 1 Lattice Minkowski decompositions of facet 96
Polytope 2964
Image of polytope 2964 PALP id: 2964
grdb id: 639874
Integer points: [ 1 0 0 -1 1 1 0 -1 -2 -2 -1 -1 0 1 -1 0 0]
[ 0 1 0 1 -1 0 1 -1 1 0 1 0 0 0 0 0 -1]
[ 0 0 1 1 -1 -2 -1 1 1 1 0 1 0 -1 0 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + x-1*y*z + 2*x*z-1 + y*z-1 + 2*x-1*y + x-1*z + x-2*y*z + x*z-2 + x*y-1*z-1 + 3*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Polytope 2965
Image of polytope 2965 PALP id: 2965
grdb id: 639875
Integer points: [ 1 0 0 0 1 -1 1 1 0 -1 0 1 0 0 0 -1 -1]
[ 0 1 0 0 0 2 -1 -2 -2 -1 -1 -1 -1 0 1 0 1]
[ 0 0 1 -1 -1 2 0 -1 -1 -1 0 -1 -1 0 1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x-1*y2*z2 + 2*y*z + x + y + z + 3*x-1*y*z + x*z-1 + x*y-1 + 2*x*y-1*z-1 + z-1 + 2*y-1 + 3*x-1 + x*y-2*z-1 + 2*y-1*z-1 + y-2*z-1 + x-1*y-1*z-1
51 rank 2, number 7 x-1*y2*z2 + 2*y*z + x + y + z + 3*x-1*y*z + x*z-1 + x*y-1 + 2*x*y-1*z-1 + z-1 + 2*y-1 + 3*x-1 + x*y-2*z-1 + 3*y-1*z-1 + y-2*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2966
Image of polytope 2966 PALP id: 2966
grdb id: 639881
Integer points: [ 1 0 1 -1 -1 -1 0 0 -1 -1 -1 0 0 -1 0 1 0]
[ 0 1 0 0 0 1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 0 2 -2 0 -1 1 -1 0 -2 -1 0 -1 -1 0 1 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x*z2 + 2*x*z + x + y + 2*z + y-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + x-1 + y-1*z-1 + 2*x-1*z-1 + x-1*y-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-1*z-2
40 rank 2, number 10 x*z2 + 2*x*z + x + y + 2*z + y-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + x-1 + y-1*z-1 + 3*x-1*z-1 + x-1*y-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Image of facet 1 1 irreducible and admissible
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2967
Image of polytope 2967 PALP id: 2967
grdb id: 639888
Integer points: [ 1 0 1 1 -1 -1 -1 1 -1 -1 0 0 -1 0 0 0 1]
[ 0 1 0 -1 1 0 0 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 0 2 1 -1 0 -2 0 -2 -1 -1 0 -1 -1 0 1 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x*z2 + 2*x*z + x + y + x*y-1*z + 2*z + x*y-1 + 2*z-1 + x-1*y*z-1 + 2*y-1 + x-1 + 2*y-1*z-1 + x-1*z-1 + x-1*z-2 + x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 3 Lattice Minkowski decompositions of facet 15
Polytope 2968
Image of polytope 2968 PALP id: 2968
grdb id: 639889
Integer points: [ 1 1 0 0 0 0 -1 -1 -2 -2 0 -1 -1 0 1 -1 0]
[ 0 2 0 1 -1 0 -2 0 -2 -1 -1 -1 -1 0 1 0 1]
[ 0 0 1 1 -1 -1 0 0 1 1 0 0 1 0 0 1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 x*y2 + 2*x*y + y*z + x + 2*y + z + 2*x-1*z + z-1 + 2*y-1 + x-1 + 2*x-1*y-1*z + y-1*z-1 + 3*x-1*y-1 + x-2*y-1*z + x-1*y-2 + x-2*y-2*z
20 rank 1, V16 x*y2 + 2*x*y + y*z + x + 2*y + z + 2*x-1*z + z-1 + 2*y-1 + x-1 + 2*x-1*y-1*z + y-1*z-1 + 2*x-1*y-1 + x-2*y-1*z + x-1*y-2 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 3 Lattice Minkowski decompositions of facet 15
Polytope 2969
Image of polytope 2969 PALP id: 2969
grdb id: 639834
Integer points: [ 1 0 0 -1 1 0 -1 -2 -1 -3 -2 -2 -1 0 -1 0 1]
[ 0 1 0 1 -2 -1 0 2 0 2 1 1 0 -1 1 0 -1]
[ 0 0 1 -1 0 1 -1 -1 1 -1 -1 0 0 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + z + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + x-1*y*z-1 + x-2*y2*z-1 + x*y-2 + 3*y-1 + 3*x-1 + 2*x-2*y + x-1*z-1 + 2*x-2*y*z-1 + x-3*y2*z-1
151 ? x + y + z + 2*x*y-1 + 3*x-1*y + y-1*z + x-1*z + x-1*y*z-1 + x-2*y2*z-1 + x*y-2 + 3*y-1 + 3*x-1 + 2*x-2*y + x-1*z-1 + 2*x-2*y*z-1 + x-3*y2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Polytope 2970
Image of polytope 2970 PALP id: 2970
grdb id: 638861
Integer points: [ 1 0 0 -1 0 -1 -1 0 -1 -1 -1 -1 -1 -1 0 0 -1]
[ 0 1 0 1 -1 0 0 -1 -2 -2 -1 -2 -1 0 -1 0 -1]
[ 0 0 1 0 -1 -1 1 1 -1 1 1 0 0 0 0 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
85 rank 3, number 8 x + y + z + x-1*y + y-1*z + x-1*z + 2*y-1 + 4*x-1 + 2*x-1*y-1*z + y-1*z-1 + x-1*z-1 + 5*x-1*y-1 + x-1*y-2*z + 2*x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-2*z-1
85 rank 3, number 8 x + y + z + x-1*y + y-1*z + x-1*z + 3*y-1 + 3*x-1 + 2*x-1*y-1*z + y-1*z-1 + x-1*z-1 + 4*x-1*y-1 + x-1*y-2*z + 2*x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-2*z-1
36 rank 3, number 7 x + y + z + x-1*y + y-1*z + x-1*z + 2*y-1 + 3*x-1 + 2*x-1*y-1*z + y-1*z-1 + x-1*z-1 + 4*x-1*y-1 + x-1*y-2*z + 2*x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-2*z-1
134 ? x + y + z + x-1*y + y-1*z + x-1*z + 3*y-1 + 4*x-1 + 2*x-1*y-1*z + y-1*z-1 + x-1*z-1 + 5*x-1*y-1 + x-1*y-2*z + 2*x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2971
Image of polytope 2971 PALP id: 2971
grdb id: 638863
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 -1 1 1 -1 -2 0 1 0 -1 0 0 -1]
[ 0 0 1 -1 1 -1 1 -1 1 0 -1 0 0 0 1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 y*z + x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + x-1*y-1*z + 2*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
39 ? y*z + x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 5*x-1 + x-1*y-1*z + 2*x-1*z-1 + 4*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Polytope 2972
Image of polytope 2972 PALP id: 2972
grdb id: 639684
Integer points: [ 1 0 0 0 0 -1 -1 0 -1 -1 -1 -1 0 -1 -1 0 0]
[ 0 1 0 1 -1 1 1 -1 -2 -2 -1 0 0 -1 0 -1 0]
[ 0 0 1 -1 1 1 0 -1 1 0 0 0 -1 1 1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
56 rank 2, number 11 x + y + z + x-1*y*z + y*z-1 + x-1*y + y-1*z + 3*x-1*z + 2*z-1 + y-1 + 3*x-1 + 3*x-1*y-1*z + y-1*z-1 + 3*x-1*y-1 + x-1*y-2*z + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2973
Image of polytope 2973 PALP id: 2973
grdb id: 639032
Integer points: [ 1 0 0 0 0 -1 0 -1 -1 -1 -1 -1 -1 0 0 -1 -1]
[ 0 1 0 0 -1 1 -1 -1 -2 -2 0 -1 -2 0 -1 0 -1]
[ 0 0 1 -1 1 -1 -1 1 1 -1 0 0 0 0 0 -1 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + y-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + 3*x-1*z-1 + 4*x-1*y-1 + x-1*y-2*z + 3*x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-2*z-1
17 rank 1, V22 x + y + z + y-1*z + z-1 + x-1*y*z-1 + 3*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + 3*x-1*z-1 + 4*x-1*y-1 + x-1*y-2*z + 3*x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 2974
Image of polytope 2974 PALP id: 2974
grdb id: 639652
Integer points: [ 1 0 0 0 0 0 -1 -1 -2 -2 -1 -2 -1 0 -1 -1 0]
[ 0 1 0 0 -1 -1 1 1 1 1 0 1 0 -1 0 1 0]
[ 0 0 1 -1 1 -1 -1 1 -1 1 -1 0 0 0 1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + x-1*y*z + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + 2*x-2*y + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1
52 rank 2, number 52 x + y + z + x-1*y*z + 3*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + 2*x-2*y + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 2975
Image of polytope 2975 PALP id: 2975
grdb id: 639467
Integer points: [ 1 0 0 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 -1 1 0 1 -1 0 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 0 0 1 -1 0 -2 -2 -1 0 -1 0 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + x*y-1 + x-1*y + x-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + 2*y-1*z-1 + 4*x-1*z-1 + x-1*y-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-1*z-2
13 rank 2, number 12 x + y + z + x*y-1 + x-1*y + x-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + x-1*y-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2976
Image of polytope 2976 PALP id: 2976
grdb id: 639040
Integer points: [ 1 0 0 1 -1 0 -1 -1 0 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 1 0 1 0 -2 -2 -1 0 -1 0 -1 -1 0]
[ 0 0 1 0 0 -1 -1 1 -1 -1 -1 -1 0 0 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*y-1 + x-1*y + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + 2*y-1*z-1 + 3*x-1*z-1 + 2*x-1*y-1 + y-2*z-1 + 3*x-1*y-1*z-1 + x-1*y-2*z-1
39 ? x + y + z + x*y-1 + x-1*y + x-1*z + z-1 + x-1*y*z-1 + 3*y-1 + 3*x-1 + 2*y-1*z-1 + 3*x-1*z-1 + 2*x-1*y-1 + y-2*z-1 + 3*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2977
Image of polytope 2977 PALP id: 2977
grdb id: 639026
Integer points: [ 1 0 0 1 -1 0 -1 0 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 1 0 0 -1 -1 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 1 0 0 -1 1 1 1 -2 0 -1 0 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + x*y-1 + x-1*y + y-1*z + x-1*z + z-1 + 3*y-1 + 3*x-1 + x-1*y-1*z + 2*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Polytope 2978
Image of polytope 2978 PALP id: 2978
grdb id: 639673
Integer points: [ 1 0 0 1 -1 1 -1 -1 0 -1 0 -1 -1 0 0 -1 0]
[ 0 1 0 -1 1 -1 0 -1 -1 -1 -1 -1 0 -1 0 0 0]
[ 0 0 1 0 0 -1 1 0 -2 -2 0 -1 0 -1 0 -1 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*y-1 + x-1*y + x-1*z + x*y-1*z-1 + 2*z-1 + 2*y-1 + 2*x-1 + 3*y-1*z-1 + 2*x-1*z-1 + x-1*y-1 + y-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2979
Image of polytope 2979 PALP id: 2979
grdb id: 639732
Integer points: [ 1 0 0 1 -1 1 -1 -1 0 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 0 1 -1 0 0 -2 -2 -1 -1 0 -1 0 -1 0]
[ 0 0 1 -1 0 0 1 -1 1 1 0 1 0 0 -1 1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*z-1 + x*y-1 + x-1*y + 2*y-1*z + x-1*z + 2*z-1 + 3*y-1 + 2*x-1 + y-2*z + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2980
Image of polytope 2980 PALP id: 2980
grdb id: 639783
Integer points: [ 1 0 0 1 0 1 -2 1 0 -2 -1 -1 0 0 -1 -1 0]
[ 0 1 0 0 -1 -1 0 -1 -1 -1 -1 0 -1 0 -1 0 0]
[ 0 0 1 -1 0 -1 1 -2 -2 0 0 1 -1 0 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*z-1 + 2*x-1*z + x*y-1*z-1 + 2*z-1 + y-1 + 2*x-1 + x-2*z + x*y-1*z-2 + 3*y-1*z-1 + 2*x-1*y-1 + y-1*z-2 + 2*x-1*y-1*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2981
Image of polytope 2981 PALP id: 2981
grdb id: 639027
Integer points: [ 1 0 0 1 1 -1 -1 -2 1 -2 0 -1 0 -1 0 0 -1]
[ 0 1 0 -1 -1 0 1 1 -2 1 -1 0 -1 0 0 0 1]
[ 0 0 1 0 -1 1 -1 0 -1 -1 -1 -1 0 0 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*y-1 + 2*x-1*y + x-1*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + 3*y-1*z-1 + 3*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 2982
Image of polytope 2982 PALP id: 2982
grdb id: 639703
Integer points: [ 1 0 1 -1 0 0 -1 0 -2 -2 -1 -2 -1 -1 0 -1 0]
[ 0 1 -1 1 0 -1 0 -2 0 -2 -1 -1 0 -2 -1 -1 0]
[ 0 0 0 0 1 -1 -1 -1 -1 -1 0 -1 0 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x*y-1 + x-1*y + 2*y-1 + 2*x-1 + y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + y-2*z-1 + 3*x-1*y-1*z-1 + x-2*z-1 + 2*x-1*y-2*z-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 2983
Image of polytope 2983 PALP id: 2983
grdb id: 639786
Integer points: [ 1 0 0 -2 2 0 -1 -2 1 0 0 -1 1 1 0 -1 -1]
[ 0 1 0 2 -2 0 0 1 -2 -1 -1 0 -1 -1 0 1 1]
[ 0 0 1 1 -1 -1 1 1 -1 -1 0 0 -1 0 0 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 x + y + z + 2*x-1*y*z + x-2*y2*z + 2*x*y-1 + 2*x-1*y + x-1*z + x-2*y*z + x2*y-2*z-1 + 2*x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + x*y-2*z-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 15 3 Lattice Minkowski decompositions of facet 15
Polytope 2984
Image of polytope 2984 PALP id: 2984
grdb id: 639695
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 0 -1 0 0 -1 0]
[ 0 1 0 0 -2 1 2 -1 2 1 0 -1 1 0 1 0 -1]
[ 0 0 1 -1 1 0 -1 0 -2 -2 0 1 -1 0 -1 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + 2*y*z-1 + x-1*y2*z-1 + x-1*y + 2*y-1*z + x-1*y2*z-2 + z-1 + 3*x-1*y*z-1 + 2*y-1 + 2*x-1 + y-2*z + x-1*y*z-2 + 2*x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2985
Image of polytope 2985 PALP id: 2985
grdb id: 639042
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 0 -1 -1 -2 2 0 1 -1 0 1 -1 0]
[ 0 0 1 -1 -1 1 1 -1 0 -1 -1 -1 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + y*z-1 + x-1*y2*z-1 + 2*x-1*y + x-1*z + z-1 + 3*x-1*y*z-1 + 2*y-1 + 4*x-1 + x-1*y-1*z + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Polytope 2986
Image of polytope 2986 PALP id: 2986
grdb id: 639750
Integer points: [ 1 0 0 1 -1 0 -2 1 -2 1 -1 0 -1 0 -1 0 1]
[ 0 1 0 -1 1 0 1 -2 1 -2 0 -1 0 -1 1 0 -1]
[ 0 0 1 0 0 -1 -1 1 -2 2 -1 0 0 1 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + 2*x*y-1*z + z + x*y-2*z2 + x*y-1 + x-1*y + x*y-2*z + 3*y-1*z + z-1 + 2*x-1*y*z-1 + 3*y-1 + 3*x-1 + 3*x-1*z-1 + x-2*y*z-1 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 2987
Image of polytope 2987 PALP id: 2987
grdb id: 639688
Integer points: [ 1 0 0 1 -1 0 2 -2 0 -1 1 0 1 0 -1 0 -1]
[ 0 1 0 0 0 -1 -1 1 -1 0 -1 -1 -1 0 0 0 1]
[ 0 0 1 -1 1 1 -1 0 -1 -1 -1 0 0 -1 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + x2*y-1*z-1 + x*z-1 + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + 2*x*y-1*z-1 + 2*z-1 + 2*y-1 + 2*x-1 + x-2*y + y-1*z-1 + x-1*z-1
20 rank 1, V16 x + y + z + x2*y-1*z-1 + x*z-1 + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + 2*x*y-1*z-1 + 2*z-1 + 2*y-1 + 3*x-1 + x-2*y + y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 2988
Image of polytope 2988 PALP id: 2988
grdb id: 639710
Integer points: [ 1 0 0 1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 0 1 0 -1 0 -2 -2 0 -1 -1 0 0 -1 -1]
[ 0 0 1 -1 -1 1 2 -1 2 1 0 0 1 -1 0 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*z-1 + y*z-1 + 2*y-1*z + x-1*z + x-1*y-1*z2 + 2*z-1 + 2*y-1 + 2*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2989
Image of polytope 2989 PALP id: 2989
grdb id: 639751
Integer points: [ 1 0 1 0 0 -1 0 -1 -1 -1 -1 0 0 0 -1 -1 0]
[ 0 1 -1 0 0 0 -2 2 -1 2 1 -1 0 1 0 1 -1]
[ 0 0 0 1 -1 1 1 -1 1 -2 0 1 0 -1 0 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + 2*y*z-1 + x-1*y2*z-1 + x*y-1 + 2*x-1*y + 2*y-1*z + x-1*z + x-1*y2*z-2 + z-1 + 3*x-1*y*z-1 + 2*y-1 + 3*x-1 + y-2*z + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 5 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Polytope 2990
Image of polytope 2990 PALP id: 2990
grdb id: 639036
Integer points: [ 1 0 -1 0 0 -1 -1 0 -1 -1 -1 -1 -1 0 0 -1 -1]
[ 0 1 1 0 -1 0 0 -2 -1 -3 -2 -1 0 -1 0 -2 -1]
[ 0 0 0 1 -1 -1 1 -1 1 -1 0 0 0 0 0 -1 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
85 rank 3, number 8 x + y + z + x-1*y + x-1*z + 3*y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 4*x-1*y-1 + y-2*z-1 + 3*x-1*y-1*z-1 + 2*x-1*y-2 + 3*x-1*y-2*z-1 + x-1*y-3*z-1
36 rank 3, number 7 x + y + z + x-1*y + x-1*z + 2*y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + x-1*z-1 + 4*x-1*y-1 + y-2*z-1 + 3*x-1*y-1*z-1 + 2*x-1*y-2 + 3*x-1*y-2*z-1 + x-1*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 2991
Image of polytope 2991 PALP id: 2991
grdb id: 638807
Integer points: [ 1 0 0 -1 -1 -1 -1 0 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 1 0 0 -2 -2 -3 -1 -2 0 -1 -1 0 -1]
[ 0 0 1 0 1 -1 1 -1 -2 -2 0 -1 0 -1 0 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + x-1*y*z + x-1*y + x-1*z + 2*y-1 + 3*x-1 + 2*y-1*z-1 + x-1*z-1 + 3*x-1*y-1 + y-2*z-1 + 3*x-1*y-1*z-1 + 3*x-1*y-2*z-1 + x-1*y-2*z-2 + x-1*y-3*z-2
17 rank 1, V22 x + y + z + x-1*y*z + x-1*y + x-1*z + 2*y-1 + 4*x-1 + 2*y-1*z-1 + x-1*z-1 + 3*x-1*y-1 + y-2*z-1 + 4*x-1*y-1*z-1 + 3*x-1*y-2*z-1 + x-1*y-2*z-2 + x-1*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2992
Image of polytope 2992 PALP id: 2992
grdb id: 639704
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -3 -2 -2 -1 -2 -1 -1 0]
[ 0 1 0 0 -1 1 -1 1 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 -1 0 1 -1 1 1 1 0 1 0 1 0 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? y*z + x + y + z + x-1*y*z + 3*x-1*z + z-1 + y-1 + 3*x-1 + x-1*y-1*z + 2*x-2*z + 2*x-1*y-1 + 2*x-2*y-1*z + x-1*y-1*z-1 + 2*x-2*y-1 + x-3*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Polytope 2993
Image of polytope 2993 PALP id: 2993
grdb id: 639761
Integer points: [ 1 0 1 0 -1 0 0 -1 -2 -3 -2 -1 -2 -1 0 -1 0]
[ 0 1 -1 0 1 0 -1 -1 1 1 1 0 0 1 0 0 -1]
[ 0 0 0 1 0 -1 1 0 -2 -2 -1 0 -1 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*y-1 + x-1*y + y-1*z + z-1 + 2*x-1*y*z-1 + 2*y-1 + 3*x-1 + 3*x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1 + x-2*y*z-2 + 2*x-2*z-1 + x-3*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2994
Image of polytope 2994 PALP id: 2994
grdb id: 651661
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 -1 1 1 -1 -1 -1 0 0 0 1 -1 0]
[ 0 0 1 -1 -1 1 -1 1 1 -1 0 -1 0 1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y*z + 2*x-1*y + y-1*z + 2*x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + x-1*y-1*z + y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 2995
Image of polytope 2995 PALP id: 2995
grdb id: 649245
Integer points: [ 1 0 0 0 -1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 -1 -1 1 -1 -1 -1 -1 0 0 0 -1 0]
[ 0 0 1 -1 0 -1 1 -1 -1 2 0 1 -1 0 1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + x-1*y + y-1*z + 2*x-1*z + x-1*y-1*z2 + z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + 3*x-1*y-1*z + y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2996
Image of polytope 2996 PALP id: 2996
grdb id: 648677
Integer points: [ 1 0 0 -1 0 -1 -1 -2 -1 -2 -2 -2 -1 -1 -1 0 0]
[ 0 1 0 1 -1 1 -1 1 -2 -2 -1 0 -1 0 0 -1 0]
[ 0 0 1 -1 1 0 -1 -1 0 -1 -1 -1 0 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*y + y-1*z + x-1*y*z-1 + 2*y-1 + 3*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2 + 3*x-2*y-1*z-1 + x-2*y-2*z-1
85 rank 3, number 8 x + y + z + x-1*y + y-1*z + x-1*y*z-1 + 2*y-1 + 4*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 4*x-1*y-1 + x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2 + 3*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 2997
Image of polytope 2997 PALP id: 2997
grdb id: 651274
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 0 0 -1 -2 -1 -2 -2 -1 -1 0 -1 -1 0]
[ 0 0 1 -1 1 -1 1 0 -2 -2 -1 0 -1 0 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*z + z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + 2*y-1*z-1 + x-1*z-1 + 4*x-1*y-1 + 4*x-1*y-1*z-1 + x-1*y-2 + x-1*y-1*z-2 + 2*x-1*y-2*z-1 + x-1*y-2*z-2
38 ? x + y + z + x-1*z + z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + 2*y-1*z-1 + x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2 + x-1*y-1*z-2 + 2*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 96 1 Lattice Minkowski decompositions of facet 96
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 2998
Image of polytope 2998 PALP id: 2998
grdb id: 651804
Integer points: [ 1 0 0 0 0 -1 -1 0 -2 -2 -1 -2 -1 -1 0 -1 0]
[ 0 1 0 0 -1 1 1 -1 1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 -1 1 0 -1 -1 -1 -1 0 -1 0 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y + y-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + y-1*z-1 + 3*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 2999
Image of polytope 2999 PALP id: 2999
grdb id: 651604
Integer points: [ 1 0 0 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 -1 1 1 -1 -2 -2 -1 0 -1 0 -1 0 0]
[ 0 0 1 -1 1 0 -1 -1 0 -1 0 0 -1 -1 0 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + y*z-1 + x-1*y + y-1*z + 2*z-1 + x-1*y*z-1 + y-1 + 3*x-1 + y-1*z-1 + 3*x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3000
Image of polytope 3000 PALP id: 3000
grdb id: 651861
Integer points: [ 1 0 0 1 0 0 -1 -2 0 -2 0 -1 -1 0 0 -1 -1]
[ 0 1 0 -1 -1 1 0 1 -1 1 -1 0 0 0 0 1 1]
[ 0 0 1 0 1 -1 1 0 -1 -1 0 -1 0 -1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + z + y*z-1 + x*y-1 + 2*x-1*y + y-1*z + x-1*z + 2*z-1 + 2*x-1*y*z-1 + 2*y-1 + 3*x-1 + x-2*y + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3001
Image of polytope 3001 PALP id: 3001
grdb id: 651803
Integer points: [ 1 0 1 -1 0 -1 1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 -1 1 0 1 -2 0 0 -2 -1 0 -1 -1 0 -2 -1]
[ 0 0 0 0 1 1 -1 -1 1 -1 0 0 -1 0 0 -1 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y*z + x*y-1 + x-1*y + x-1*z + 3*y-1 + 3*x-1 + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + 2*y-2*z-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 3002
Image of polytope 3002 PALP id: 3002
grdb id: 649478
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -3 -3 -2 -3 -2 -1 -2 -1 0]
[ 0 1 -1 0 -1 1 -1 1 1 -1 -1 0 0 0 1 0 0]
[ 0 0 0 1 0 0 -1 -1 -2 -2 -1 -2 -1 0 -1 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
32 ? x + y + z + x-1*y + x-1*y*z-1 + y-1 + 4*x-1 + 2*x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1 + x-1*y-1*z-1 + 5*x-2*z-1 + x-3*y*z-2 + 2*x-2*y-1*z-1 + 2*x-3*z-2 + x-3*y-1*z-2
8 ? x + y + z + x-1*y + x-1*y*z-1 + y-1 + 3*x-1 + 2*x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1 + x-1*y-1*z-1 + 4*x-2*z-1 + x-3*y*z-2 + 2*x-2*y-1*z-1 + 2*x-3*z-2 + x-3*y-1*z-2
144 rank 3, number 12 x + y + z + x-1*y + x-1*y*z-1 + y-1 + 3*x-1 + 3*x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1 + x-1*y-1*z-1 + 4*x-2*z-1 + x-3*y*z-2 + 2*x-2*y-1*z-1 + 2*x-3*z-2 + x-3*y-1*z-2
159 ? x + y + z + x-1*y + x-1*y*z-1 + y-1 + 4*x-1 + 3*x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1 + x-1*y-1*z-1 + 5*x-2*z-1 + x-3*y*z-2 + 2*x-2*y-1*z-1 + 2*x-3*z-2 + x-3*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 3003
Image of polytope 3003 PALP id: 3003
grdb id: 651573
Integer points: [ 1 0 0 0 0 0 -1 -1 -2 -2 -2 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -1 0 0 -2 -1 -3 -2 0 -1 -1 -2 0 -1]
[ 0 0 1 -1 1 -1 1 0 1 1 1 0 0 1 1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + y*z-1 + y-1*z + x-1*z + z-1 + 2*y-1 + 2*x-1 + 3*x-1*y-1*z + 3*x-1*y-1 + 2*x-1*y-2*z + x-2*y-1*z + x-1*y-2 + 2*x-2*y-2*z + x-2*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3004
Image of polytope 3004 PALP id: 3004
grdb id: 651989
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -3 -2 -2 -1 -2 -1 -1 0]
[ 0 1 0 0 -1 -1 0 0 -2 -2 -1 -1 0 -2 -1 -1 0]
[ 0 0 1 -1 0 1 -1 1 1 1 0 1 0 1 0 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + y-1*z + x-1*z + z-1 + y-1 + 2*x-1 + 3*x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z + 2*x-2*y-1*z + 2*x-2*y-1 + 2*x-2*y-2*z + x-3*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Polytope 3005
Image of polytope 3005 PALP id: 3005
grdb id: 649168
Integer points: [ 1 0 0 0 -1 0 -1 -1 -3 -4 -2 -3 -1 -2 -1 -2 0]
[ 0 1 -1 0 0 -1 -1 -1 -1 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 0 1 -1 1 -1 1 -2 -2 0 -1 0 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
144 rank 3, number 12 x + y + z + y-1*z + y-1 + 3*x-1 + x-1*y-1*z + x-1*z-1 + 4*x-1*y-1 + x-1*y-1*z-1 + 2*x-2*z-1 + 3*x-2*y-1 + 4*x-2*y-1*z-1 + 3*x-3*y-1*z-1 + x-3*y-1*z-2 + x-4*y-1*z-2
8 ? x + y + z + y-1*z + y-1 + 3*x-1 + x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + 2*x-2*z-1 + 3*x-2*y-1 + 3*x-2*y-1*z-1 + 3*x-3*y-1*z-1 + x-3*y-1*z-2 + x-4*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3006
Image of polytope 3006 PALP id: 3006
grdb id: 646162
Integer points: [ 1 0 0 0 0 0 -1 -1 -2 -2 -1 -2 -1 -1 0 0 -1]
[ 0 1 0 0 -1 -1 0 0 -1 -1 -1 -1 0 -1 0 -1 -1]
[ 0 0 1 -1 1 -1 -1 1 1 -1 1 0 0 0 0 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
3 ? x + y + z + y-1*z + x-1*z + z-1 + 2*y-1 + 3*x-1 + 2*x-1*y-1*z + y-1*z-1 + x-1*z-1 + 4*x-1*y-1 + x-2*y-1*z + 2*x-1*y-1*z-1 + 2*x-2*y-1 + x-2*y-1*z-1
36 rank 3, number 7 x + y + z + y-1*z + x-1*z + z-1 + 2*y-1 + 2*x-1 + 2*x-1*y-1*z + y-1*z-1 + x-1*z-1 + 4*x-1*y-1 + x-2*y-1*z + 2*x-1*y-1*z-1 + 2*x-2*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 3007
Image of polytope 3007 PALP id: 3007
grdb id: 53123
Integer points: [ 1 0 1 -1 0 0 0 -1 -1 -1 -1 -1 -1 0 0 0 1]
[ 0 1 0 0 -1 -1 1 -1 1 1 -1 0 0 0 0 0 0]
[ 0 0 2 -2 0 1 1 -1 -1 0 0 0 -1 1 0 -1 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x*z2 + 2*x*z + y*z + x + y + 2*z + x-1*y + y-1*z + 2*z-1 + x-1*y*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + x-1*y-1 + x-1*z-2 + x-1*y-1*z-1
40 rank 2, number 10 x*z2 + 2*x*z + y*z + x + y + 2*z + x-1*y + y-1*z + 2*z-1 + x-1*y*z-1 + y-1 + 2*x-1 + 3*x-1*z-1 + x-1*y-1 + x-1*z-2 + x-1*y-1*z-1
161 ? x*z2 + 2*x*z + y*z + x + y + 3*z + x-1*y + y-1*z + 2*z-1 + x-1*y*z-1 + y-1 + 2*x-1 + 3*x-1*z-1 + x-1*y-1 + x-1*z-2 + x-1*y-1*z-1
40 rank 2, number 10 x*z2 + 2*x*z + y*z + x + y + 3*z + x-1*y + y-1*z + 2*z-1 + x-1*y*z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + x-1*y-1 + x-1*z-2 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 23 2 Lattice Minkowski decompositions of facet 23
Polytope 3008
Image of polytope 3008 PALP id: 3008
grdb id: 53115
Integer points: [ 1 0 0 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 1 -1 0 -1 -1 0 -1 -1 -1 0 -1 0 0]
[ 0 0 1 -1 -1 1 1 2 -1 -1 -1 0 1 0 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
56 rank 2, number 11 x + y + z + x*z-1 + y*z-1 + y-1*z + x-1*z + x-1*y-1*z2 + z-1 + 2*y-1 + 2*x-1 + 3*x-1*y-1*z + y-1*z-1 + x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Polytope 3009
Image of polytope 3009 PALP id: 3009
grdb id: 53121
Integer points: [ 1 0 0 -1 0 1 -1 -1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 0 -1 1 0 0 -2 -2 -1 0 -1 -1 0 -1]
[ 0 0 1 1 -1 -1 0 1 -1 -1 -1 0 0 -1 0 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y*z + x-1*y + x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 3*x-1 + 3*y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1
13 rank 2, number 12 x + y + z + x-1*y*z + x-1*y + x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 3*x-1 + 2*y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3010
Image of polytope 3010 PALP id: 3010
grdb id: 53085
Integer points: [ 1 0 0 0 1 0 -1 -2 1 -1 1 0 -1 1 0 -1 0]
[ 0 1 0 0 -1 -1 0 1 -2 0 -2 -1 0 -1 0 1 -1]
[ 0 0 1 -1 -1 1 1 0 0 -1 -1 0 0 0 0 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? x + y + z + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + x*y-1*z-1 + z-1 + x*y-2 + 4*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
10 rank 1, V18 x + y + z + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + x*y-1*z-1 + z-1 + x*y-2 + 2*y-1 + 2*x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 5 Lattice Minkowski decompositions of facet 11
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Polytope 3011
Image of polytope 3011 PALP id: 3011
grdb id: 53112
Integer points: [ 1 0 0 0 0 0 1 -1 -1 -2 -2 -1 0 -1 1 0 -1]
[ 0 1 0 1 -1 0 -2 0 2 1 2 1 -1 0 -1 0 1]
[ 0 0 1 -1 1 -1 0 1 -1 0 -1 -1 0 0 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + y*z-1 + x-1*y2*z-1 + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
40 rank 2, number 10 x + y + z + y*z-1 + x-1*y2*z-1 + 2*x*y-1 + 3*x-1*y + y-1*z + x-1*z + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3012
Image of polytope 3012 PALP id: 3012
grdb id: 53111
Integer points: [ 1 0 0 1 0 2 1 0 -2 -1 -2 0 1 -1 0 -1 -1]
[ 0 1 0 0 0 -1 -1 -1 1 -1 0 -1 -1 0 0 0 1]
[ 0 0 1 -1 -1 -1 -1 1 0 1 1 0 0 0 0 1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x2*y-1*z-1 + x*z-1 + 2*x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 3*x-1 + x-2*y + x-1*y-1*z + x-2*z
62 rank 2, number 9 x + y + z + x2*y-1*z-1 + x*z-1 + 2*x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + x-2*y + x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 3013
Image of polytope 3013 PALP id: 3013
grdb id: 57324
Integer points: [ 1 0 0 1 0 1 -1 1 -1 -1 -1 0 0 0 0 -1 -1]
[ 0 1 0 0 1 -1 1 -1 1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 1 -1 -1 0 0 -1 -1 2 1 0 1 -1 0 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + x*z-1 + y*z-1 + x*y-1 + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3014
Image of polytope 3014 PALP id: 3014
grdb id: 57336
Integer points: [ 1 0 0 -1 1 -1 -1 1 -1 1 0 -1 0 0 0 0 1]
[ 0 1 0 1 -1 1 0 -2 0 -2 -1 0 -1 -1 0 0 -1]
[ 0 0 1 1 0 0 1 -1 -1 -2 -2 0 0 -1 0 -1 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + x*y-1 + x-1*y + x-1*z + 2*x*y-1*z-1 + 2*z-1 + 2*y-1 + 2*x-1 + x*y-2*z-1 + 3*y-1*z-1 + x-1*z-1 + x*y-2*z-2 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3015
Image of polytope 3015 PALP id: 3015
grdb id: 56731
Integer points: [ 1 0 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 0 0 -1 -1]
[ 0 1 0 0 1 0 -1 1 -1 -2 -2 -1 0 -1 0 -1 0]
[ 0 0 1 -1 0 1 -1 -1 1 0 -1 0 0 0 0 -1 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + x-1*y + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + x-1*y-1*z + y-1*z-1 + 3*x-1*z-1 + 4*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
17 rank 1, V22 x + y + z + x-1*y + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + 3*x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Polytope 3016
Image of polytope 3016 PALP id: 3016
grdb id: 57186
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 1 0 1 -1 -2 -2 -1 0 -1 0 0 -1]
[ 0 0 1 -1 0 1 1 0 -2 -1 -2 0 0 -1 -1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + x-1*y*z + x-1*y + x-1*z + z-1 + y-1 + 3*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-1*z-2 + x-1*y-2*z-1 + x-1*y-2*z-2
17 rank 1, V22 x + y + z + x-1*y*z + x-1*y + x-1*z + z-1 + y-1 + 4*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + 4*x-1*y-1*z-1 + x-1*y-1*z-2 + x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 96 1 Lattice Minkowski decompositions of facet 96
Polytope 3017
Image of polytope 3017 PALP id: 3017
grdb id: 57061
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 1 0 1 -1 -2 -2 0 -1 0 -1 -1 0]
[ 0 0 1 -1 1 0 1 -1 -1 0 1 -1 0 0 1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + x-1*y + y-1*z + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + 2*x-1*y-1*z + 2*x-1*z-1 + 4*x-1*y-1 + x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
17 rank 1, V22 x + y + z + x-1*y + y-1*z + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + 2*x-1*y-1*z + 2*x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 96 1 Lattice Minkowski decompositions of facet 96
Polytope 3018
Image of polytope 3018 PALP id: 3018
grdb id: 57357
Integer points: [ 1 0 0 0 0 -1 1 -1 1 -2 1 -1 0 1 0 -1 0]
[ 0 1 0 1 -1 1 -1 -1 -1 0 0 0 0 0 -1 0 0]
[ 0 0 1 -1 1 0 0 1 -1 1 -2 1 0 -1 0 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 x + y + z + 2*x*z-1 + y*z-1 + x*y-1 + x-1*y + y-1*z + 2*x-1*z + x*z-2 + x*y-1*z-1 + 3*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 5 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3019
Image of polytope 3019 PALP id: 3019
grdb id: 57256
Integer points: [ 1 0 0 0 0 1 1 -1 -1 -2 -2 -1 0 -1 0 -1 0]
[ 0 1 0 1 -1 0 -1 -1 1 -1 0 -1 -1 0 0 0 0]
[ 0 0 1 -1 1 -1 0 1 -1 0 -1 0 0 0 0 -1 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*z-1 + y*z-1 + x*y-1 + y-1*z + 3*z-1 + x-1*y*z-1 + 3*y-1 + 2*x-1 + x-1*y-1*z + 3*x-1*z-1 + 3*x-1*y-1 + x-2*z-1 + x-2*y-1
31 rank 3, number 3 x + y + z + x*z-1 + y*z-1 + x*y-1 + y-1*z + 3*z-1 + x-1*y*z-1 + 3*y-1 + 3*x-1 + x-1*y-1*z + 3*x-1*z-1 + 3*x-1*y-1 + x-2*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 3020
Image of polytope 3020 PALP id: 3020
grdb id: 57255
Integer points: [ 1 0 0 1 -1 0 -1 -1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 1 0 1 0 0 -2 -2 -1 0 -1 -1 0 -1]
[ 0 0 1 0 0 -1 -1 -1 1 1 1 0 0 1 0 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*y-1 + x-1*y + 2*y-1*z + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + y-2*z + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
39 ? x + y + z + x*y-1 + x-1*y + 2*y-1*z + x-1*z + z-1 + x-1*y*z-1 + 3*y-1 + 3*x-1 + y-2*z + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3021
Image of polytope 3021 PALP id: 3021
grdb id: 57254
Integer points: [ 1 0 0 1 -1 0 -1 0 -1 -2 -2 -2 -1 -1 0 -1 0]
[ 0 1 0 -1 1 0 1 -1 -1 1 -1 0 0 -1 -1 0 0]
[ 0 0 1 0 0 -1 -1 -1 0 -1 -1 -1 0 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*y-1 + x-1*y + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + 3*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1*z-1
146 ? x + y + z + x*y-1 + x-1*y + z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + y-1*z-1 + 3*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3022
Image of polytope 3022 PALP id: 3022
grdb id: 57226
Integer points: [ 1 0 0 1 0 0 -1 -1 -1 -1 -1 -1 -1 0 -1 0 0]
[ 0 1 0 -1 -1 1 1 0 -1 -1 1 1 0 0 0 0 -1]
[ 0 0 1 0 1 -1 0 1 1 0 -2 -1 0 0 -1 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + y*z-1 + x*y-1 + x-1*y + y-1*z + x-1*z + 2*z-1 + 2*x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + x-1*y*z-2 + 2*x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 3023
Image of polytope 3023 PALP id: 3023
grdb id: 57290
Integer points: [ 1 0 0 1 0 0 -1 1 -1 -2 -2 -1 -1 0 -1 0 0]
[ 0 1 0 -1 1 -1 1 0 -1 1 0 1 0 0 0 0 -1]
[ 0 0 1 0 -1 1 0 -1 0 -1 -1 -1 0 0 -1 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*z-1 + y*z-1 + x*y-1 + x-1*y + y-1*z + 3*z-1 + 2*x-1*y*z-1 + 2*y-1 + 2*x-1 + 3*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + x-2*z-1
31 rank 3, number 3 x + y + z + x*z-1 + y*z-1 + x*y-1 + x-1*y + y-1*z + 3*z-1 + 2*x-1*y*z-1 + 2*y-1 + 3*x-1 + 3*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Polytope 3024
Image of polytope 3024 PALP id: 3024
grdb id: 57272
Integer points: [ 1 0 0 1 0 1 -1 -1 -2 0 -2 0 -1 -1 0 0 -1]
[ 0 1 0 -1 -1 -1 0 1 1 -1 1 -1 0 0 0 0 1]
[ 0 0 1 0 1 -1 1 -1 0 -1 -1 0 -1 0 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*y-1 + 2*x-1*y + y-1*z + x-1*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-2*y + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3025
Image of polytope 3025 PALP id: 3025
grdb id: 57234
Integer points: [ 1 0 0 1 1 0 0 -1 1 -2 0 -1 0 -1 0 -1 0]
[ 0 1 0 0 -1 -1 1 1 -1 1 -1 0 -1 0 0 1 0]
[ 0 0 1 -1 0 1 -1 1 -1 1 -1 0 0 1 -1 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y*z + x*z-1 + y*z-1 + x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + x*y-1*z-1 + 2*z-1 + 2*y-1 + 2*x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Polytope 3026
Image of polytope 3026 PALP id: 3026
grdb id: 57359
Integer points: [ 1 0 0 1 1 0 -1 -2 1 -2 0 1 0 -1 0 -1 -1]
[ 0 1 0 0 -1 -1 1 1 -1 1 -1 -1 0 0 0 0 1]
[ 0 0 1 -1 0 0 0 2 -2 1 -1 -1 -1 0 0 1 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + 2*x-1*y*z + x-2*y*z2 + x*z-1 + x*y-1 + x-1*y + 2*x-1*z + x-2*y*z + 2*x*y-1*z-1 + 2*z-1 + y-1 + 2*x-1 + x*y-1*z-2 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 11 6 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3027
Image of polytope 3027 PALP id: 3027
grdb id: 56158
Integer points: [ 1 0 0 0 0 -1 -1 -1 0 -1 -1 -1 0 -1 -1 0 0]
[ 0 1 0 1 -1 1 0 -1 -1 1 -1 -1 -1 0 0 0 0]
[ 0 0 1 -1 1 0 1 1 -1 -1 -1 0 0 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + y*z-1 + x-1*y + y-1*z + x-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3028
Image of polytope 3028 PALP id: 3028
grdb id: 56368
Integer points: [ 1 0 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 1 -1 0 -1 -1 1 -1 1 -1 0 0 0 1 0]
[ 0 0 1 -1 1 -1 0 1 -1 -1 1 0 -1 0 1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + x-1*y*z + y*z-1 + 2*x-1*y + y-1*z + 2*x-1*z + z-1 + x-1*y*z-1 + y-1 + 4*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Polytope 3029
Image of polytope 3029 PALP id: 3029
grdb id: 56365
Integer points: [ 1 0 0 0 0 0 0 -1 -1 -2 -2 -1 -2 -1 -1 0 -1]
[ 0 1 0 1 -1 0 -1 1 -1 1 -1 -1 0 0 0 0 1]
[ 0 0 1 -1 1 -1 0 0 -1 -1 -1 0 -1 0 -1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + y*z-1 + x-1*y + y-1*z + z-1 + 2*x-1*y*z-1 + y-1 + 3*x-1 + 3*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Polytope 3030
Image of polytope 3030 PALP id: 3030
grdb id: 54918
Integer points: [ 1 0 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 0 -1 -1]
[ 0 1 0 1 -1 -1 0 0 1 1 -2 -1 0 1 0 -1 0]
[ 0 0 1 -1 1 0 -1 1 0 -2 1 1 0 -1 0 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + y*z-1 + x-1*y + y-1*z + x-1*z + z-1 + 2*x-1*y*z-1 + y-1 + 4*x-1 + 2*x-1*y-1*z + x-1*y*z-2 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Polytope 3031
Image of polytope 3031 PALP id: 3031
grdb id: 11582
Integer points: [ 1 1 0 0 0 0 -1 -1 -1 -1 -1 -1 0 -1 0 1 0]
[ 0 2 0 1 -1 0 -2 0 -1 0 -2 -1 1 -1 0 1 -1]
[ 0 0 1 1 -1 -1 0 0 1 1 -1 -1 0 0 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 x*y2 + 2*x*y + y*z + x + 2*y + z + x-1*z + z-1 + 2*y-1 + x-1 + x-1*y-1*z + y-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
20 rank 1, V16 x*y2 + 2*x*y + y*z + x + 2*y + z + x-1*z + z-1 + 2*y-1 + x-1 + x-1*y-1*z + y-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 6 Lattice Minkowski decompositions of facet 11
Polytope 3032
Image of polytope 3032 PALP id: 3032
grdb id: 12194
Integer points: [ 1 0 0 1 -1 0 1 0 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 1 0 -1 -1 0 0 -1 -1 -1 0 -1 -1 0]
[ 0 0 1 0 0 -1 -1 1 1 -1 1 -1 0 0 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*y-1 + x-1*y + y-1*z + x-1*z + x*y-1*z-1 + z-1 + 3*y-1 + 2*x-1 + x-1*y-1*z + 2*y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
39 ? x + y + z + x*y-1 + x-1*y + y-1*z + x-1*z + x*y-1*z-1 + z-1 + 3*y-1 + 3*x-1 + x-1*y-1*z + 2*y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 5 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 3033
Image of polytope 3033 PALP id: 3033
grdb id: 12197
Integer points: [ 1 0 0 -1 -1 0 0 1 1 -1 -1 1 -1 0 1 0 0]
[ 0 1 0 1 1 -1 1 -1 -1 0 -1 0 0 0 0 0 -1]
[ 0 0 1 1 0 1 -1 0 -1 0 1 -2 1 0 -1 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y*z + 2*x*z-1 + y*z-1 + x*y-1 + x-1*y + y-1*z + 2*x-1*z + x*z-2 + x*y-1*z-1 + 2*z-1 + 2*y-1 + x-1 + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 6 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3034
Image of polytope 3034 PALP id: 3034
grdb id: 12193
Integer points: [ 1 0 0 1 -1 1 0 1 -1 -2 -2 -1 0 -1 0 -1 0]
[ 0 1 0 -1 1 -1 0 -2 0 1 1 0 -1 0 0 1 -1]
[ 0 0 1 0 1 -1 -1 -1 1 1 0 -1 0 0 0 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + x*y-1 + 2*x-1*y + x-1*z + x-2*y*z + x*y-1*z-1 + z-1 + 2*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3035
Image of polytope 3035 PALP id: 3035
grdb id: 12198
Integer points: [ 1 0 0 -1 2 0 0 -2 1 0 0 -1 1 1 0 -1 -1]
[ 0 1 0 1 -1 1 -1 1 -1 0 -1 0 0 -1 0 1 0]
[ 0 0 1 1 -1 -1 1 1 -1 -1 0 0 -1 0 0 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 x + y + z + x-1*y*z + x2*y-1*z-1 + 2*x*z-1 + y*z-1 + 2*x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + x*y-1*z-1 + z-1 + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 8 Lattice Minkowski decompositions of facet 11
Polytope 3036
Image of polytope 3036 PALP id: 3036
grdb id: 12161
Integer points: [ 1 0 0 1 1 -1 1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 0 -1 1 -1 1 0 0 -1 -1 0 -1 -1 0 0]
[ 0 0 1 -1 0 1 -1 0 1 -1 0 -1 0 -1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + z + x-1*y*z + x*z-1 + x*y-1 + x-1*y + x-1*z + x*y-1*z-1 + 2*z-1 + 2*y-1 + 3*x-1 + 2*y-1*z-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
10 rank 1, V18 x + y + z + x-1*y*z + x*z-1 + x*y-1 + x-1*y + x-1*z + x*y-1*z-1 + 2*z-1 + 2*y-1 + 2*x-1 + 2*y-1*z-1 + x-1*z-1 + x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3037
Image of polytope 3037 PALP id: 3037
grdb id: 1505
Integer points: [ 1 0 0 1 1 0 0 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 -1 -1 1 1 0 -1 1 -1 0 0 0 -1 0]
[ 0 0 1 -1 0 1 -1 0 1 1 -1 0 -1 0 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + z + x*z-1 + y*z-1 + x*y-1 + x-1*y + y-1*z + x-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
10 rank 1, V18 x + y + z + x*z-1 + y*z-1 + x*y-1 + x-1*y + y-1*z + x-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 5 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3038
Image of polytope 3038 PALP id: 3038
grdb id: 547438
Integer points: [ 1 0 1 -9 -7 -5 -3 -1 -6 -4 -2 0 -3 -1 -3 -1 1 0]
[ 0 1 0 -5 -4 -3 -2 -1 -3 -2 -1 0 -1 0 -2 -1 0 0]
[ 0 0 2 -3 -2 -1 0 1 -2 -1 0 1 -1 0 -1 0 1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 73 1 none
Image of facet 191 1 none
Polytope 3039
Image of polytope 3039 PALP id: 3039
grdb id: 545379
Integer points: [ 1 0 0 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 0]
[ 0 1 0 -3 1 -2 -1 0 -2 -1 0 1 -1 0 1 -1 0 0]
[ 0 0 1 1 -3 0 -1 -2 1 0 -1 -2 1 0 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Image of facet 123 1 none
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Polytope 3040
Image of polytope 3040 PALP id: 3040
grdb id: 545314
Integer points: [ 1 0 1 -3 -3 -3 -3 -2 -2 -2 -1 -1 -1 -1 -1 0 0 1]
[ 0 1 0 -2 -2 -2 -2 -1 -1 -1 0 0 -1 -1 -1 0 0 0]
[ 0 0 2 -3 0 -1 -2 0 -1 -2 0 -1 1 0 -1 1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 14 1 none
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Image of facet 9 1 irreducible and admissible
Polytope 3041
Image of polytope 3041 PALP id: 3041
grdb id: 545392
Integer points: [ 1 0 1 -3 -3 -3 -3 -2 -2 -2 -1 -1 -1 0 -1 -1 0 1]
[ 0 1 0 1 -2 0 -1 1 0 -1 1 0 -1 0 0 -1 0 0]
[ 0 0 2 -3 0 -2 -1 -2 -1 0 -1 0 1 1 -1 0 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 14 1 none
Image of facet 193 1 none
Polytope 3042
Image of polytope 3042 PALP id: 3042
grdb id: 545307
Integer points: [ 1 1 0 0 -3 -2 -1 -2 -1 0 -1 0 -1 0 -1 0 0 1]
[ 0 2 0 -3 0 0 0 -1 -1 -1 -2 -2 1 1 0 0 -1 1]
[ 0 0 1 1 -2 -1 0 -1 0 1 0 1 -1 0 -1 0 0 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 14 2 none
Polytope 3043
Image of polytope 3043 PALP id: 3043
grdb id: 545381
Integer points: [ 1 0 0 -1 -4 -2 -1 0 -3 -2 -1 0 -3 -2 -1 0 -1 0]
[ 0 1 1 0 -3 -1 0 1 -2 -1 0 1 -2 -1 0 0 -1 0]
[ 0 0 3 2 -4 0 1 2 -2 -1 0 1 -3 -2 -1 1 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Image of facet 1 1 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 14 1 none
Image of facet 9 1 irreducible and admissible
Polytope 3044
Image of polytope 3044 PALP id: 3044
grdb id: 545304
Integer points: [ 1 0 1 -3 -6 -1 -4 -2 0 -5 -3 -1 -4 -2 -1 1 -2 0]
[ 0 1 0 -2 -2 -1 -2 -1 0 -2 -1 0 -1 0 -1 0 -1 0]
[ 0 0 2 0 -3 1 -1 0 1 -2 -1 0 -2 -1 0 1 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 194 1 Lattice Minkowski decompositions of facet 194
Image of facet 14 1 none
Image of facet 9 1 irreducible and admissible
Polytope 3045
Image of polytope 3045 PALP id: 3045
grdb id: 545386
Integer points: [ 1 0 0 -2 -6 -5 -4 -3 -4 -3 -2 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 -2 -2 -2 -2 -2 -1 -1 -1 0 0 -1 -1 -1 0 0]
[ 0 0 1 -1 3 2 1 0 2 1 0 1 0 2 1 0 1 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 80 1 none
Image of facet 14 1 none
Image of facet 121 1 none
Polytope 3046
Image of polytope 3046 PALP id: 3046
grdb id: 545372
Integer points: [ 1 0 1 1 -6 0 -1 -2 -3 -4 -5 0 -1 -2 -3 1 0 -1]
[ 0 1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0]
[ 0 0 2 3 -4 2 1 0 -1 -2 -3 1 0 -1 -2 1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 195 1 Lattice Minkowski decompositions of facet 195
Image of facet 4 1 none
Image of facet 196 1 irreducible and admissible
Polytope 3047
Image of polytope 3047 PALP id: 3047
grdb id: 545312
Integer points: [ 1 0 0 -6 -9 -6 -3 -8 -5 -2 -7 -4 -1 -3 -4 -1 -3 0]
[ 0 1 0 -3 -6 -4 -2 -5 -3 -1 -4 -2 0 -1 -3 -1 -2 0]
[ 0 0 1 -2 -2 -1 0 -2 -1 0 -2 -1 0 -1 -1 0 -1 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 194 1 Lattice Minkowski decompositions of facet 194
Image of facet 14 2 none
Polytope 3048
Image of polytope 3048 PALP id: 3048
grdb id: 528562
Integer points: [ 1 0 0 -2 0 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 1 0 2 -3 -1 0 1 -2 -1 0 1 -2 -1 0 1 -1 0]
[ 0 0 1 1 -2 -2 -1 0 -2 -1 0 1 -1 0 -1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Polytope 3049
Image of polytope 3049 PALP id: 3049
grdb id: 528553
Integer points: [ 1 0 0 -1 -1 -4 -3 -2 -3 -2 -1 -2 -1 -2 -1 -1 0 0]
[ 0 1 0 1 -2 -2 -1 0 -2 -1 0 -2 -1 -1 0 -1 0 -1]
[ 0 0 1 1 -2 1 1 1 0 0 0 -1 -1 1 1 0 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 124 1 none
Image of facet 14 1 none
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Polytope 3050
Image of polytope 3050 PALP id: 3050
grdb id: 528558
Integer points: [ 1 1 0 1 1 -3 1 1 1 -1 -1 -1 0 0 0 -2 1 -1]
[ 0 2 0 3 -1 -3 0 1 2 -2 -1 0 -1 0 1 -2 1 -1]
[ 0 0 1 -1 -1 1 -1 -1 -1 0 0 0 0 0 0 1 0 1]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x*y3*z-1 + x*y2 + 4*x*y2*z-1 + 2*x*y + 6*x*y*z-1 + x + 3*y + z + 4*x*z-1 + x*y-1*z-1 + 3*y-1 + 2*x-1 + 3*x-1*y-1*z + 4*x-1*y-1 + 2*x-1*y-2 + 3*x-2*y-2*z + x-3*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Polytope 3051
Image of polytope 3051 PALP id: 3051
grdb id: 528569
Integer points: [ 1 1 0 0 -2 -5 -1 -3 -2 -1 0 -4 -3 -2 -1 0 1 -2]
[ 0 2 0 1 -1 -4 0 -2 -1 0 1 -3 -2 -1 -1 0 1 -2]
[ 0 0 1 1 1 -2 1 0 0 0 0 -1 -1 -1 0 0 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 170 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3052
Image of polytope 3052 PALP id: 3052
grdb id: 528560
Integer points: [ 1 0 0 -3 4 3 2 3 1 2 0 1 2 -1 0 1 -2 -1]
[ 0 1 0 3 -6 -5 -3 -4 -1 -2 -1 -2 -3 1 0 -1 2 1]
[ 0 0 1 1 -3 -3 -2 -2 -1 -1 -1 -1 -1 0 0 0 1 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 14 2 none
Polytope 3053
Image of polytope 3053 PALP id: 3053
grdb id: 528309
Integer points: [ 1 0 0 -3 -2 -3 -3 -3 -3 -2 -2 -2 -1 -1 -1 -1 -1 0]
[ 0 1 0 -2 -1 -2 -2 -2 -2 -1 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 1 -2 2 2 1 0 -1 1 0 -1 1 0 1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 169 1 none
Polytope 3054
Image of polytope 3054 PALP id: 3054
grdb id: 528551
Integer points: [ 1 0 1 -3 -3 -1 -1 0 -2 -1 0 -2 -1 -2 1 0 -1 0]
[ 0 1 0 0 1 -2 1 0 1 0 -1 0 -1 -1 0 0 0 -1]
[ 0 0 2 -2 -3 2 -1 1 -2 0 2 -1 1 0 1 0 -1 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x*z2 + 2*x*z + x + y + 3*z + 2*y-1*z2 + 2*y-1*z + 3*x-1*y*z-1 + 5*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 3*x-2*y*z-2 + 4*x-2*z-1 + 2*x-2*y-1 + x-3*y*z-3 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 197 1 Lattice Minkowski decompositions of facet 197
Image of facet 9 1 irreducible and admissible
Polytope 3055
Image of polytope 3055 PALP id: 3055
grdb id: 527980
Integer points: [ 1 0 1 1 -3 -3 0 -1 -2 -1 -2 1 0 -1 1 0 -1 1]
[ 0 1 0 -2 1 0 0 0 0 1 1 -1 -1 -1 0 0 0 -1]
[ 0 0 2 2 -3 -2 1 0 -1 -1 -2 2 1 0 1 0 -1 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x*z2 + 2*x*z + 2*x*y-1*z2 + x + y + 2*x*y-1*z + 4*z + x*y-2*z2 + 4*y-1*z + 3*x-1*y*z-1 + 6*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + 3*x-2*y*z-2 + 4*x-2*z-1 + x-3*y*z-3 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Polytope 3056
Image of polytope 3056 PALP id: 3056
grdb id: 528005
Integer points: [ 1 0 1 1 -3 -3 -2 -1 -3 -2 -1 0 -2 -1 0 -1 0 1]
[ 0 1 0 -1 1 -1 1 1 0 0 0 0 -1 -1 -1 0 0 0]
[ 0 0 2 3 -3 -1 -2 -1 -2 -1 0 1 0 1 2 -1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 4 1 none
Image of facet 13 1 irreducible and admissible
Image of facet 198 1 Lattice Minkowski decompositions of facet 198
Image of facet 9 1 irreducible and admissible
Polytope 3057
Image of polytope 3057 PALP id: 3057
grdb id: 528342
Integer points: [ 1 0 0 -2 -3 0 -1 0 -1 -2 0 -1 -2 0 -1 0 -1 0]
[ 0 1 0 2 2 -4 1 -1 0 1 -2 -1 0 -3 -2 0 1 -1]
[ 0 0 1 -1 -2 1 0 1 0 -1 1 0 -1 1 0 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 13 1 irreducible and admissible
Image of facet 14 1 none
Polytope 3058
Image of polytope 3058 PALP id: 3058
grdb id: 527892
Integer points: [ 1 0 0 -3 -2 -5 -4 -4 -3 -2 -3 -2 -1 -1 -2 -1 -1 0]
[ 0 1 0 0 -2 -2 -1 -2 -1 0 -2 -1 0 -1 -1 0 -1 0]
[ 0 0 1 -2 1 -2 -2 -1 -1 -1 0 0 0 1 -1 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 14 1 none
Image of facet 199 1 Lattice Minkowski decompositions of facet 199
Polytope 3059
Image of polytope 3059 PALP id: 3059
grdb id: 528026
Integer points: [ 1 0 0 -2 -3 -5 -2 -1 -4 -3 -2 -1 -1 0 -4 -3 -2 -1]
[ 0 1 0 -1 -2 -4 -1 0 -3 -2 -1 0 -1 0 -3 -2 -2 -1]
[ 0 0 1 -2 0 -2 0 0 -1 -1 -1 -1 0 0 -2 -2 -1 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 9 1 irreducible and admissible
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Image of facet 14 1 none
Polytope 3060
Image of polytope 3060 PALP id: 3060
grdb id: 527955
Integer points: [ 1 0 0 -3 3 3 -1 1 -2 0 2 -1 1 -1 1 0 2 1]
[ 0 1 0 0 -2 -3 -1 -2 0 -1 -2 0 -1 0 -1 0 -1 0]
[ 0 0 1 -2 3 4 0 2 -1 1 3 0 2 -1 1 0 2 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x3*y-2*z3 + x3*y-3*z4 + 3*x2*y-1*z2 + 3*x2*y-2*z3 + 3*x*z + 3*x*y-1*z2 + x + y + 3*x*y-1*z + z + 3*x*y-2*z2 + 6*y-1*z + 3*x-1 + 2*x-1*z-1 + 3*x-1*y-1 + 3*x-2*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3061
Image of polytope 3061 PALP id: 3061
grdb id: 528328
Integer points: [ 1 0 0 -1 -2 -4 -1 -2 -3 -1 -2 -3 -1 -2 -1 0 -1 0]
[ 0 1 0 -2 3 4 1 2 3 0 1 2 -1 0 2 0 1 -1]
[ 0 0 1 0 -2 -3 0 -1 -2 0 -1 -2 0 -1 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 121 1 none
Polytope 3062
Image of polytope 3062 PALP id: 3062
grdb id: 528341
Integer points: [ 1 0 0 -1 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0]
[ 0 1 0 2 2 -4 1 0 -1 -2 -3 1 0 -1 -2 1 0 -1]
[ 0 0 1 -2 -3 3 -2 -1 0 1 2 -1 0 1 2 -1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 200 1 Lattice Minkowski decompositions of facet 200
Image of facet 53 1 irreducible and admissible
Image of facet 4 1 none
Polytope 3063
Image of polytope 3063 PALP id: 3063
grdb id: 528525
Integer points: [ 1 0 1 -2 1 -4 0 -1 -2 -3 0 -1 -2 -3 -1 1 0 -1]
[ 0 1 0 1 -1 -1 -1 -1 -1 -1 0 0 0 0 1 0 0 0]
[ 0 0 2 -2 3 -2 2 1 0 -1 1 0 -1 -2 -1 1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 43 1 irreducible and admissible
Image of facet 4 1 none
Image of facet 201 1 Lattice Minkowski decompositions of facet 201
Polytope 3064
Image of polytope 3064 PALP id: 3064
grdb id: 528308
Integer points: [ 1 0 0 -4 -1 -5 -4 -3 -2 -3 -2 -1 -2 -1 -2 -1 0 0]
[ 0 1 0 -1 -2 -2 -2 -2 -2 -1 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 1 -2 2 -2 -1 0 1 -1 0 1 -1 0 -1 0 1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 202 1 none
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 3065
Image of polytope 3065 PALP id: 3065
grdb id: 528512
Integer points: [ 1 0 0 -1 -4 -6 -5 -4 -3 -2 -3 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 0 -4 -5 -4 -3 -2 -1 -3 -2 -1 -2 -1 0 -1 0]
[ 0 0 1 1 -3 -4 -3 -2 -1 0 -2 -1 0 -2 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 8 1 none
Image of facet 13 1 irreducible and admissible
Image of facet 73 1 none
Image of facet 157 1 Lattice Minkowski decompositions of facet 157
Polytope 3066
Image of polytope 3066 PALP id: 3066
grdb id: 527910
Integer points: [ 1 0 0 0 -3 -6 -2 -4 -1 -3 -5 -2 -4 -1 -3 0 -2 -1]
[ 0 1 0 -1 -3 -3 -1 -2 -1 -2 -3 -2 -3 0 -1 0 -1 -1]
[ 0 0 1 -1 -2 -2 0 -1 0 -1 -2 -1 -2 0 -1 0 -1 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 14 1 none
Image of facet 56 1 Lattice Minkowski decompositions of facet 56
Polytope 3067
Image of polytope 3067 PALP id: 3067
grdb id: 527908
Integer points: [ 1 0 0 0 -3 -6 -4 -5 -2 -3 -4 -1 -2 -1 -2 -3 0 -1]
[ 0 1 0 -1 -2 -5 -3 -4 -1 -2 -3 0 -1 -1 -2 -3 0 -1]
[ 0 0 1 -1 0 -3 -1 -2 0 -1 -2 0 -1 0 -1 -2 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 14 1 none
Polytope 3068
Image of polytope 3068 PALP id: 3068
grdb id: 527903
Integer points: [ 1 0 0 0 -3 -6 -4 -2 -5 -3 -1 -4 -2 -3 -1 -2 0 -1]
[ 0 1 0 -1 0 -3 -2 -1 -2 -1 0 -1 0 -2 -1 -1 0 0]
[ 0 0 1 -1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + 3*x-1*z + 3*x-1 + 3*x-2*z + y-1*z-1 + 3*x-1*y-1 + 3*x-2*y-1*z + x-3*z + 3*x-2*y-1 + 6*x-3*y-1*z + 3*x-4*y-1*z + 2*x-3*y-2 + 3*x-4*y-2*z + 3*x-5*y-2*z + x-6*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 56 1 Lattice Minkowski decompositions of facet 56
Polytope 3069
Image of polytope 3069 PALP id: 3069
grdb id: 528337
Integer points: [ 1 0 0 0 -2 -6 -3 -4 -5 -1 -2 -3 -4 -1 -2 -1 -2 0]
[ 0 1 0 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 1 1 1 -3 0 -1 -2 1 0 -1 -2 0 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 64 1 none
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Polytope 3070
Image of polytope 3070 PALP id: 3070
grdb id: 527890
Integer points: [ 1 0 0 -3 -4 -7 -5 -6 -4 -2 -5 -3 -1 -2 -3 -1 -2 0]
[ 0 1 0 -2 -1 -4 -3 -3 -2 -1 -2 -1 0 0 -2 -1 -1 0]
[ 0 0 1 0 -2 -2 -1 -2 -1 0 -2 -1 0 -1 -1 0 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 14 1 none
Image of facet 199 1 Lattice Minkowski decompositions of facet 199
Polytope 3071
Image of polytope 3071 PALP id: 3071
grdb id: 527904
Integer points: [ 1 0 0 -1 -3 -6 -4 -2 -5 -3 -1 -4 -2 -1 -2 0 -3 -1]
[ 0 1 0 -1 -2 -2 -2 -1 -2 -1 0 -1 0 -1 -1 0 -1 0]
[ 0 0 1 -1 0 3 1 0 2 1 0 2 1 0 1 0 2 1]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 124 1 none
Image of facet 14 1 none
Polytope 3072
Image of polytope 3072 PALP id: 3072
grdb id: 527905
Integer points: [ 1 0 0 0 -3 -6 -4 -2 -5 -3 -1 -4 -2 -3 -1 -2 0 -1]
[ 0 1 -1 0 0 3 2 1 2 1 0 1 0 2 1 1 0 0]
[ 0 0 0 1 -2 -2 -1 0 -2 -1 0 -2 -1 -1 0 -1 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 132 1 Lattice Minkowski decompositions of facet 132
Image of facet 14 1 none
Polytope 3073
Image of polytope 3073 PALP id: 3073
grdb id: 528325
Integer points: [ 1 0 1 0 -5 -8 -6 -4 -2 -5 -3 -1 -2 0 -3 -1 -2 0]
[ 0 1 -1 0 -2 -4 -3 -2 -1 -3 -2 -1 -2 -1 -1 0 -1 0]
[ 0 0 0 1 -2 -3 -2 -1 0 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 64 1 none
Image of facet 121 1 none
Polytope 3074
Image of polytope 3074 PALP id: 3074
grdb id: 527110
Integer points: [ 1 0 0 -1 0 -3 -1 -2 0 -1 -2 0 -1 -1 -2 0 -1 0]
[ 0 1 0 1 -3 -3 -1 -2 -1 -2 -3 -2 -3 0 -1 0 -1 -1]
[ 0 0 1 0 -2 -2 0 -1 0 -1 -2 -1 -2 0 -1 0 -1 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 9 1 irreducible and admissible
Image of facet 14 1 none
Polytope 3075
Image of polytope 3075 PALP id: 3075
grdb id: 527214
Integer points: [ 1 0 0 0 -3 -3 -2 -1 -3 -2 -1 0 -2 -1 -1 0 -1 0]
[ 0 1 0 -2 0 -2 0 0 -1 -1 -1 -1 -2 -2 0 0 -1 -1]
[ 0 0 1 1 -2 -2 -1 0 -2 -1 0 1 -1 0 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Image of facet 14 1 none
Polytope 3076
Image of polytope 3076 PALP id: 3076
grdb id: 465966
Integer points: [ 1 0 0 1 -1 -1 -3 -2 -1 0 -2 -1 0 -2 -1 0 -1 0]
[ 0 1 0 -1 1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 0 1 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + 4*y-1*z-1 + 4*x-1*z-1 + 4*x-1*y-1 + 6*x-1*y-1*z-1 + 2*x-2*z-1 + 2*x-2*y-1 + 4*x-2*y-1*z-1 + x-3*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 32 2 Lattice Minkowski decompositions of facet 32
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3077
Image of polytope 3077 PALP id: 3077
grdb id: 465964
Integer points: [ 1 0 0 0 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 2 -1 3 2 1 0 1 0 -1 2 1 0 1 0]
[ 0 0 0 1 -2 2 -2 -1 0 1 -1 0 1 -1 0 1 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 80 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3078
Image of polytope 3078 PALP id: 3078
grdb id: 466014
Integer points: [ 1 1 -1 -1 0 0 1 1 1 1 0 0 0 0 0 0 0 -1]
[ 0 2 -2 0 0 3 -2 0 -1 1 -1 -2 1 0 -1 2 1 -1]
[ 0 0 0 0 1 1 -2 -1 -1 0 -1 -1 0 0 0 1 1 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
11 rank 2, number 6 y3*z + x*y2 + 3*y2*z + 2*x*y + 3*y*z + x + 2*y + z + 2*x*z-1 + 2*x*y-1*z-1 + 2*y-1 + x-1 + 2*y-1*z-1 + 2*x-1*y-1 + x*y-2*z-2 + 2*y-2*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Polytope 3079
Image of polytope 3079 PALP id: 3079
grdb id: 465930
Integer points: [ 1 0 0 -2 1 -3 -1 -1 0 -1 -2 0 -1 -2 1 0 -1 0]
[ 0 1 0 2 -2 2 -2 1 -1 0 1 -2 -1 0 -1 0 1 -1]
[ 0 0 1 -1 2 -2 0 0 1 0 -1 1 0 -1 1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
23 ? x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*x-1*y + 2*y-1*z + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 3*x-1 + 2*y-2*z + 2*x-2*y*z-1 + 2*x-1*y-1 + x-3*y2*z-2 + 2*x-2*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 176 1 Lattice Minkowski decompositions of facet 176
Polytope 3080
Image of polytope 3080 PALP id: 3080
grdb id: 465994
Integer points: [ 1 0 0 -2 1 -1 -3 0 -2 -1 0 -2 -1 0 1 -1 0 -1]
[ 0 1 0 1 -2 -2 0 -2 -1 -1 -1 0 0 -1 -1 0 0 1]
[ 0 0 1 -2 2 0 -2 1 -1 0 1 -1 0 0 1 -1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
23 ? x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*y-1*z + 2*x-1*y*z-1 + 2*y-1 + 3*x-1 + 2*y-2*z + 2*x-1*z-1 + 4*x-1*y-1 + x-2*y*z-2 + 3*x-2*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Polytope 3081
Image of polytope 3081 PALP id: 3081
grdb id: 465958
Integer points: [ 1 0 0 -2 2 2 0 -1 0 1 1 -1 0 1 -1 0 1 0]
[ 0 1 0 2 -1 -2 -2 1 0 -1 0 0 -1 -2 1 0 -1 -1]
[ 0 0 1 1 -2 -3 -1 0 -1 -2 -1 0 -1 -2 1 0 -1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*x-1*y*z + x-2*y2*z + 2*x*z-1 + 4*x-1*y + x2*y-1*z-2 + 3*x*y-1*z-1 + 6*z-1 + 2*y-1 + 2*x-1 + 4*x*y-1*z-2 + 4*y-1*z-1 + x2*y-2*z-3 + 2*x*y-2*z-2 + y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3082
Image of polytope 3082 PALP id: 3082
grdb id: 466103
Integer points: [ 1 0 0 -1 0 -3 2 1 0 -1 -2 1 0 -1 1 0 -1 -2]
[ 0 1 0 0 -1 2 -3 -2 -1 0 1 -1 0 1 -2 -1 0 1]
[ 0 0 1 1 1 -1 -1 0 0 0 0 0 0 0 -1 -1 -1 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 8 2 none
Image of facet 58 1 Lattice Minkowski decompositions of facet 58
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Polytope 3083
Image of polytope 3083 PALP id: 3083
grdb id: 466081
Integer points: [ 1 0 0 1 -3 -2 -3 -1 -2 -1 0 -3 -2 -1 -1 0 1 -1]
[ 0 1 0 -2 2 2 0 1 1 0 -1 1 0 -1 1 0 -1 0]
[ 0 0 1 2 -2 -1 -2 0 -1 0 1 -2 -1 0 -1 0 1 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 177 1 none
Polytope 3084
Image of polytope 3084 PALP id: 3084
grdb id: 466029
Integer points: [ 1 0 1 0 0 -2 -2 -2 -2 -2 -1 -1 -1 0 -1 -1 -1 0]
[ 0 1 -1 0 -2 -3 1 0 -1 -2 0 -1 -2 -1 1 0 -1 0]
[ 0 0 0 1 -1 -2 2 1 0 -1 1 0 -1 0 1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 182 1 none
Polytope 3085
Image of polytope 3085 PALP id: 3085
grdb id: 465916
Integer points: [ 1 0 1 0 -1 -3 -4 -3 -2 -2 -1 -1 0 -2 -1 -1 0 1]
[ 0 1 -2 0 1 0 1 1 1 0 0 -1 -1 1 1 0 0 -1]
[ 0 0 0 1 1 -2 -2 -1 0 -1 0 -1 0 -1 0 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 136 1 none
Image of facet 14 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3086
Image of polytope 3086 PALP id: 3086
grdb id: 465975
Integer points: [ 1 0 1 -2 0 -2 -4 -1 -2 -3 0 -1 -2 -3 -1 1 0 -1]
[ 0 1 0 -1 1 1 1 1 1 1 0 0 0 0 1 0 0 0]
[ 0 0 2 -1 1 -2 -3 0 -1 -2 1 0 -1 -2 -1 1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 1 none
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 133 1 Lattice Minkowski decompositions of facet 133
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Polytope 3087
Image of polytope 3087 PALP id: 3087
grdb id: 465969
Integer points: [ 1 0 1 0 0 -2 -4 -1 0 -1 -2 -3 -1 -2 -3 1 0 -1]
[ 0 1 0 1 -1 1 -1 1 0 0 0 0 -1 -1 -1 0 0 0]
[ 0 0 2 1 1 -1 -3 0 1 0 -1 -2 0 -1 -2 1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 1 none
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 180 1 Lattice Minkowski decompositions of facet 180
Image of facet 13 1 irreducible and admissible
Polytope 3088
Image of polytope 3088 PALP id: 3088
grdb id: 465965
Integer points: [ 1 0 0 -1 -1 -1 -5 -4 -3 -2 -3 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 -1 1 -1 -3 -2 -1 0 -2 -1 0 -2 -1 0 -1 0]
[ 0 0 1 -1 1 1 1 1 1 1 0 0 0 1 1 1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 80 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 3089
Image of polytope 3089 PALP id: 3089
grdb id: 464399
Integer points: [ 1 0 0 0 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 1 -2 1 0 -1 1 0 -1 1 0 -1 1 0 0]
[ 0 0 1 0 -2 1 -2 -1 0 -1 0 1 -2 -1 0 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + 2*y*z-1 + y*z-2 + 2*z-1 + 2*x-1*y*z-1 + y-1 + 4*x-1 + 2*x-1*y-1*z + 2*x-1*y*z-2 + 4*x-1*z-1 + 2*x-1*y-1 + x-2*y*z-2 + 3*x-2*z-1 + 3*x-2*y-1 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Polytope 3090
Image of polytope 3090 PALP id: 3090
grdb id: 464068
Integer points: [ 1 0 0 0 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 0 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 0 1 0 -2 2 -2 -1 0 1 -1 0 1 -1 0 1 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + 2*x-1*z + 2*z-1 + y-1 + 4*x-1 + 2*x-1*y-1*z + x-2*y-1*z2 + 3*x-1*z-1 + 4*x-1*y-1 + 4*x-2*y-1*z + x-1*z-2 + 2*x-1*y-1*z-1 + 6*x-2*y-1 + 4*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3091
Image of polytope 3091 PALP id: 3091
grdb id: 464388
Integer points: [ 1 0 0 0 -1 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 2 -2 -1 2 0 1 -1 0 1 0 1 2 -1 0 1]
[ 0 0 1 1 -2 -2 1 -1 0 -1 0 1 -1 0 1 -1 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 y2*z + 2*y*z + 2*x-1*y2*z + x + y + z + 2*x-1*y*z + x-2*y2*z + 4*x-1*y + 3*x-1 + 3*x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 56 1 Lattice Minkowski decompositions of facet 56
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3092
Image of polytope 3092 PALP id: 3092
grdb id: 464421
Integer points: [ 1 0 0 0 -2 0 -2 -2 -2 -1 -1 -1 0 -1 -1 -1 0 0]
[ 0 1 0 0 1 -2 -2 -1 0 -2 -1 0 -1 -1 0 1 -1 0]
[ 0 0 1 -1 0 -1 -3 -2 -1 -2 -1 0 0 -2 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + 2*x-1*y + z-1 + 2*y-1 + 2*x-1 + x-2*y + 2*y-1*z-1 + 4*x-1*z-1 + y-2*z-1 + 4*x-1*y-1*z-1 + 3*x-2*z-1 + 2*x-1*y-1*z-2 + 2*x-1*y-2*z-2 + 3*x-2*y-1*z-2 + x-2*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Polytope 3093
Image of polytope 3093 PALP id: 3093
grdb id: 464170
Integer points: [ 1 0 0 0 -2 -1 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 -1 2 3 0 1 2 0 1 2 -1 0 1 0 1]
[ 0 0 0 1 -2 2 2 -1 0 1 -1 0 1 -1 0 1 0 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x-1*y2*z2 + x-2*y3*z2 + 2*y*z + 2*x-1*y2*z + x + y + z + 4*x-1*y*z + 4*x-2*y2*z + 4*x-1*y + y-1 + 5*x-1 + 6*x-2*y + 2*x-1*z-1 + 2*x-1*y-1*z-1 + 4*x-2*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 3094
Image of polytope 3094 PALP id: 3094
grdb id: 464210
Integer points: [ 1 0 0 -2 -1 -3 -3 -2 -3 -2 -1 -2 -1 -1 -1 0 -1 0]
[ 0 1 0 1 -2 0 -2 -2 -1 -1 -1 0 0 1 -1 -1 0 0]
[ 0 0 1 -2 2 -2 0 1 -1 0 1 -1 0 -1 0 1 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + 2*y-1*z + 2*x-1*y*z-1 + 5*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 2*x-1*y-1 + x-2*y*z-2 + 5*x-2*z-1 + 5*x-2*y-1 + 2*x-2*y-2*z + x-3*z-2 + 2*x-3*y-1*z-1 + x-3*y-2
60 rank 2, number 18 x + y + z + 2*y-1*z + 2*x-1*y*z-1 + 3*x-1 + 2*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 2*x-1*y-1 + x-2*y*z-2 + 3*x-2*z-1 + 4*x-2*y-1 + 2*x-2*y-2*z + x-3*z-2 + 2*x-3*y-1*z-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 203 1 Lattice Minkowski decompositions of facet 203
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 3095
Image of polytope 3095 PALP id: 3095
grdb id: 464394
Integer points: [ 1 0 0 -2 2 2 0 0 0 1 1 1 -1 -1 0 0 1 -1]
[ 0 1 0 1 -2 -3 -3 -1 -2 -1 -2 -3 0 -1 0 -1 -1 1]
[ 0 0 1 0 -1 -2 -2 0 -1 0 -1 -2 0 -1 0 -1 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Polytope 3096
Image of polytope 3096 PALP id: 3096
grdb id: 464237
Integer points: [ 1 0 0 -1 -2 -3 -3 -1 -2 -1 -3 -2 -1 -2 -1 0 -1 0]
[ 0 1 0 -2 2 0 2 1 1 0 1 0 -1 -1 1 0 0 -1]
[ 0 0 1 0 -1 -2 -2 0 -1 0 -2 -1 0 -1 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
60 rank 2, number 18 x + y + z + 2*x-1*y + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + x-1 + 2*x-1*z-1 + 2*x-2*y*z-1 + 2*x-1*y-1 + x-3*y2*z-2 + 4*x-2*z-1 + x-1*y-2 + 2*x-3*y*z-2 + 2*x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 175 1 Lattice Minkowski decompositions of facet 175
Polytope 3097
Image of polytope 3097 PALP id: 3097
grdb id: 463419
Integer points: [ 1 0 0 0 -2 -3 -3 -3 -3 -2 -2 -2 -1 -1 -1 -1 -1 0]
[ 0 1 0 -1 2 2 -1 1 0 1 0 -1 1 0 -1 1 0 0]
[ 0 0 1 1 -1 -2 -2 -2 -2 -1 -1 -1 0 0 0 -1 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 14 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 174 1 Lattice Minkowski decompositions of facet 174
Polytope 3098
Image of polytope 3098 PALP id: 3098
grdb id: 464419
Integer points: [ 1 0 0 0 -1 -1 -3 -2 -1 -2 -1 -2 -1 0 -1 0 0 0]
[ 0 1 0 -2 2 -2 0 0 0 1 1 -1 -1 -1 0 0 1 -1]
[ 0 0 1 1 -2 0 -2 -1 0 -2 -1 -1 0 1 -1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 3*x-1*y*z-1 + 2*y-1 + 3*x-1 + y-2*z + 4*x-1*z-1 + 4*x-1*y-1 + 2*x-2*y*z-2 + 3*x-2*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3099
Image of polytope 3099 PALP id: 3099
grdb id: 463651
Integer points: [ 1 0 0 0 0 -2 -3 -1 -2 0 -1 -2 0 -1 0 -1 0 -1]
[ 0 1 0 -1 -1 2 2 0 1 -1 0 1 -1 0 0 1 0 1]
[ 0 0 1 1 -2 1 1 -1 0 -1 0 1 0 1 -1 0 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + 2*x-1*y*z + x-2*y2*z + 3*x-1*y + y-1*z + 3*x-1*z + 3*x-2*y*z + x-3*y2*z + 2*z-1 + 3*y-1 + 6*x-1 + 3*x-2*y + 3*y-1*z-1 + 3*x-1*z-1 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3100
Image of polytope 3100 PALP id: 3100
grdb id: 463655
Integer points: [ 1 0 0 1 -2 -1 -2 -2 -2 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 1 0 0 0 -2 -3 -2 -1 -2 -1 0 -1 0 -1 0 -1 0]
[ 0 0 1 -1 -1 2 2 1 0 1 0 -1 0 -1 1 0 1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 66 1 none
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 9 1 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3101
Image of polytope 3101 PALP id: 3101
grdb id: 464112
Integer points: [ 1 0 0 2 -2 -2 2 -1 0 1 1 -2 -1 0 -1 0 1 -1]
[ 0 1 0 -2 1 1 -3 0 -1 -2 -1 1 0 -1 1 0 -1 1]
[ 0 0 1 -1 0 2 -2 1 0 -1 0 1 0 -1 1 0 -1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
51 rank 2, number 7 x + y + z + 2*x-1*y*z + x-2*y*z2 + 2*x*y-1 + 2*x-1*y + 4*x-1*z + 2*x-2*y*z + x2*y-2*z-1 + 2*x*y-1*z-1 + 6*y-1 + 4*x-1 + x-2*y + 4*x*y-2*z-1 + 2*y-1*z-1 + x2*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 3102
Image of polytope 3102 PALP id: 3102
grdb id: 464065
Integer points: [ 1 0 -1 0 0 -2 -4 -1 -2 -3 -1 -2 -3 0 -1 -2 0 -1]
[ 0 1 1 0 -2 0 -4 -1 -2 -3 0 -1 -2 -1 -2 -3 0 -1]
[ 0 0 0 1 -1 -1 -3 0 -1 -2 0 -1 -2 0 -1 -2 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 80 1 none
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 3103
Image of polytope 3103 PALP id: 3103
grdb id: 463542
Integer points: [ 1 0 0 -2 0 -3 -3 -2 -1 -3 -2 -1 -2 -1 -1 0 -1 0]
[ 0 1 0 0 -1 -2 -4 -3 -2 -3 -2 -1 -1 0 -2 -1 -1 0]
[ 0 0 1 -1 1 -2 -2 -1 0 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 155 1 Lattice Minkowski decompositions of facet 155
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Polytope 3104
Image of polytope 3104 PALP id: 3104
grdb id: 464122
Integer points: [ 1 0 0 -1 -2 -1 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 0 -3 -4 -3 -2 -1 -2 -1 0 -2 -1 0 -1 0]
[ 0 0 1 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 134 1 Lattice Minkowski decompositions of facet 134
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 13 1 irreducible and admissible
Polytope 3105
Image of polytope 3105 PALP id: 3105
grdb id: 463440
Integer points: [ 1 0 0 -1 -1 -2 -4 -3 -2 -3 -2 -1 -2 -1 -1 -1 0 0]
[ 0 1 0 1 -2 -1 -2 -1 0 -2 -1 0 -2 -1 0 -1 0 -1]
[ 0 0 1 0 0 -2 -3 -2 -1 -2 -1 0 -1 0 -1 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y + 2*y-1 + 2*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2 + 5*x-2*y-1*z-1 + x-2*y-1*z-2 + 3*x-2*y-2*z-1 + 3*x-3*y-1*z-2 + 3*x-3*y-2*z-2 + x-4*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 132 1 Lattice Minkowski decompositions of facet 132
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3106
Image of polytope 3106 PALP id: 3106
grdb id: 463423
Integer points: [ 1 0 0 -1 -1 -2 -4 -2 -1 -3 -2 -1 -3 -2 -1 0 -1 0]
[ 0 1 0 1 -2 1 1 1 0 1 0 -1 0 -1 1 0 0 -1]
[ 0 0 1 0 0 -2 -3 -1 0 -2 -1 0 -2 -1 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 124 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3107
Image of polytope 3107 PALP id: 3107
grdb id: 463569
Integer points: [ 1 0 0 0 -2 -1 -4 -3 -2 -3 -2 -1 -1 -2 -1 0 -1 0]
[ 0 1 -1 0 1 -2 1 0 -1 1 0 -1 0 1 0 -1 1 0]
[ 0 0 0 1 0 -2 -2 -2 -2 -1 -1 -1 0 -1 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + 2*x-1*y + y-1 + 4*x-1 + x-2*y + 2*y-1*z-1 + 4*x-1*z-1 + 2*x-2*y*z-1 + 3*x-1*y-1*z-1 + 5*x-2*z-1 + 2*x-3*y*z-1 + x-1*y-2*z-2 + 3*x-2*y-1*z-2 + 3*x-3*z-2 + x-4*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 138 1 Lattice Minkowski decompositions of facet 138
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 3108
Image of polytope 3108 PALP id: 3108
grdb id: 464417
Integer points: [ 1 0 0 0 0 -2 -2 0 -1 -1 -1 -2 -2 0 0 -1 -1 -1]
[ 0 1 0 0 -2 -1 -4 -1 -3 -2 -1 -3 -2 -1 0 -2 -1 0]
[ 0 0 1 -1 -1 0 -3 0 -2 -1 0 -2 -1 -1 0 -2 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
25 ? x + y + z + z-1 + 2*y-1 + 2*x-1 + 2*y-1*z-1 + 2*x-1*y-1 + y-2*z-1 + 4*x-1*y-1*z-1 + x-2*y-1 + 4*x-1*y-2*z-1 + 2*x-1*y-2*z-2 + 3*x-2*y-2*z-1 + 2*x-1*y-3*z-2 + 3*x-2*y-3*z-2 + x-2*y-4*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Polytope 3109
Image of polytope 3109 PALP id: 3109
grdb id: 464064
Integer points: [ 1 0 1 0 0 -2 -4 -3 -2 -1 -2 -1 0 -3 -2 -1 -1 0]
[ 0 1 -1 0 -2 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 0 0 1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + x*y-1 + 3*y-1 + 2*x-1 + 4*x-1*y-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-2*z-1 + 2*x-2*y-1 + 4*x-1*y-2*z-1 + 4*x-2*y-1*z-1 + 6*x-2*y-2*z-1 + 2*x-3*y-1*z-1 + 4*x-3*y-2*z-1 + x-4*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 3110
Image of polytope 3110 PALP id: 3110
grdb id: 464971
Integer points: [ 1 0 0 -2 -3 -1 -3 -3 -3 -3 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 0 -1 -2 -1 -2 -2 -2 -2 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 1 -1 -1 2 3 2 1 0 2 1 0 1 0 1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 64 1 none
Image of facet 148 1 none
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Polytope 3111
Image of polytope 3111 PALP id: 3111
grdb id: 464458
Integer points: [ 1 0 0 0 -1 -2 -2 -2 -1 -1 -1 0 0 -1 -1 0 0 0]
[ 0 1 0 -3 2 3 1 2 -1 0 1 -2 -1 1 2 -1 0 1]
[ 0 0 1 -2 2 2 0 1 -1 0 1 -1 0 0 1 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x-1*y2*z2 + x-2*y3*z2 + 2*y*z + 2*x-1*y2*z + x + y + z + 4*x-1*y*z + 2*x-2*y2*z + 2*x-1*y + 3*y-1 + 5*x-1 + x-2*y + 2*y-1*z-1 + 3*y-2*z-1 + 2*x-1*y-1*z-1 + y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 9 1 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3112
Image of polytope 3112 PALP id: 3112
grdb id: 463563
Integer points: [ 1 0 0 -2 -3 -1 -3 -2 -3 -2 -1 -3 -2 -1 -1 0 -1 0]
[ 0 1 0 0 -1 -2 -4 -3 -3 -2 -1 -2 -1 0 -2 -1 -1 0]
[ 0 0 1 -1 -1 2 2 2 1 1 1 0 0 0 1 1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 204 1 Lattice Minkowski decompositions of facet 204
Image of facet 14 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 3113
Image of polytope 3113 PALP id: 3113
grdb id: 463929
Integer points: [ 1 0 0 0 -2 -2 -4 -1 -2 -3 -1 0 -1 -2 -3 0 -1 -1]
[ 0 1 0 2 -2 -1 -2 1 0 -1 0 1 0 -1 -2 0 -1 -1]
[ 0 0 1 1 -1 -2 -3 0 -1 -2 -1 1 0 -1 -2 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 8 1 none
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3114
Image of polytope 3114 PALP id: 3114
grdb id: 463456
Integer points: [ 1 0 -1 0 -1 -2 -4 -2 -1 -3 -2 -1 -3 -2 0 -1 0 -1]
[ 0 1 1 0 -2 -3 -5 -3 -1 -4 -2 0 -3 -1 -1 -2 0 -1]
[ 0 0 0 1 0 -2 -3 -1 0 -2 -1 0 -2 -1 0 -1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 124 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3115
Image of polytope 3115 PALP id: 3115
grdb id: 463532
Integer points: [ 1 0 0 -1 -2 -3 -5 -3 -4 -2 -3 -4 -1 -2 -1 -2 0 -1]
[ 0 1 0 0 -1 -2 -4 -2 -3 -1 -2 -3 0 -1 -1 -2 0 -1]
[ 0 0 1 1 1 -2 -2 0 -1 0 -1 -2 0 -1 0 -1 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + x-1*z + 3*x-1 + 3*x-1*y-1 + x-2*y-1*z + 2*x-1*y-1*z-1 + 3*x-2*y-1 + 2*x-2*y-1*z-1 + 2*x-2*y-2*z-1 + 3*x-3*y-2 + 4*x-3*y-2*z-1 + x-3*y-2*z-2 + 3*x-4*y-3*z-1 + 2*x-4*y-3*z-2 + x-5*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 184 1 Lattice Minkowski decompositions of facet 184
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3116
Image of polytope 3116 PALP id: 3116
grdb id: 464073
Integer points: [ 1 0 0 -1 -1 -1 -5 -4 -3 -2 -3 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 1 -1 -1 -3 -2 -1 0 -2 -1 0 -2 -1 0 -1 0]
[ 0 0 1 -1 -1 1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + x-1*y*z-1 + 4*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + 4*x-2*z-1 + 5*x-2*y-1 + 4*x-2*y-1*z-1 + 6*x-3*y-1*z-1 + 2*x-3*y-2 + 2*x-3*y-2*z-1 + 4*x-4*y-2*z-1 + x-5*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 3117
Image of polytope 3117 PALP id: 3117
grdb id: 465588
Integer points: [ 1 0 0 -1 0 -3 -5 -4 -3 -2 -1 -3 -2 -1 -2 -1 -1 0]
[ 0 1 0 0 1 -3 -4 -3 -2 -1 0 -2 -1 0 -2 -1 -1 0]
[ 0 0 1 -1 1 1 1 1 1 1 1 0 0 0 1 1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 8 1 none
Image of facet 146 1 Lattice Minkowski decompositions of facet 146
Image of facet 9 1 irreducible and admissible
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Polytope 3118
Image of polytope 3118 PALP id: 3118
grdb id: 463650
Integer points: [ 1 0 1 0 -2 -3 -5 -3 -4 -1 -2 -3 0 -1 -1 -2 0 -1]
[ 0 1 -1 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 0 1 0 -2 -3 -1 -2 0 -1 -2 0 -1 0 -1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x*y-1 + 3*y-1 + 2*x-1 + 2*x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1 + 6*x-2*y-1*z-1 + x-3*z-2 + 3*x-3*y-1*z-1 + 3*x-3*y-1*z-2 + 3*x-4*y-1*z-2 + x-5*y-1*z-3
3 ? x + y + z + x*y-1 + 3*y-1 + 3*x-1 + 2*x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + 4*x-2*z-1 + x-2*y-1 + 6*x-2*y-1*z-1 + x-3*z-2 + 3*x-3*y-1*z-1 + 3*x-3*y-1*z-2 + 3*x-4*y-1*z-2 + x-5*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Image of facet 9 1 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3119
Image of polytope 3119 PALP id: 3119
grdb id: 465572
Integer points: [ 1 0 0 0 -3 -3 -5 -1 -2 -3 -4 -1 -2 0 -1 -2 0 -1]
[ 0 1 0 1 -2 -3 -4 0 -1 -2 -3 -1 -2 1 0 -1 0 -1]
[ 0 0 1 2 -2 -2 -3 1 0 -1 -2 0 -1 1 0 -1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? y*z2 + 2*y*z + x + y + z + 5*x-1*z + 5*x-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + 10*x-2*y-1 + 4*x-2*y-1*z-1 + 3*x-2*y-2*z-1 + 10*x-3*y-2*z-1 + x-3*y-2*z-2 + x-3*y-3*z-2 + 5*x-4*y-3*z-2 + x-5*y-4*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 146 1 Lattice Minkowski decompositions of facet 146
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3120
Image of polytope 3120 PALP id: 3120
grdb id: 463566
Integer points: [ 1 0 -1 0 -2 -3 -3 -2 -1 -3 -2 -1 -2 -1 -1 0 -1 0]
[ 0 1 1 0 -1 -4 -6 -4 -2 -5 -3 -1 -2 0 -3 -1 -2 0]
[ 0 0 0 1 -1 -2 -2 -1 0 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 179 1 none
Image of facet 14 1 none
Polytope 3121
Image of polytope 3121 PALP id: 3121
grdb id: 464036
Integer points: [ 1 0 0 0 -2 -2 -8 -6 -4 -2 -5 -3 -1 -5 -3 -1 -2 0]
[ 0 1 -1 0 0 2 4 3 2 1 2 1 0 3 2 1 1 0]
[ 0 0 0 1 -1 -1 -3 -2 -1 0 -2 -1 0 -2 -1 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 80 2 none
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 3122
Image of polytope 3122 PALP id: 3122
grdb id: 460182
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 -1 -2 -2 -1 -2 0 -1 -2 0 -1 -1 0 -1 0]
[ 0 0 1 0 -2 0 -3 0 -1 0 -1 -2 -1 -2 0 0 -1 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + x-1*y + 2*z-1 + 2*y-1 + 3*x-1 + 3*y-1*z-1 + 3*x-1*z-1 + 3*x-1*y-1 + y-1*z-2 + 6*x-1*y-1*z-1 + x-1*y-2 + 3*x-1*y-1*z-2 + 3*x-1*y-2*z-1 + 3*x-1*y-2*z-2 + x-1*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3123
Image of polytope 3123 PALP id: 3123
grdb id: 459912
Integer points: [ 1 0 0 0 -2 0 -3 -1 -2 0 -1 -2 0 -1 0 -1 0 -1]
[ 0 1 0 1 1 -2 1 -1 0 -1 0 1 0 1 -1 0 0 1]
[ 0 0 1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + y*z-1 + 2*x-1*y + 3*z-1 + 3*x-1*y*z-1 + 2*y-1 + 3*x-1 + x-2*y + 3*y-1*z-1 + 6*x-1*z-1 + 3*x-2*y*z-1 + y-2*z-1 + 3*x-1*y-1*z-1 + 3*x-2*z-1 + x-3*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3124
Image of polytope 3124 PALP id: 3124
grdb id: 460154
Integer points: [ 1 0 0 0 -1 -1 -4 -2 -3 -1 -2 -3 -1 -2 -1 -2 0 -1]
[ 0 1 -1 0 -1 2 2 0 1 0 1 2 1 2 0 1 0 1]
[ 0 0 0 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y2*z-1 + 3*x-1*y + 3*x-1*y*z-1 + 3*x-2*y2*z-1 + y-1 + 3*x-1 + 2*x-2*y + 3*x-1*z-1 + 6*x-2*y*z-1 + 3*x-3*y2*z-1 + x-1*y-1*z-1 + 3*x-2*z-1 + 3*x-3*y*z-1 + x-4*y2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Polytope 3125
Image of polytope 3125 PALP id: 3125
grdb id: 338525
Integer points: [ 1 0 0 -2 2 -3 1 -2 -2 -1 0 -1 0 1 -1 -1 0 1]
[ 0 1 0 2 -3 2 -2 1 1 0 -1 0 -1 -2 1 1 0 -1]
[ 0 0 1 -1 2 -2 2 -2 -1 0 1 -1 0 1 0 -1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
26 rank 2, number 8 x + y + x*y-1*z + z + x2*y-3*z2 + x*y-2*z2 + 2*x-1*y + 4*x*y-2*z + 4*y-1*z + x-1*y*z-1 + x-2*y2*z-1 + 6*y-1 + 6*x-1 + 4*x-1*z-1 + 4*x-2*y*z-1 + x-2*y*z-2 + x-3*y2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 10 2 Lattice Minkowski decompositions of facet 10
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 13 1 irreducible and admissible
Image of facet 134 1 Lattice Minkowski decompositions of facet 134
Polytope 3126
Image of polytope 3126 PALP id: 3126
grdb id: 338527
Integer points: [ 1 1 0 0 -1 -1 -1 -1 -1 0 -1 0 -1 0 1 -1 0 -1]
[ 0 2 0 2 -3 -1 -1 1 0 1 0 1 -1 0 1 -2 -1 -2]
[ 0 0 1 1 -1 -1 1 1 1 1 0 0 0 0 0 0 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 2 none
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 15 3 Lattice Minkowski decompositions of facet 15
Polytope 3127
Image of polytope 3127 PALP id: 3127
grdb id: 337772
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 -1 0 -2 -2 -2 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 -1 1 -2 0 -2 -1 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
35 rank 2, number 15 x + y + z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + 2*y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + x-1*z-2 + 3*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-1*z-2 + 2*x-1*y-2*z-1 + x-1*y-2*z-2
17 rank 1, V22 x + y + z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + 2*y-1*z-1 + 4*x-1*z-1 + 4*x-1*y-1 + x-1*z-2 + 6*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-1*z-2 + 2*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 135 1 Lattice Minkowski decompositions of facet 135
Polytope 3128
Image of polytope 3128 PALP id: 3128
grdb id: 338106
Integer points: [ 1 0 0 -1 1 -2 -1 -2 -1 0 -2 -1 0 -1 0 1 -1 0]
[ 0 1 0 1 -2 1 0 1 0 -1 1 0 -1 1 0 -1 1 0]
[ 0 0 1 1 0 0 -2 -2 0 0 -1 -1 -1 0 0 0 -1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + 2*z-1 + 2*x-1*y*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + 2*y-1*z-1 + 4*x-1*z-1 + 2*x-2*y*z-1 + x-1*z-2 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3129
Image of polytope 3129 PALP id: 3129
grdb id: 338179
Integer points: [ 1 0 0 -1 1 -2 1 0 0 1 -1 0 1 -1 0 1 -1 0]
[ 0 1 0 1 0 0 -2 -2 -1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 0 1 1 -2 1 0 1 1 0 1 0 -1 1 0 -1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x-1*y*z + 2*x*z-1 + 2*x*y-1 + 2*y-1*z + 2*x-1*z + x*z-2 + 2*x*y-1*z-1 + 3*z-1 + x*y-2 + 4*y-1 + 3*x-1 + y-2*z + 2*x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3130
Image of polytope 3130 PALP id: 3130
grdb id: 338225
Integer points: [ 1 0 0 0 -2 1 -2 0 -1 -2 -1 0 -1 -1 0 1 -1 0]
[ 0 1 0 0 2 -2 0 -2 1 1 0 -1 -1 1 0 -1 0 -1]
[ 0 0 1 -1 1 -2 1 -1 0 1 0 -1 0 1 0 -1 1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + 2*x-1*y*z + x-2*y2*z + 2*x-1*y + 2*x-1*z + 2*x-2*y*z + 2*x*y-1*z-1 + z-1 + 2*y-1 + 5*x-1 + x-2*z + 4*y-1*z-1 + 2*x-1*y-1 + x*y-2*z-2 + y-2*z-1
62 rank 2, number 9 x + y + z + 2*x-1*y*z + x-2*y2*z + 2*x-1*y + 2*x-1*z + 2*x-2*y*z + 2*x*y-1*z-1 + z-1 + 2*y-1 + 4*x-1 + x-2*z + 3*y-1*z-1 + 2*x-1*y-1 + x*y-2*z-2 + y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Polytope 3131
Image of polytope 3131 PALP id: 3131
grdb id: 338235
Integer points: [ 1 0 0 0 1 0 -2 -2 -1 -2 -1 0 -1 -1 0 -1 0 1]
[ 0 1 0 0 -2 -2 2 0 -1 1 0 -1 1 0 -1 1 0 -1]
[ 0 0 1 -1 0 1 -1 1 1 0 0 0 -1 1 1 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 x + y + z + 2*x*y-1 + 2*x-1*y + 2*y-1*z + 2*x-1*z + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + x*y-2 + 4*y-1 + 5*x-1 + 2*x-2*y + y-2*z + 2*x-1*y-1*z + x-2*z
20 rank 1, V16 x + y + z + 2*x*y-1 + 2*x-1*y + 2*y-1*z + 2*x-1*z + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + x*y-2 + 3*y-1 + 4*x-1 + 2*x-2*y + y-2*z + 2*x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3132
Image of polytope 3132 PALP id: 3132
grdb id: 338167
Integer points: [ 1 0 1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 1]
[ 0 1 0 0 1 1 1 -2 -1 0 -1 0 -1 0 -1 0 0 0]
[ 0 0 2 -2 1 -1 0 0 0 0 -1 -1 1 1 0 0 -1 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
51 rank 2, number 7 x*z2 + 2*x*z + y*z + x + y + 3*z + x-1*y + 2*y-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Polytope 3133
Image of polytope 3133 PALP id: 3133
grdb id: 338175
Integer points: [ 1 0 0 -1 1 1 -2 1 0 1 0 -1 1 0 0 -1 0 -1]
[ 0 1 0 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 1 -2 -1 0 -3 0 -2 -1 0 -1 0 -2 -1 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + 2*x*z-1 + x*z-2 + x*y-1*z-1 + 3*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + 2*x*y-1*z-2 + 4*y-1*z-1 + 2*x-1*y-1 + x*y-1*z-3 + 3*y-1*z-2 + 3*x-1*y-1*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3134
Image of polytope 3134 PALP id: 3134
grdb id: 338158
Integer points: [ 1 0 0 0 -1 0 -1 -3 -2 -1 -2 -1 0 -2 -1 0 -1 0]
[ 0 1 0 0 1 -2 1 1 0 -1 1 0 -1 1 0 -1 1 0]
[ 0 0 1 -1 -1 1 1 1 1 1 0 0 0 1 1 1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + x-1*y*z + 2*x-1*y + 2*y-1*z + 4*x-1*z + 2*x-2*y*z + z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + 2*x-2*y + y-2*z + 3*x-1*y-1*z + 3*x-2*z + x-3*y*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Polytope 3135
Image of polytope 3135 PALP id: 3135
grdb id: 338159
Integer points: [ 1 0 0 1 0 -1 -1 -3 -2 -1 -2 -1 -2 -1 -1 0 0 0]
[ 0 1 0 -1 1 1 -1 1 1 1 0 0 1 1 0 0 -1 0]
[ 0 0 1 -1 1 -1 1 1 1 1 1 1 0 0 0 0 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 y*z + x + y + z + 3*x-1*y*z + 3*x-1*y + 3*x-1*z + 3*x-2*y*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + 2*x-2*y + x-1*y-1*z + 2*x-2*z + x-3*y*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Polytope 3136
Image of polytope 3136 PALP id: 3136
grdb id: 338256
Integer points: [ 1 0 0 -2 -2 2 2 3 1 -1 2 0 1 -1 0 1 -1 0]
[ 0 1 0 1 0 -1 -2 -2 -1 0 -1 0 0 1 -1 -1 0 0]
[ 0 0 1 0 1 -2 -1 -2 0 1 -1 0 -1 0 0 -1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
26 rank 2, number 8 x + y + z + 2*x2*y-1*z-1 + 2*x*z-1 + 2*x*y-1 + 2*x-1*y + 2*x-1*z + x3*y-2*z-2 + x2*y-1*z-2 + x2*y-2*z-1 + 2*x*y-1*z-1 + 2*z-1 + 2*y-1 + x-1 + x-2*y + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 15 3 Lattice Minkowski decompositions of facet 15
Image of facet 71 1 Lattice Minkowski decompositions of facet 71
Polytope 3137
Image of polytope 3137 PALP id: 3137
grdb id: 338151
Integer points: [ 1 1 -1 0 1 1 -2 -2 -1 0 -1 0 -1 0 -1 0 1 0]
[ 0 2 -2 0 2 3 -1 0 1 2 0 1 0 1 -1 0 1 -1]
[ 0 0 0 1 -1 -1 -1 -1 -1 -1 0 0 -1 -1 0 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 8 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 3138
Image of polytope 3138 PALP id: 3138
grdb id: 337781
Integer points: [ 1 0 -1 0 -2 -1 -3 1 0 -2 -1 0 -2 -1 0 1 -1 0]
[ 0 1 1 0 1 -2 0 -2 -2 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 0 1 -1 0 -2 2 1 -1 0 1 -1 0 0 1 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + 2*x*y-1*z + z + x*y-2*z2 + x-1*y + 3*y-1*z + 2*y-1 + 5*x-1 + 2*y-2*z + 2*x-1*z-1 + x-2*y*z-1 + 4*x-1*y-1 + 3*x-2*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 185 1 Lattice Minkowski decompositions of facet 185
Polytope 3139
Image of polytope 3139 PALP id: 3139
grdb id: 337697
Integer points: [ 1 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 -1 0 2 2 -3 -1 0 1 -2 -1 0 1 -2 -1 0 1]
[ 0 0 0 1 -2 -1 2 2 1 0 2 1 0 -1 1 1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 158 1 Lattice Minkowski decompositions of facet 158
Polytope 3140
Image of polytope 3140 PALP id: 3140
grdb id: 337773
Integer points: [ 1 0 0 -2 1 -3 -3 1 -1 0 -1 -2 0 -1 -2 1 0 -1]
[ 0 1 0 2 -2 2 1 -3 1 -1 0 1 -2 -1 0 -1 0 1]
[ 0 0 1 -1 2 -2 -2 2 0 1 0 -1 1 0 -1 1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*x-1*y + 5*y-1*z + x*y-3*z2 + 2*x-1*y*z-1 + x-2*y2*z-1 + 8*x-1 + 4*y-2*z + 5*x-2*y*z-1 + 6*x-1*y-1 + x-3*y2*z-2 + 4*x-2*z-1 + x-3*y*z-2
31 rank 3, number 3 x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*x-1*y + 4*y-1*z + x*y-3*z2 + 2*x-1*y*z-1 + x-2*y2*z-1 + 6*x-1 + 4*y-2*z + 4*x-2*y*z-1 + 6*x-1*y-1 + x-3*y2*z-2 + 4*x-2*z-1 + x-3*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 1 3 irreducible and admissible
Image of facet 187 1 Lattice Minkowski decompositions of facet 187
Image of facet 13 1 irreducible and admissible
Polytope 3141
Image of polytope 3141 PALP id: 3141
grdb id: 338191
Integer points: [ 1 0 1 0 -2 0 -3 -3 -1 -2 -1 0 -2 -1 -1 0 -1 0]
[ 0 1 -1 0 2 -2 2 1 1 1 0 -1 0 -1 1 0 0 -1]
[ 0 0 0 1 -1 1 -2 -2 0 -1 0 1 -1 0 -1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 14 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3142
Image of polytope 3142 PALP id: 3142
grdb id: 337653
Integer points: [ 1 0 0 -1 -1 -1 0 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
[ 0 1 0 1 0 0 -3 -4 -3 -2 -1 -2 -1 -2 -1 0 -1 0]
[ 0 0 1 0 -1 1 -2 -3 -2 -1 0 -1 0 -2 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 80 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 9 1 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Polytope 3143
Image of polytope 3143 PALP id: 3143
grdb id: 338018
Integer points: [ 1 0 0 -1 1 -2 1 0 1 0 -1 0 -1 1 0 1 0 -1]
[ 0 1 0 1 -2 1 -4 -3 -3 -2 -1 -1 0 -2 -1 -1 0 1]
[ 0 0 1 1 0 0 -2 -2 -1 -1 -1 0 0 -1 -1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + 2*x*y-2*z-1 + 2*y-1*z-1 + 2*x*y-3*z-1 + 4*y-2*z-1 + 2*x-1*y-1*z-1 + x*y-4*z-2 + y-3*z-2
10 rank 1, V18 x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + x*y-2 + 3*y-1 + 2*x-1 + x-2*y + 2*x*y-2*z-1 + 2*y-1*z-1 + 2*x*y-3*z-1 + 3*y-2*z-1 + 2*x-1*y-1*z-1 + x*y-4*z-2 + y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 143 1 Lattice Minkowski decompositions of facet 143
Polytope 3144
Image of polytope 3144 PALP id: 3144
grdb id: 337513
Integer points: [ 1 0 0 0 0 -1 -2 -4 -3 -2 -3 -2 -1 -1 -2 -1 -1 0]
[ 0 1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 0 1 -1 1 -2 -2 -1 0 -2 -1 0 -1 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + 4*x-1*y-1*z-1 + 2*x-2*z-1 + 3*x-2*y-1 + 5*x-2*y-1*z-1 + x-2*y-1*z-2 + 3*x-3*y-1*z-1 + 2*x-3*y-1*z-2 + x-4*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 138 1 Lattice Minkowski decompositions of facet 138
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3145
Image of polytope 3145 PALP id: 3145
grdb id: 338162
Integer points: [ 1 0 0 0 0 -1 -2 -4 -3 -2 -3 -2 -1 -1 -2 -1 -1 0]
[ 0 1 -1 0 1 -1 1 -1 -1 -1 0 0 0 1 -1 -1 0 0]
[ 0 0 0 1 -1 1 -2 -2 -1 0 -2 -1 0 -1 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 14 1 none
Polytope 3146
Image of polytope 3146 PALP id: 3146
grdb id: 337637
Integer points: [ 1 0 -1 1 -3 2 -2 2 -1 0 1 -2 -1 0 1 -1 0 1]
[ 0 1 -1 0 0 1 1 1 1 1 1 0 0 0 1 0 0 0]
[ 0 0 0 2 -2 2 -1 3 0 1 2 -1 0 1 1 -1 0 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x2*y*z3 + x2*y*z2 + 4*x*y*z2 + 2*x*y*z + x*z2 + 2*x*z + 6*y*z + x + y + 2*z + 4*x-1*y + 3*x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + 3*x-2*z-1 + x-3*z-2
127 ? x2*y*z3 + x2*y*z2 + 4*x*y*z2 + 2*x*y*z + x*z2 + 2*x*z + 6*y*z + x + y + 5*z + 4*x-1*y + 6*x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + 4*x-2*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 137 1 Lattice Minkowski decompositions of facet 137
Polytope 3147
Image of polytope 3147 PALP id: 3147
grdb id: 337584
Integer points: [ 1 0 0 -2 -1 1 -3 -4 -3 -2 -1 -2 -1 0 -1 -1 0 1]
[ 0 1 0 1 1 -2 0 1 1 0 -1 1 0 -1 0 1 0 -1]
[ 0 0 1 -2 0 2 -2 -3 -2 -1 0 -1 0 1 -1 -1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 136 1 none
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3148
Image of polytope 3148 PALP id: 3148
grdb id: 337640
Integer points: [ 1 0 0 -2 1 -3 -4 0 -1 -2 -3 0 -1 -2 -1 1 0 -1]
[ 0 1 0 -2 2 -2 -3 1 0 -1 -2 1 0 -1 -1 1 0 -1]
[ 0 0 1 -1 2 -2 -2 2 1 0 -1 1 0 -1 0 1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
91 ? x*y2*z2 + 2*x*y*z + y*z2 + 4*y*z + x + y + z + 4*x-1*z + 7*x-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 6*x-2*y-1 + 4*x-2*y-1*z-1 + x-2*y-2*z-1 + 4*x-3*y-2*z-1 + x-3*y-2*z-2 + x-4*y-3*z-2
17 rank 1, V22 x*y2*z2 + 2*x*y*z + y*z2 + 2*y*z + x + y + z + 4*x-1*z + 2*x-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 6*x-2*y-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1 + 4*x-3*y-2*z-1 + x-3*y-2*z-2 + x-4*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 139 1 Lattice Minkowski decompositions of facet 139
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Polytope 3149
Image of polytope 3149 PALP id: 3149
grdb id: 338160
Integer points: [ 1 0 0 0 0 -1 -2 -4 -3 -2 -3 -2 -1 -1 -2 -1 -1 0]
[ 0 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 1 -1 0 -1 2 2 1 0 2 1 0 1 1 0 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
25 ? x + y + z + 2*x-1*z + z-1 + y-1 + 3*x-1 + 2*x-1*y-1*z + 2*x-2*z + x-2*y-1*z2 + 2*x-1*y-1 + 4*x-2*y-1*z + 2*x-3*y-1*z2 + x-1*y-1*z-1 + 3*x-2*y-1 + 3*x-3*y-1*z + x-4*y-1*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Polytope 3150
Image of polytope 3150 PALP id: 3150
grdb id: 338244
Integer points: [ 1 0 0 1 0 -2 -3 -4 0 -1 -2 -1 -2 -3 1 0 -1 -1]
[ 0 1 -1 0 1 1 0 1 0 0 0 1 1 1 0 0 0 1]
[ 0 0 0 2 1 -2 -2 -3 1 0 -1 0 -1 -2 1 0 -1 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x*z2 + 2*x*z + y*z + x + y + 4*z + 4*x-1*y + 2*x-1*y*z-1 + y-1 + 6*x-1 + x-1*z-1 + 6*x-2*y*z-1 + x-2*y*z-2 + 4*x-2*z-1 + 4*x-3*y*z-2 + x-3*z-2 + x-4*y*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 134 1 Lattice Minkowski decompositions of facet 134
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 13 1 irreducible and admissible
Polytope 3151
Image of polytope 3151 PALP id: 3151
grdb id: 337649
Integer points: [ 1 0 0 0 -1 -1 -3 -5 -4 -3 -2 -2 -1 -3 -2 -1 -1 0]
[ 0 1 -1 0 1 1 0 1 1 1 1 0 0 1 1 1 0 0]
[ 0 0 0 1 -1 1 -2 -3 -2 -1 0 -1 0 -2 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 80 1 none
Image of facet 93 1 Lattice Minkowski decompositions of facet 93
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3152
Image of polytope 3152 PALP id: 3152
grdb id: 335125
Integer points: [ 1 0 0 -1 1 -2 0 1 -1 0 -1 0 1 -1 0 1 0 1]
[ 0 1 0 1 -2 1 -1 -2 0 -1 0 -1 -2 1 0 -1 0 -1]
[ 0 0 1 1 0 0 -2 -2 0 0 -1 -1 -1 0 0 0 -1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + 2*x*y-1*z-1 + 2*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + 2*x*y-2*z-1 + 4*y-1*z-1 + 2*x-1*z-1 + x*y-2*z-2 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3153
Image of polytope 3153 PALP id: 3153
grdb id: 335029
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 1 1 -2 -2 0 -1 1 0 -1 -2 0 -1 0 -1]
[ 0 0 1 1 -1 1 1 -1 1 1 0 0 0 0 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 8 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Polytope 3154
Image of polytope 3154 PALP id: 3154
grdb id: 335142
Integer points: [ 1 0 0 1 1 0 -2 -2 -1 -1 0 -2 -1 0 -1 0 -1 0]
[ 0 1 0 0 -1 -2 0 -2 -2 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 1 -1 0 1 -1 1 1 1 1 0 0 0 0 0 -1 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*z-1 + x*y-1 + 2*y-1*z + 3*z-1 + 4*y-1 + 2*x-1 + y-2*z + 2*x-1*y-1*z + 3*x-1*z-1 + 5*x-1*y-1 + 2*x-1*y-2*z + x-2*z-1 + 2*x-2*y-1 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3155
Image of polytope 3155 PALP id: 3155
grdb id: 331417
Integer points: [ 1 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 1 0 0 -2 -1 -2 -2 -2 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 0 1 -1 -1 2 2 1 0 1 0 -1 1 0 1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 155 1 Lattice Minkowski decompositions of facet 155
Image of facet 14 1 none
Polytope 3156
Image of polytope 3156 PALP id: 3156
grdb id: 333577
Integer points: [ 1 0 0 -1 -1 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 -2 2 2 -2 1 0 -1 1 0 -1 1 0 0 -1]
[ 0 0 1 -1 0 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y2*z-1 + 2*x-1*y + 3*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 4*x-1 + 3*x-1*z-1 + 4*x-2*y*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + 6*x-2*z-1 + x-1*y-2 + 4*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Polytope 3157
Image of polytope 3157 PALP id: 3157
grdb id: 335307
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 0 0 -2 -1 -2 0 0 -1 -1 -1 -2 0 0 -1 -1]
[ 0 0 1 1 -2 0 2 2 -1 0 -1 0 1 1 -1 0 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + 2*y-1*z + x-1*z + x-1*y-1*z2 + 2*z-1 + 2*y-1 + 3*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + 3*x-1*z-1 + 5*x-1*y-1 + 2*x-1*y-2*z + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3158
Image of polytope 3158 PALP id: 3158
grdb id: 331666
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 2 -2 -1 -2 0 -1 -2 1 0 -1 1 -1 0 -1]
[ 0 0 1 -1 -1 0 2 2 1 1 1 0 0 0 -1 1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + x-1*y2*z-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + 2*x-1*y*z-1 + 2*y-1 + 6*x-1 + 5*x-1*y-1*z + x-1*y-2*z2 + x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-2*z + x-1*y-2
52 rank 2, number 52 x + y + z + x-1*y2*z-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + 2*x-1*y*z-1 + 2*y-1 + 5*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-2*z + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 155 1 Lattice Minkowski decompositions of facet 155
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3159
Image of polytope 3159 PALP id: 3159
grdb id: 333359
Integer points: [ 1 0 0 -1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 0 0]
[ 0 0 1 0 1 -2 2 -2 -1 0 1 -1 0 1 -1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y + y-1*z + 2*x-1*z + x-1*y-1*z2 + 2*z-1 + 3*y-1 + 4*x-1 + 4*x-1*y-1*z + 3*y-1*z-1 + 2*x-1*z-1 + 6*x-1*y-1 + y-1*z-2 + 4*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Polytope 3160
Image of polytope 3160 PALP id: 3160
grdb id: 335731
Integer points: [ 1 0 0 0 -2 2 -2 0 0 1 1 -1 -1 0 0 1 -1 -1]
[ 0 1 0 0 1 -2 0 -2 -1 -2 -1 -1 0 -1 0 -1 0 1]
[ 0 0 1 -1 0 -1 -1 -1 0 -1 0 -1 0 -1 0 -1 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + 2*x*y-1 + 2*x-1*y + x2*y-2*z-1 + 2*x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + x-2*y + 2*x*y-2*z-1 + 4*y-1*z-1 + 2*x-1*z-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3161
Image of polytope 3161 PALP id: 3161
grdb id: 335117
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 0 -1 -1 -1 0 0 0 0]
[ 0 1 -1 1 1 0 1 -2 -1 0 0 -1 0 1 -1 0 1 0]
[ 0 0 0 2 1 -2 -1 -2 -1 0 1 -2 -1 0 -1 0 1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 y*z2 + 2*y*z + x + y + 2*z + x-1*y*z + 2*x-1*y + 2*z-1 + x-1*y*z-1 + y-1 + 3*x-1 + 2*y-1*z-1 + 4*x-1*z-1 + x-1*z-2 + 3*x-1*y-1*z-1 + 2*x-1*y-1*z-2 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 3 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3162
Image of polytope 3162 PALP id: 3162
grdb id: 333329
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 -1 -1 -1]
[ 0 1 0 -1 2 0 -2 -2 -1 1 0 -1 -2 0 -1 1 0 -1]
[ 0 0 1 1 -1 1 1 -1 1 0 0 0 0 0 0 -1 -1 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 8 1 none
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 13 1 irreducible and admissible
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3163
Image of polytope 3163 PALP id: 3163
grdb id: 331116
Integer points: [ 1 0 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 1 -1 -2 -2 -2 -2 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 1 -1 -1 -1 -1 2 0 1 -1 0 1 -1 0 0 1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + 2*y-1*z + z-1 + x-1*y*z-1 + 3*y-1 + 3*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + y-1*z-1 + 3*x-1*z-1 + 6*x-1*y-1 + 3*x-1*y-2*z + 3*x-1*y-1*z-1 + 3*x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Polytope 3164
Image of polytope 3164 PALP id: 3164
grdb id: 333356
Integer points: [ 1 0 0 0 0 -2 -1 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 0 1 1 -2 2 2 -1 0 1 -1 0 1 -1 0 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + y-1*z + 2*x-1*z + x-1*y-1*z2 + y-1 + 4*x-1 + 4*x-1*y-1*z + x-2*y-1*z2 + 2*x-1*z-1 + 5*x-1*y-1 + 4*x-2*y-1*z + 2*x-1*y-1*z-1 + 6*x-2*y-1 + 4*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Polytope 3165
Image of polytope 3165 PALP id: 3165
grdb id: 333526
Integer points: [ 1 0 1 -1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 -1 1 0 0 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0]
[ 0 0 0 0 1 -1 -2 2 -1 0 1 -1 0 1 -1 0 1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + z + x*y-1 + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + z-1 + 4*y-1 + 4*x-1 + 4*x-1*y-1*z + 2*y-1*z-1 + 2*x-1*z-1 + 6*x-1*y-1 + 4*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 32 2 Lattice Minkowski decompositions of facet 32
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Polytope 3166
Image of polytope 3166 PALP id: 3166
grdb id: 333423
Integer points: [ 1 0 1 0 -1 -2 -1 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 1 2 -2 -2 -1 0 1 -1 0 1 -1 0 -1 0]
[ 0 0 0 1 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 8 1 none
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Polytope 3167
Image of polytope 3167 PALP id: 3167
grdb id: 334859
Integer points: [ 1 0 -1 0 0 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 1 0 -1 -1 0 -3 -2 -1 -2 -1 0 -2 -1 0 -1 0]
[ 0 0 0 1 -1 1 1 1 1 1 0 0 0 1 1 1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + x-1*y + y-1*z + 2*x-1*z + 2*y-1 + 3*x-1 + 4*x-1*y-1*z + x-2*z + y-1*z-1 + 3*x-1*y-1 + 2*x-1*y-2*z + 3*x-2*y-1*z + 2*x-1*y-2 + 3*x-2*y-2*z + x-2*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 56 1 Lattice Minkowski decompositions of facet 56
Polytope 3168
Image of polytope 3168 PALP id: 3168
grdb id: 333898
Integer points: [ 1 0 0 -1 -1 -2 -3 -3 -2 -3 -2 -1 -2 -1 -1 0 -1 0]
[ 0 1 0 1 -2 1 0 -2 -2 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 0 0 -1 -2 -2 -1 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + x-1*y + 2*y-1 + 3*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 5*x-2*z-1 + x-1*y-2 + 5*x-2*y-1*z-1 + x-3*z-2 + 2*x-2*y-2*z-1 + 2*x-3*y-1*z-2 + x-3*y-2*z-2
55 rank 2, number 19 x + y + z + x-1*y + 2*y-1 + 2*x-1 + 2*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + x-1*y-2 + 3*x-2*y-1*z-1 + x-3*z-2 + 2*x-2*y-2*z-1 + 2*x-3*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 190 1 Lattice Minkowski decompositions of facet 190
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 3169
Image of polytope 3169 PALP id: 3169
grdb id: 331684
Integer points: [ 1 0 0 -1 -1 -2 -3 -3 -3 -2 -1 -3 -2 -1 -2 -1 -1 0]
[ 0 1 0 1 1 -2 1 -2 -1 -1 -1 0 0 0 1 -1 0 0]
[ 0 0 1 0 -1 -1 -2 -2 -2 -1 0 -2 -1 0 -1 -1 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + x-1*y + x-1*y*z-1 + 3*x-1 + 3*x-1*z-1 + 2*x-2*y*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 5*x-2*z-1 + x-3*y*z-2 + 4*x-2*y-1*z-1 + 3*x-3*z-2 + x-2*y-2*z-1 + 3*x-3*y-1*z-2 + x-3*y-2*z-2
144 rank 3, number 12 x + y + z + x-1*y + x-1*y*z-1 + 4*x-1 + 3*x-1*z-1 + 2*x-2*y*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 6*x-2*z-1 + x-3*y*z-2 + 5*x-2*y-1*z-1 + 3*x-3*z-2 + x-2*y-2*z-1 + 3*x-3*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 155 1 Lattice Minkowski decompositions of facet 155
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3170
Image of polytope 3170 PALP id: 3170
grdb id: 333608
Integer points: [ 1 0 0 -1 0 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -1 -2 1 -3 -2 -1 0 -1 0 -2 -1 0 -1 0]
[ 0 0 1 0 -1 0 -1 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
85 rank 3, number 8 x + y + z + x-1*y + 2*y-1 + 4*x-1 + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1 + 4*x-1*y-1 + 4*x-1*y-1*z-1 + 4*x-2*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 6*x-2*y-1*z-1 + 4*x-2*y-2*z-1 + x-2*y-3*z-1
36 rank 3, number 7 x + y + z + x-1*y + 2*y-1 + 3*x-1 + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1 + 3*x-1*y-1 + 4*x-1*y-1*z-1 + 4*x-2*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 6*x-2*y-1*z-1 + 4*x-2*y-2*z-1 + x-2*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 93 1 Lattice Minkowski decompositions of facet 93
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3171
Image of polytope 3171 PALP id: 3171
grdb id: 335194
Integer points: [ 1 0 0 0 -1 -1 -3 -3 -2 -1 -3 -2 -1 -2 -1 0 -1 0]
[ 0 1 0 -1 1 -2 0 -2 0 0 -1 -1 -1 -2 0 0 -1 -1]
[ 0 0 1 1 -1 0 -2 -2 -1 0 -2 -1 0 -1 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + y-1*z + x-1*y*z-1 + 2*y-1 + 3*x-1 + 2*x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2 + 5*x-2*y-1*z-1 + x-3*z-2 + 2*x-2*y-2*z-1 + 2*x-3*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3172
Image of polytope 3172 PALP id: 3172
grdb id: 331225
Integer points: [ 1 0 0 0 -1 -1 -3 -3 -2 -1 -3 -2 -1 -3 -2 -1 0 -1]
[ 0 1 0 1 0 -1 -2 -2 -1 0 -2 -1 0 -2 -1 -1 0 -1]
[ 0 0 1 1 -1 1 -2 1 1 1 0 0 0 -1 -1 0 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? y*z + x + y + z + 3*x-1*z + 4*x-1 + x-1*y-1*z + x-1*z-1 + 3*x-1*y-1 + 3*x-2*y-1*z + 2*x-1*y-1*z-1 + 6*x-2*y-1 + 3*x-2*y-1*z-1 + x-3*y-2*z + 3*x-3*y-2 + 3*x-3*y-2*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 153 1 Lattice Minkowski decompositions of facet 153
Polytope 3173
Image of polytope 3173 PALP id: 3173
grdb id: 333422
Integer points: [ 1 0 0 1 -1 1 -2 -3 -2 -1 0 -2 -1 0 -1 0 -1 0]
[ 0 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 1 -1 1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*z-1 + x*y-1*z-1 + 3*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + 4*y-1*z-1 + 3*x-1*z-1 + 4*x-1*y-1 + 6*x-1*y-1*z-1 + x-2*z-1 + 2*x-2*y-1 + 4*x-2*y-1*z-1 + x-3*y-1*z-1
39 ? x + y + z + x*z-1 + x*y-1*z-1 + 3*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + 4*y-1*z-1 + 3*x-1*z-1 + 4*x-1*y-1 + 6*x-1*y-1*z-1 + x-2*z-1 + 2*x-2*y-1 + 4*x-2*y-1*z-1 + x-3*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 9 1 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3174
Image of polytope 3174 PALP id: 3174
grdb id: 334909
Integer points: [ 1 0 1 -1 0 0 -1 -3 -2 -1 -2 -1 -2 -1 0 -1 0 0]
[ 0 1 -1 1 0 -1 -3 -3 -2 -1 -1 0 -3 -2 -1 -1 0 -2]
[ 0 0 0 0 1 -1 -2 -2 -1 0 -1 0 -2 -1 0 -1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 14 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Polytope 3175
Image of polytope 3175 PALP id: 3175
grdb id: 335193
Integer points: [ 1 0 1 0 -2 1 0 -2 0 0 -1 -1 -1 0 0 -2 -1 -1]
[ 0 1 -1 0 1 -2 -3 -1 -2 -1 -2 -1 0 -1 0 0 0 1]
[ 0 0 0 1 0 -1 -2 -2 -1 0 -2 -1 0 -1 0 -1 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*y-1 + 2*x-1*y + 3*y-1 + 2*x-1 + x-2*y + x*y-2*z-1 + 3*y-1*z-1 + 2*x-1*z-1 + 3*y-2*z-1 + 4*x-1*y-1*z-1 + 2*x-2*z-1 + y-3*z-2 + 2*x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Polytope 3176
Image of polytope 3176 PALP id: 3176
grdb id: 331526
Integer points: [ 1 0 0 -1 -1 -3 -2 -3 -3 -2 -1 -3 -2 -1 -2 -1 -1 0]
[ 0 1 0 0 -1 -2 -1 -2 -2 -1 0 -2 -1 0 -1 -1 -1 0]
[ 0 0 1 -1 -1 -1 2 2 1 1 1 0 0 0 -1 1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
122 ? x + y + z + 2*x-1*z + 4*x-1 + 2*x-1*y-1*z + x-2*y-1*z2 + x-1*z-1 + 3*x-1*y-1 + 5*x-2*y-1*z + x-1*y-1*z-1 + 6*x-2*y-1 + x-3*y-2*z2 + 2*x-2*y-1*z-1 + 3*x-3*y-2*z + 3*x-3*y-2 + x-3*y-2*z-1
16 ? x + y + z + 2*x-1*z + 3*x-1 + 2*x-1*y-1*z + x-2*y-1*z2 + x-1*z-1 + 3*x-1*y-1 + 4*x-2*y-1*z + x-1*y-1*z-1 + 5*x-2*y-1 + x-3*y-2*z2 + 2*x-2*y-1*z-1 + 3*x-3*y-2*z + 3*x-3*y-2 + x-3*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 155 1 Lattice Minkowski decompositions of facet 155
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3177
Image of polytope 3177 PALP id: 3177
grdb id: 335683
Integer points: [ 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 -1 2 -3 -3 1 1 0 0 -1 -2 1 0 -1 -1 -2]
[ 0 0 1 -1 2 -2 -2 2 1 0 1 0 -1 1 0 -1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x-1*y2*z2 + 2*y*z + x-1*y*z2 + x + y + z + 3*x-1*y*z + 4*x-1*z + 3*y-1 + 3*x-1 + 2*y-1*z-1 + 6*x-1*y-1 + 3*y-2*z-1 + x-1*y-1*z-1 + 4*x-1*y-2*z-1 + y-3*z-2 + x-1*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 90 2 Lattice Minkowski decompositions of facet 90
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 9 2 irreducible and admissible
Polytope 3178
Image of polytope 3178 PALP id: 3178
grdb id: 335643
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 -2 2 -2 -3 1 1 0 -1 0 -1 -2 1 0 -1 -1]
[ 0 0 1 -1 2 -2 -2 2 1 0 -1 1 0 -1 1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? x-1*y2*z2 + 2*y*z + x-1*y*z2 + x + y + z + 4*x-1*y*z + 4*x-1*z + 2*y-1 + 6*x-1 + 2*y-1*z-1 + 6*x-1*y-1 + y-2*z-1 + 4*x-1*y-1*z-1 + 4*x-1*y-2*z-1 + x-1*y-2*z-2 + x-1*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 13 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 134 1 Lattice Minkowski decompositions of facet 134
Polytope 3179
Image of polytope 3179 PALP id: 3179
grdb id: 335733
Integer points: [ 1 0 0 0 0 -1 -2 -2 -1 -2 -1 -1 0 -1 0 -1 0 0]
[ 0 1 0 0 -2 2 0 2 0 1 1 -1 -1 0 0 1 1 -1]
[ 0 0 1 -1 1 -2 -1 -3 0 -2 -1 0 1 -1 0 -2 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + z-1 + 3*x-1*y*z-1 + 2*y-1 + 2*x-1 + y-2*z + 2*x-1*y*z-2 + 4*x-1*z-1 + 2*x-1*y-1 + x-2*y2*z-3 + 2*x-2*y*z-2 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3180
Image of polytope 3180 PALP id: 3180
grdb id: 332292
Integer points: [ 1 0 -1 0 -2 -1 -3 -3 -2 -3 -2 -1 -2 -1 -1 0 -1 0]
[ 0 1 1 0 0 -2 -2 -4 -3 -3 -2 -1 -1 0 -2 -1 -1 0]
[ 0 0 0 1 -1 0 -2 -2 -1 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + x-1*y + 2*y-1 + 2*x-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 3*x-2*y-1*z-1 + 3*x-2*y-2*z-1 + 2*x-2*y-3*z-1 + x-3*y-2*z-2 + 2*x-3*y-3*z-2 + x-3*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 189 1 Lattice Minkowski decompositions of facet 189
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 3181
Image of polytope 3181 PALP id: 3181
grdb id: 333581
Integer points: [ 1 0 -1 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 1 0 0 0 -3 -4 -3 -2 -1 -2 -1 0 -2 -1 -1 0]
[ 0 0 0 1 -1 1 1 1 1 1 1 0 0 0 1 1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Polytope 3182
Image of polytope 3182 PALP id: 3182
grdb id: 335518
Integer points: [ 1 0 0 0 -2 -1 -2 -4 -1 -3 -2 -1 -3 -2 -1 0 -1 0]
[ 0 1 0 -1 0 -2 -1 -2 0 -1 -1 -1 -2 -2 0 0 -1 -1]
[ 0 0 1 1 -1 0 -2 -3 0 -2 -1 0 -2 -1 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + y-1*z + 2*y-1 + 2*x-1 + 2*x-1*z-1 + 4*x-1*y-1 + 3*x-1*y-1*z-1 + x-2*z-1 + x-1*y-2 + 5*x-2*y-1*z-1 + x-2*y-1*z-2 + 3*x-2*y-2*z-1 + 2*x-3*y-1*z-2 + 3*x-3*y-2*z-2 + x-4*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3183
Image of polytope 3183 PALP id: 3183
grdb id: 334911
Integer points: [ 1 0 0 0 0 -1 -2 -4 -3 -2 -3 -2 -1 -1 -2 -1 -1 0]
[ 0 1 -1 0 -1 0 -3 -3 -2 -1 -3 -2 -1 -2 -1 0 -1 0]
[ 0 0 0 1 -1 1 -2 -2 -1 0 -2 -1 0 -1 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 14 1 none
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 3184
Image of polytope 3184 PALP id: 3184
grdb id: 334949
Integer points: [ 1 0 0 0 0 -1 -2 -4 -3 -2 -2 -1 -3 -2 -1 -1 0 -1]
[ 0 1 0 0 -1 0 -1 -3 -2 -1 -2 -1 -2 -1 0 -1 0 0]
[ 0 0 1 -1 0 1 -2 -2 -1 0 -1 0 -2 -1 0 -1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*z + z-1 + y-1 + 2*x-1 + 2*x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + 3*x-2*y-1 + 4*x-2*y-1*z-1 + x-2*y-1*z-2 + 2*x-2*y-2*z-1 + 3*x-3*y-2*z-1 + 2*x-3*y-2*z-2 + x-4*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3185
Image of polytope 3185 PALP id: 3185
grdb id: 335313
Integer points: [ 1 0 1 0 0 -2 -2 -4 -1 0 -3 -2 -1 -1 0 -3 -2 -1]
[ 0 1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 -1 0 0]
[ 0 0 0 1 -1 0 -2 -2 0 0 -1 -1 -1 0 0 -2 -1 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x*y-1 + 3*y-1 + 2*x-1 + y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + 4*x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1 + 5*x-2*y-1*z-1 + x-2*y-1*z-2 + 2*x-3*y-1*z-1 + 2*x-3*y-1*z-2 + x-4*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3186
Image of polytope 3186 PALP id: 3186
grdb id: 331214
Integer points: [ 1 0 0 -1 -2 -3 -1 -3 -3 -2 -3 -2 -1 -2 -1 -1 -1 0]
[ 0 1 0 0 -1 -2 -1 -2 -2 -1 -2 -1 0 -1 0 -1 -1 0]
[ 0 0 1 -1 -1 0 2 3 1 0 2 1 0 2 1 0 1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + 3*x-1*z + x-1*y-1*z2 + 3*x-1 + 3*x-1*y-1*z + 3*x-2*y-1*z2 + x-1*z-1 + 2*x-1*y-1 + 6*x-2*y-1*z + x-3*y-2*z3 + 4*x-2*y-1 + 3*x-3*y-2*z2 + x-2*y-1*z-1 + 3*x-3*y-2*z + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 153 1 Lattice Minkowski decompositions of facet 153
Polytope 3187
Image of polytope 3187 PALP id: 3187
grdb id: 331189
Integer points: [ 1 0 0 0 -1 -1 -3 -3 -1 -2 -1 -2 -3 -2 -3 0 -1 -1]
[ 0 1 -1 0 -1 2 0 3 0 0 1 1 1 2 2 0 0 1]
[ 0 0 0 1 -1 -1 -2 -2 0 -1 0 -1 -2 -1 -2 0 -1 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y2*z-1 + 3*x-1*y + 4*x-1*y*z-1 + 3*x-2*y2*z-1 + y-1 + 3*x-1 + x-3*y3*z-2 + 3*x-1*z-1 + 6*x-2*y*z-1 + 3*x-3*y2*z-2 + x-1*y-1*z-1 + 3*x-2*z-1 + 3*x-3*y*z-2 + x-3*z-2
55 rank 2, number 19 x + y + z + x-1*y2*z-1 + 3*x-1*y + 2*x-1*y*z-1 + 3*x-2*y2*z-1 + y-1 + 3*x-1 + x-3*y3*z-2 + 2*x-1*z-1 + 6*x-2*y*z-1 + 3*x-3*y2*z-2 + x-1*y-1*z-1 + 3*x-2*z-1 + 3*x-3*y*z-2 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Polytope 3188
Image of polytope 3188 PALP id: 3188
grdb id: 332295
Integer points: [ 1 0 0 -1 -1 -3 -3 -5 -4 -4 -3 -2 -2 -1 -2 -1 -1 0]
[ 0 1 0 1 -1 0 -2 -2 -2 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 -1 1 -2 0 -2 -1 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + x-1*y*z-1 + 3*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + 3*x-2*z-1 + 3*x-2*y-1 + 2*x-2*y-1*z-1 + x-3*z-2 + 4*x-3*y-1*z-1 + x-3*y-2 + 2*x-4*y-1*z-2 + 2*x-4*y-2*z-1 + x-5*y-2*z-2
122 ? x + y + z + x-1*y*z-1 + 4*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + 5*x-2*z-1 + 4*x-2*y-1 + 2*x-2*y-1*z-1 + x-3*z-2 + 6*x-3*y-1*z-1 + x-3*y-2 + 2*x-4*y-1*z-2 + 2*x-4*y-2*z-1 + x-5*y-2*z-2
16 ? x + y + z + x-1*y*z-1 + 3*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + 4*x-2*z-1 + 4*x-2*y-1 + 2*x-2*y-1*z-1 + x-3*z-2 + 5*x-3*y-1*z-1 + x-3*y-2 + 2*x-4*y-1*z-2 + 2*x-4*y-2*z-1 + x-5*y-2*z-2
122 ? x + y + z + x-1*y*z-1 + 4*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + 4*x-2*z-1 + 5*x-2*y-1 + 2*x-2*y-1*z-1 + x-3*z-2 + 6*x-3*y-1*z-1 + x-3*y-2 + 2*x-4*y-1*z-2 + 2*x-4*y-2*z-1 + x-5*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 205 1 Lattice Minkowski decompositions of facet 205
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 3189
Image of polytope 3189 PALP id: 3189
grdb id: 334947
Integer points: [ 1 0 0 0 -1 -2 -1 -5 -3 -4 -1 -2 -3 -1 -2 -3 0 -1]
[ 0 1 -1 0 0 -1 -2 -4 -2 -3 -1 -2 -3 0 -1 -2 0 -1]
[ 0 0 0 1 -1 0 -1 -3 -1 -2 0 -1 -2 0 -1 -2 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + y-1 + 2*x-1 + x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + x-1*y-2*z-1 + 4*x-2*y-1*z-1 + 4*x-2*y-2*z-1 + 3*x-3*y-2*z-1 + 2*x-3*y-2*z-2 + 2*x-3*y-3*z-2 + 3*x-4*y-3*z-2 + x-5*y-4*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 3190
Image of polytope 3190 PALP id: 3190
grdb id: 333554
Integer points: [ 1 0 0 0 -1 -1 -3 -5 -4 -3 -2 -3 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 0 -2 -2 -4 -3 -2 -1 -3 -2 -1 -1 0 -1 0]
[ 0 0 0 1 1 -1 -2 -3 -2 -1 0 -2 -1 0 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 64 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3191
Image of polytope 3191 PALP id: 3191
grdb id: 333580
Integer points: [ 1 0 0 0 -1 -1 -3 -5 -2 -3 -4 -1 -2 -3 -1 -2 0 -1]
[ 0 1 0 1 -1 1 -2 -3 0 -1 -2 0 -1 -2 0 -1 0 -1]
[ 0 0 1 1 0 0 -3 -4 -1 -2 -3 0 -1 -2 -1 -2 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 8 1 none
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 9 1 irreducible and admissible
Polytope 3192
Image of polytope 3192 PALP id: 3192
grdb id: 334858
Integer points: [ 1 0 0 0 -1 -1 -2 -5 -3 -4 -1 -2 -3 -1 -2 -3 0 -1]
[ 0 1 -1 0 1 -1 1 1 1 1 0 0 0 1 1 1 0 0]
[ 0 0 0 1 -1 -1 0 -3 -1 -2 0 -1 -2 0 -1 -2 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + 2*x-1*y + x-1*y*z-1 + y-1 + 3*x-1 + x-2*y + 2*x-1*z-1 + 4*x-2*y*z-1 + x-1*y-1*z-1 + 4*x-2*z-1 + 3*x-3*y*z-1 + 2*x-3*y*z-2 + 2*x-3*z-2 + 3*x-4*y*z-2 + x-5*y*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 3193
Image of polytope 3193 PALP id: 3193
grdb id: 334855
Integer points: [ 1 0 0 0 0 -1 -2 -4 -2 -3 -1 -2 -1 -2 -3 0 -1 -1]
[ 0 1 -1 0 -1 0 1 3 1 2 1 2 0 1 2 0 1 0]
[ 0 0 0 1 1 1 -2 -2 0 -1 0 -1 0 -1 -2 0 -1 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + 3*x-1*y + y-1*z + x-1*z + 2*x-1*y*z-1 + 2*x-2*y2*z-1 + y-1 + 4*x-1 + 3*x-2*y + 2*x-1*z-1 + 5*x-2*y*z-1 + 3*x-3*y2*z-1 + x-2*y*z-2 + 2*x-3*y2*z-2 + x-4*y3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3194
Image of polytope 3194 PALP id: 3194
grdb id: 328289
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 0 -1 0 -2 -2 -2 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 1 1 -2 0 -2 -1 0 -1 -2 0 -1 0 -1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + x-1*z + 2*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + 2*y-1*z-1 + 3*x-1*z-1 + 4*x-1*y-1 + x-1*z-2 + 5*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-1*z-2 + 2*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3195
Image of polytope 3195 PALP id: 3195
grdb id: 325509
Integer points: [ 1 0 0 0 -1 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 -2 2 2 -2 -1 0 1 -1 0 1 -1 0 1 0]
[ 0 0 0 1 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + x-1*y2*z-1 + 2*x-1*y + 4*x-1*y*z-1 + x-2*y2*z-1 + y-1 + 4*x-1 + 6*x-1*z-1 + 4*x-2*y*z-1 + 2*x-1*y-1 + 4*x-1*y-1*z-1 + 6*x-2*z-1 + x-1*y-2*z-1 + 4*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 13 1 irreducible and admissible
Image of facet 134 1 Lattice Minkowski decompositions of facet 134
Polytope 3196
Image of polytope 3196 PALP id: 3196
grdb id: 327940
Integer points: [ 1 0 0 0 0 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 -1 2 -1 1 0 1 0 -1 1 0 -1 0 -1]
[ 0 0 1 -1 1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + 2*x-1*y + y-1*z + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 4*x-1 + y-1*z-1 + 4*x-1*z-1 + 3*x-2*y*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Polytope 3197
Image of polytope 3197 PALP id: 3197
grdb id: 327838
Integer points: [ 1 0 0 0 -1 -1 0 -3 -2 -1 -2 -1 0 -2 -1 0 -1 0]
[ 0 1 0 0 0 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 0 1 -1 -1 1 1 1 1 1 0 0 0 1 1 1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + 2*y-1*z + x-1*z + z-1 + 2*y-1 + 2*x-1 + y-2*z + 4*x-1*y-1*z + x-1*z-1 + 4*x-1*y-1 + 3*x-1*y-2*z + 2*x-2*y-1*z + 2*x-2*y-1 + 3*x-2*y-2*z + x-3*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 3198
Image of polytope 3198 PALP id: 3198
grdb id: 327875
Integer points: [ 1 0 0 0 0 -1 -2 -4 -2 -3 -1 -2 -1 -2 -3 0 -1 -1]
[ 0 1 -1 0 -1 -1 -1 -1 -1 -1 0 0 -1 -1 -1 0 0 -1]
[ 0 0 0 1 1 1 -2 -2 0 -1 0 -1 0 -1 -2 0 -1 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + y-1*z + y-1 + 3*x-1 + x-1*y-1*z + 2*x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + 3*x-2*y-1 + 5*x-2*y-1*z-1 + x-2*y-1*z-2 + 3*x-3*y-1*z-1 + 2*x-3*y-1*z-2 + x-4*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3199
Image of polytope 3199 PALP id: 3199
grdb id: 166780
Integer points: [ 1 0 0 -1 1 1 0 -2 -2 -1 -2 -1 0 -1 0 1 -1 0]
[ 0 1 0 1 -2 -2 -1 1 1 0 1 0 -1 1 0 -1 0 -1]
[ 0 0 1 1 0 -1 1 1 -1 1 0 0 0 0 0 0 -1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 8 1 none
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3200
Image of polytope 3200 PALP id: 3200
grdb id: 166803
Integer points: [ 1 0 0 1 -1 0 0 -2 -2 -2 -1 -1 -1 -1 0 -1 0 0]
[ 0 1 0 -1 1 -1 -1 1 -1 0 0 -1 1 0 0 -1 -1 0]
[ 0 0 1 -1 1 0 -2 0 -2 -1 0 -1 0 -1 0 -2 -1 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + x-1*y*z + 2*x-1*y + x*y-1*z-1 + 2*z-1 + y-1 + 3*x-1 + x-2*y + 2*y-1*z-1 + 4*x-1*z-1 + y-1*z-2 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + 2*x-1*y-1*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3201
Image of polytope 3201 PALP id: 3201
grdb id: 166804
Integer points: [ 1 0 1 -1 1 -1 -1 0 -1 -1 -1 -1 0 0 0 0 0 1]
[ 0 1 0 1 -1 0 -1 1 1 1 0 0 0 1 0 0 -1 0]
[ 0 0 2 -1 1 -2 -1 2 1 0 -1 0 -1 1 0 1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x*z2 + y*z2 + 2*x*z + 2*y*z + x + y + x*y-1*z + 3*z + x-1*y*z + 2*x-1*y + 2*z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + 2*x-1*z-1 + x-1*z-2 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 3 Lattice Minkowski decompositions of facet 15
Polytope 3202
Image of polytope 3202 PALP id: 3202
grdb id: 166785
Integer points: [ 1 0 0 1 0 -1 0 -2 -3 -2 -1 -2 -1 0 -1 -1 0 1]
[ 0 1 0 -2 -1 0 -1 2 2 1 0 1 0 -1 1 1 0 -1]
[ 0 0 1 0 -1 -1 1 1 1 1 1 0 0 0 1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3203
Image of polytope 3203 PALP id: 3203
grdb id: 164443
Integer points: [ 1 0 0 -1 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 0 0 -1 -2 -2 -1 -2 -1 0 -2 -1 -1 0 -1]
[ 0 0 1 0 -1 1 1 1 -2 1 0 0 0 -1 -1 0 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + x-1*y + y-1*z + x-1*z + 3*y-1 + 4*x-1 + 2*x-1*y-1*z + 2*y-1*z-1 + x-1*z-1 + 5*x-1*y-1 + x-1*y-2*z + 3*x-1*y-1*z-1 + 3*x-1*y-2 + 3*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 138 1 Lattice Minkowski decompositions of facet 138
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3204
Image of polytope 3204 PALP id: 3204
grdb id: 164775
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 1 -1 1 0 -2 1 0 0 0 -1 -1 0 0 -1]
[ 0 0 1 1 1 1 -1 -2 0 0 1 0 -1 0 -1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 y*z + x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 6*x-1 + x-1*y-1*z + 4*x-1*z-1 + 4*x-1*y-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
56 rank 2, number 11 y*z + x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 135 1 Lattice Minkowski decompositions of facet 135
Polytope 3205
Image of polytope 3205 PALP id: 3205
grdb id: 166027
Integer points: [ 1 0 0 0 -1 1 0 -2 -2 -1 -2 -1 0 -1 0 -1 -1 0]
[ 0 1 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 -1 0 0]
[ 0 0 1 0 1 -1 -2 0 -2 0 -1 -1 -1 0 0 -2 -1 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + x-1*z + x*y-1*z-1 + 2*z-1 + y-1 + 2*x-1 + 3*y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + y-1*z-2 + 4*x-1*y-1*z-1 + x-2*y-1 + 2*x-1*y-1*z-2 + 2*x-2*y-1*z-1 + x-2*y-1*z-2
128 ? x + y + z + x-1*z + x*y-1*z-1 + 2*z-1 + y-1 + 2*x-1 + 4*y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + y-1*z-2 + 5*x-1*y-1*z-1 + x-2*y-1 + 2*x-1*y-1*z-2 + 2*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 3206
Image of polytope 3206 PALP id: 3206
grdb id: 165903
Integer points: [ 1 0 0 0 0 -1 -1 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 1 -2 1 -2 0 -1 1 0 -1 0 -1 0 -1]
[ 0 0 1 -1 -1 1 0 1 1 1 1 0 0 0 1 1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y*z + y*z-1 + 2*x-1*y + 3*x-1*z + x-2*y*z + z-1 + 2*y-1 + 4*x-1 + 2*x-1*y-1*z + 3*x-2*z + 3*x-1*y-1 + 3*x-2*y-1*z + x-1*y-2 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3207
Image of polytope 3207 PALP id: 3207
grdb id: 166026
Integer points: [ 1 0 0 0 1 -1 0 -2 -2 -1 -1 0 -2 -1 0 -1 0 -1]
[ 0 1 0 0 -1 1 -2 0 -2 -2 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 0 -1 1 -1 1 1 1 1 0 0 0 0 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*y-1 + 2*y-1*z + z-1 + x-1*y*z-1 + 3*y-1 + 3*x-1 + y-2*z + 2*x-1*y-1*z + 2*x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-2*z + x-2*z-1 + 2*x-2*y-1 + x-2*y-2*z
39 ? x + y + z + x*y-1 + 2*y-1*z + z-1 + x-1*y*z-1 + 4*y-1 + 3*x-1 + y-2*z + 2*x-1*y-1*z + 2*x-1*z-1 + 5*x-1*y-1 + 2*x-1*y-2*z + x-2*z-1 + 2*x-2*y-1 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3208
Image of polytope 3208 PALP id: 3208
grdb id: 166302
Integer points: [ 1 0 0 1 -1 1 -2 0 -2 -1 0 -1 0 0 -1 1 0 -1]
[ 0 1 0 -1 1 -2 1 -2 0 -1 -1 0 0 -1 0 -1 0 1]
[ 0 0 1 -1 -1 0 0 1 1 1 0 0 -1 1 1 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + 2*x*y-1 + 2*x-1*y + 2*y-1*z + 2*x-1*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + y-2*z + 2*x-1*y-1*z + x-2*z
40 rank 2, number 10 x + y + z + 2*x*y-1 + 2*x-1*y + 2*y-1*z + 2*x-1*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + x*y-2 + 4*y-1 + 4*x-1 + x-2*y + y-2*z + 2*x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 96 1 Lattice Minkowski decompositions of facet 96
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3209
Image of polytope 3209 PALP id: 3209
grdb id: 165850
Integer points: [ 1 0 0 -1 -1 -2 2 -2 1 -1 0 0 1 -1 0 -1 0 1]
[ 0 1 0 1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 0 1 0 1 1 -2 1 -2 0 -1 0 -1 0 -1 1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + 2*x*z-1 + x-1*y + 2*x-1*z + x2*y-1*z-2 + 3*x*y-1*z-1 + 2*z-1 + 3*y-1 + 3*x-1 + x-1*y-1*z + x-2*z + x*y-1*z-2 + 3*y-1*z-1 + 3*x-1*y-1 + x-2*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3210
Image of polytope 3210 PALP id: 3210
grdb id: 165592
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 1 2 -2 -1 2 1 0 1 0 -1 0 1 0 -1]
[ 0 0 1 0 -2 -2 2 2 -1 0 1 -1 0 1 -1 -1 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + 2*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + x-1*y2*z-2 + 3*x-1*y*z-1 + 4*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + x-1*y*z-2 + 2*x-1*z-1 + x-1*y-1
109 ? x + y + z + 2*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + x-1*y2*z-2 + 5*x-1*y*z-1 + 7*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + x-1*y*z-2 + 2*x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 166 1 Lattice Minkowski decompositions of facet 166
Polytope 3211
Image of polytope 3211 PALP id: 3211
grdb id: 165945
Integer points: [ 1 0 0 0 -1 0 -2 -1 -2 -2 -2 -1 -1 -1 0 -1 -1 0]
[ 0 1 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 -1 1 -1 2 2 0 1 -1 0 1 0 0 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + y-1*z + 2*x-1*z + x-1*y-1*z2 + 2*y-1 + 3*x-1 + 4*x-1*y-1*z + x-2*y-1*z2 + y-1*z-1 + x-1*z-1 + 5*x-1*y-1 + 3*x-2*y-1*z + 2*x-1*y-1*z-1 + 3*x-2*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3212
Image of polytope 3212 PALP id: 3212
grdb id: 166385
Integer points: [ 1 0 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 0 2 -2 2 -1 -2 1 0 -1 1 0 -1 1 0 -1]
[ 0 0 1 -1 -1 1 -2 2 2 -1 0 1 0 1 0 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + 2*y*z-1 + x-1*y2*z-1 + 3*x-1*y + y-1*z + 3*x-1*z + x-1*y-1*z2 + x-1*y2*z-2 + z-1 + 4*x-1*y*z-1 + 2*y-1 + 6*x-1 + y-2*z + 4*x-1*y-1*z + x-1*y-2*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Polytope 3213
Image of polytope 3213 PALP id: 3213
grdb id: 165796
Integer points: [ 1 0 0 0 2 -2 -1 -2 2 1 -1 0 1 -1 0 1 -1 0]
[ 0 1 0 -1 -1 1 -1 0 -1 -1 0 0 0 1 -1 -1 0 0]
[ 0 0 1 1 -1 0 1 1 -2 0 1 0 -1 0 0 -1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x2*y-1*z-1 + 2*x*z-1 + 2*x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x2*y-1*z-2 + 3*x*y-1*z-1 + 2*z-1 + 3*y-1 + 3*x-1 + x-2*y + x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3214
Image of polytope 3214 PALP id: 3214
grdb id: 166515
Integer points: [ 1 0 0 0 2 0 -2 -1 -2 -1 -1 -2 1 0 -1 -1 1 0]
[ 0 1 0 -1 -2 1 1 1 1 1 0 1 -1 0 1 0 -1 0]
[ 0 0 1 0 1 -1 0 -2 -2 0 0 -1 1 0 -1 -1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
51 rank 2, number 7 x + y + x2*y-2*z + 2*x*y-1*z + z + y*z-1 + 3*x*y-1 + 2*x-1*y + 3*z-1 + 3*x-1*y*z-1 + y-1 + 2*x-1 + x-2*y + x-1*y*z-2 + 2*x-1*z-1 + 2*x-2*y*z-1 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3215
Image of polytope 3215 PALP id: 3215
grdb id: 166501
Integer points: [ 1 0 0 1 1 -2 1 -2 -1 0 0 -1 1 0 1 0 -1 -1]
[ 0 1 0 0 -2 2 -2 1 0 -1 -1 0 -1 0 -1 0 1 1]
[ 0 0 1 -1 0 1 -1 0 -1 -1 0 0 -1 -1 0 0 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*x-1*y*z + x-2*y2*z + x*z-1 + 2*x*y-1 + 2*x-1*y + 2*x*y-1*z-1 + 2*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
51 rank 2, number 7 x + y + z + 2*x-1*y*z + x-2*y2*z + x*z-1 + 2*x*y-1 + 3*x-1*y + 2*x*y-1*z-1 + 2*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3216
Image of polytope 3216 PALP id: 3216
grdb id: 165868
Integer points: [ 1 0 0 1 1 -1 -2 -1 -2 0 -1 0 0 -1 -2 0 -1 -1]
[ 0 1 0 -1 -1 1 1 -1 -1 -1 -1 -1 0 0 0 0 0 1]
[ 0 0 1 0 -1 -1 0 2 2 0 1 1 -1 0 1 0 1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + x*y-1 + 2*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 3*y-1 + 4*x-1 + x-2*y + 3*x-1*y-1*z + 2*x-2*z + x-2*y-1*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3217
Image of polytope 3217 PALP id: 3217
grdb id: 165844
Integer points: [ 1 0 1 0 -1 0 -2 -1 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 2 -1 2 -1 -1 1 0 1 0 -1 1 0 0 -1]
[ 0 0 0 1 -1 1 -1 -1 -1 -1 -1 0 0 0 -1 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 3218
Image of polytope 3218 PALP id: 3218
grdb id: 166517
Integer points: [ 1 1 0 0 -1 -1 -1 -1 -1 0 -1 -1 0 0 1 -1 0 0]
[ 0 2 0 1 -2 0 0 -1 -2 1 -1 -1 0 0 1 -2 -1 -1]
[ 0 0 1 1 0 0 1 1 -2 0 -1 0 -1 0 0 -1 -1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x*y2 + 2*x*y + y*z + x + 2*y + z + x-1*z + 2*z-1 + 2*y-1 + x-1 + x-1*y-1*z + 2*y-1*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 3 Lattice Minkowski decompositions of facet 16
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3219
Image of polytope 3219 PALP id: 3219
grdb id: 165811
Integer points: [ 1 0 -1 0 0 -1 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 1 0 -1 0 -1 0 -3 -2 -1 -2 -1 0 -2 -1 -1 0]
[ 0 0 0 1 -1 -1 1 -1 -1 -1 -1 0 0 0 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*y + y-1*z + 2*y-1 + 3*x-1 + y-1*z-1 + x-1*z-1 + 4*x-1*y-1 + 3*x-1*y-1*z-1 + x-2*z-1 + 2*x-1*y-2 + 2*x-1*y-2*z-1 + 3*x-2*y-1*z-1 + 3*x-2*y-2*z-1 + x-2*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 3220
Image of polytope 3220 PALP id: 3220
grdb id: 165806
Integer points: [ 1 0 0 -1 0 1 -2 1 1 -1 0 -1 0 1 -1 0 0 1]
[ 0 1 0 1 0 -1 0 -2 -3 -1 -2 0 -1 -2 0 -1 0 -1]
[ 0 0 1 1 -1 0 1 -2 -2 0 -1 1 0 -1 0 -1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + x*y-1 + 2*x-1*z + 2*x*y-1*z-1 + z-1 + 4*y-1 + 2*x-1 + x-2*z + 2*x*y-2*z-1 + 3*y-1*z-1 + 3*x-1*y-1 + x*y-2*z-2 + 3*y-2*z-1 + x*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3221
Image of polytope 3221 PALP id: 3221
grdb id: 165882
Integer points: [ 1 0 0 0 -1 -1 0 -1 -1 -1 -1 0 -1 -1 -1 0 0 -1]
[ 0 1 0 0 1 0 -2 -1 -3 -2 -1 -1 -2 -1 0 -1 0 0]
[ 0 0 1 -1 0 1 -1 -2 -2 -1 0 0 -2 -1 0 -1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
128 ? x + y + z + x-1*y + x-1*z + z-1 + 2*y-1 + 2*x-1 + 3*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + y-2*z-1 + 4*x-1*y-1*z-1 + x-1*y-1*z-2 + 3*x-1*y-2*z-1 + 2*x-1*y-2*z-2 + x-1*y-3*z-2
59 rank 2, number 16 x + y + z + x-1*y + x-1*z + z-1 + 2*y-1 + 2*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + y-2*z-1 + 4*x-1*y-1*z-1 + x-1*y-1*z-2 + 3*x-1*y-2*z-1 + 2*x-1*y-2*z-2 + x-1*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Polytope 3222
Image of polytope 3222 PALP id: 3222
grdb id: 165904
Integer points: [ 1 0 0 0 0 -1 -1 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 -1 -1 0 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
[ 0 0 1 0 -1 1 -2 0 -3 -1 -2 0 -1 0 -1 -2 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + 2*z-1 + y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*z-2 + 4*x-1*y-1*z-1 + x-2*y-1 + 2*x-1*y-1*z-2 + 3*x-2*y-1*z-1 + 3*x-2*y-1*z-2 + x-2*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3223
Image of polytope 3223 PALP id: 3223
grdb id: 165764
Integer points: [ 1 0 0 1 -1 0 -2 1 1 1 0 -1 0 -1 1 0 0 -1]
[ 0 1 0 -1 1 0 0 -2 -3 -2 -1 0 -2 -1 -1 0 -1 0]
[ 0 0 1 0 0 -1 1 -2 -2 -1 0 1 -1 0 -1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 66 1 none
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3224
Image of polytope 3224 PALP id: 3224
grdb id: 165968
Integer points: [ 1 0 0 0 0 -1 -2 -1 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 1 1 -2 -2 -1 0 -1 0 -1 0 1 -1 0]
[ 0 0 1 -1 0 -1 0 2 3 2 1 1 0 2 1 0 1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + 2*x-1*y + 2*y-1*z + 4*x-1*z + 2*x-1*y-1*z2 + z-1 + x-1*y*z-1 + y-1 + 3*x-1 + x-2*y + 3*x-1*y-1*z + 3*x-2*z + x-1*y-2*z2 + 3*x-2*y-1*z2 + x-2*y-2*z3
17 rank 1, V22 x + y + z + 2*x-1*y + 2*y-1*z + 4*x-1*z + 2*x-1*y-1*z2 + z-1 + x-1*y*z-1 + y-1 + 4*x-1 + x-2*y + 4*x-1*y-1*z + 3*x-2*z + x-1*y-2*z2 + 3*x-2*y-1*z2 + x-2*y-2*z3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3225
Image of polytope 3225 PALP id: 3225
grdb id: 165835
Integer points: [ 1 0 0 -1 0 -2 1 0 -3 -1 -2 0 -1 -2 -1 1 0 -1]
[ 0 1 -1 1 0 1 -2 -2 1 -1 0 -1 0 1 0 -1 0 1]
[ 0 0 0 0 1 -2 2 1 -2 0 -1 1 0 -1 -1 1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + 2*x*y-1*z + z + x*y-2*z2 + x-1*y + 3*y-1*z + 2*x-1*y*z-1 + y-1 + 4*x-1 + y-2*z + 2*x-1*z-1 + 2*x-2*y*z-1 + 3*x-1*y-1 + x-2*y*z-2 + 3*x-2*z-1 + x-3*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3226
Image of polytope 3226 PALP id: 3226
grdb id: 166025
Integer points: [ 1 0 0 -1 1 0 -1 -1 -3 -2 -2 -1 -2 -1 0 -1 0 1]
[ 0 1 0 2 -2 -1 0 0 2 1 2 1 1 0 -1 1 0 -1]
[ 0 0 1 -1 0 1 -1 1 -1 -1 -1 -1 0 0 0 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y2*z-1 + 2*x*y-1 + 3*x-1*y + y-1*z + x-1*z + 2*x-1*y*z-1 + 2*x-2*y2*z-1 + x*y-2 + 3*y-1 + 3*x-1 + 2*x-2*y + x-1*z-1 + 2*x-2*y*z-1 + x-3*y2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 65 1 Lattice Minkowski decompositions of facet 65
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3227
Image of polytope 3227 PALP id: 3227
grdb id: 166483
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 0 -1 -1 0 0 0 0]
[ 0 1 1 -1 -1 1 1 -2 -2 0 -1 0 0 -1 1 0 -1 0]
[ 0 0 2 0 -2 1 0 -2 -3 0 -1 1 -1 -2 1 0 -1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 y*z2 + 2*y*z + x + y + 2*z + x-1*y*z + x-1*y + 2*z-1 + y-1 + 3*x-1 + y-1*z-1 + 3*x-1*z-1 + y-1*z-2 + 3*x-1*y-1*z-1 + 3*x-1*y-1*z-2 + x-1*y-2*z-2 + x-1*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 3228
Image of polytope 3228 PALP id: 3228
grdb id: 166494
Integer points: [ 1 0 0 0 1 -2 1 1 0 1 1 1 0 0 -1 0 -1 -1]
[ 0 1 0 0 0 2 -2 -3 -2 -1 -2 -1 -1 0 1 -1 0 1]
[ 0 0 1 -1 1 -1 0 1 1 0 1 1 0 0 -1 1 0 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x*z + x + y + 3*x*y-1*z + z + 2*x*y-1 + 2*x-1*y + 3*x*y-2*z + 2*y-1*z + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + x*y-2 + 3*y-1 + 2*x-1 + x*y-3*z + y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3229
Image of polytope 3229 PALP id: 3229
grdb id: 165869
Integer points: [ 1 0 0 0 1 -1 -1 -2 -2 0 -1 -2 0 -1 -1 0 -1 0]
[ 0 1 0 1 0 0 -2 -1 -3 0 -1 -2 -1 -2 0 0 -1 -1]
[ 0 0 1 -1 -1 -1 2 0 2 -1 0 1 0 1 0 0 1 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*z-1 + y*z-1 + 2*y-1*z + 2*z-1 + 3*y-1 + 2*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + x-1*z-1 + 4*x-1*y-1 + 3*x-1*y-2*z + x-2*y-1 + 2*x-2*y-2*z + x-2*y-3*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3230
Image of polytope 3230 PALP id: 3230
grdb id: 164444
Integer points: [ 1 0 -1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 1 0 -1 0 -1 -3 -4 -2 -3 -1 -2 0 -1 -1 -2 0]
[ 0 0 0 1 -1 1 1 -2 -2 0 -1 0 -1 0 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 136 1 none
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3231
Image of polytope 3231 PALP id: 3231
grdb id: 165809
Integer points: [ 1 0 0 0 0 -1 -2 -1 -4 -3 -2 -2 -1 -3 -2 -1 -1 0]
[ 0 1 -1 0 -1 0 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 0 0 1 -1 -1 -1 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
107 rank 3, number 11 x + y + z + y-1 + 2*x-1 + y-1*z-1 + x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + x-2*z-1 + 2*x-2*y-1 + x-1*y-2*z-1 + 4*x-2*y-1*z-1 + 3*x-2*y-2*z-1 + 2*x-3*y-1*z-1 + 3*x-3*y-2*z-1 + x-4*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 3232
Image of polytope 3232 PALP id: 3232
grdb id: 161596
Integer points: [ 1 0 0 -1 0 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 -1 1 -1 -1 -1 0 0 0 -1 -1 0 0 -1 -1]
[ 0 0 1 1 1 0 -2 1 -2 1 0 -1 0 -1 0 -1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + x-1*y + y-1*z + 2*x-1*z + 2*z-1 + 3*y-1 + 4*x-1 + x-1*y-1*z + 3*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + y-1*z-2 + 3*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 3233
Image of polytope 3233 PALP id: 3233
grdb id: 161602
Integer points: [ 1 0 0 0 0 -1 -1 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 1 -2 1 -2 -1 0 -1 0 -1 0 1 -1 0]
[ 0 0 1 -1 -1 0 0 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + y*z-1 + x-1*y + z-1 + 2*x-1*y*z-1 + 2*y-1 + 2*x-1 + 4*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2 + 3*x-2*y-1*z-1 + x-2*y-2*z-1
146 ? x + y + z + y*z-1 + x-1*y + z-1 + 2*x-1*y*z-1 + 2*y-1 + 4*x-1 + 4*x-1*z-1 + x-2*y*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2 + 3*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3234
Image of polytope 3234 PALP id: 3234
grdb id: 163370
Integer points: [ 1 0 0 0 0 -1 0 -2 -2 -1 -2 -1 0 -1 -1 0 -1 0]
[ 0 1 0 1 -1 1 -1 1 1 0 1 0 -1 0 1 0 1 0]
[ 0 0 1 -1 1 1 -1 1 -1 -1 0 0 0 1 -1 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + y*z-1 + 3*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + 2*z-1 + 2*x-1*y*z-1 + 2*y-1 + 4*x-1 + 2*x-2*y + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3235
Image of polytope 3235 PALP id: 3235
grdb id: 163475
Integer points: [ 1 0 0 1 -1 0 0 -2 -2 -1 -2 -1 -1 0 -1 0 -1 0]
[ 0 1 0 -1 1 0 -2 0 -2 -1 -1 0 -2 -1 -1 0 0 -1]
[ 0 0 1 0 0 -1 -1 -1 -1 0 -1 0 -1 0 -1 0 -1 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*y-1 + x-1*y + z-1 + 2*y-1 + 2*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + y-2*z-1 + 4*x-1*y-1*z-1 + x-2*z-1 + 2*x-1*y-2*z-1 + 2*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Polytope 3236
Image of polytope 3236 PALP id: 3236
grdb id: 161572
Integer points: [ 1 0 0 1 1 -2 1 0 -2 0 -1 -1 1 0 -1 0 -1 0]
[ 0 1 0 0 -1 0 -1 -1 -1 -1 -1 0 -1 -1 -1 0 0 0]
[ 0 0 1 -1 0 1 -2 -2 0 0 0 1 -1 -1 -1 0 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*z-1 + x*y-1 + 2*x-1*z + 2*x*y-1*z-1 + 2*z-1 + 3*y-1 + 2*x-1 + x-2*z + x*y-1*z-2 + 4*y-1*z-1 + 3*x-1*y-1 + y-1*z-2 + 2*x-1*y-1*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3237
Image of polytope 3237 PALP id: 3237
grdb id: 161994
Integer points: [ 1 0 1 -1 0 0 -2 0 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 1 0 -1 1 -2 -2 -1 0 -1 0 -2 -1 0 -1 0]
[ 0 0 0 0 1 -1 -1 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*y-1 + x-1*y + 2*y-1 + 3*x-1 + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + y-2*z-1 + 4*x-1*y-1*z-1 + 3*x-2*z-1 + 2*x-1*y-2*z-1 + 3*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3238
Image of polytope 3238 PALP id: 3238
grdb id: 163386
Integer points: [ 1 0 0 -1 -2 2 0 0 0 -1 0 -1 0 -1 1 0 1 1]
[ 0 1 0 1 1 -1 1 -1 -1 0 -1 0 0 1 -1 0 -1 0]
[ 0 0 1 1 1 -1 -1 1 -1 0 0 1 -1 0 -1 0 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
51 rank 2, number 7 x + y + z + x-1*y*z + x2*y-1*z-1 + 2*x*z-1 + y*z-1 + 2*x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + 2*x*y-1*z-1 + 2*z-1 + 2*y-1 + 2*x-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 4 Lattice Minkowski decompositions of facet 16
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Polytope 3239
Image of polytope 3239 PALP id: 3239
grdb id: 160242
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 1 -1 -2 -1 -2 -2 -1 0 -1 0 0 -1 -1 0]
[ 0 0 1 -1 0 -1 0 2 2 1 0 -1 1 0 1 0 1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + x-1*y*z-1 + 2*y-1 + 4*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
146 ? x + y + z + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + x-1*y*z-1 + 2*y-1 + 5*x-1 + 5*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 5*x-1*y-1 + 2*x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 164 1 Lattice Minkowski decompositions of facet 164
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 3240
Image of polytope 3240 PALP id: 3240
grdb id: 157292
Integer points: [ 1 0 0 0 -1 -1 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 1 -1 -2 2 -2 1 0 -1 1 0 -1 0 0 -1]
[ 0 0 1 1 -1 -1 0 -1 -1 -1 -1 -1 0 0 0 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + 2*x-1*y + y-1*z + x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 5*x-1 + 2*x-1*z-1 + 4*x-2*y*z-1 + 4*x-1*y-1 + x-1*y-1*z-1 + 6*x-2*z-1 + x-1*y-2 + 4*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Polytope 3241
Image of polytope 3241 PALP id: 3241
grdb id: 163424
Integer points: [ 1 0 0 1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 -1 1 1 -1 -1 1 1 0 0 0 -1 0 0 -1 -1]
[ 0 0 1 0 -1 0 0 2 -2 -1 -1 0 1 1 -1 0 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + y*z-1 + x*y-1 + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + 2*z-1 + 2*x-1*y*z-1 + 2*y-1 + 4*x-1 + 2*x-1*y-1*z + x-1*y*z-2 + 2*x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Polytope 3242
Image of polytope 3242 PALP id: 3242
grdb id: 157304
Integer points: [ 1 0 -1 0 -1 0 -2 -1 -2 -2 -2 -2 -1 -1 -1 -1 0 0]
[ 0 1 1 0 0 -1 1 -2 -3 -2 -1 0 -2 -1 0 -1 -1 0]
[ 0 0 0 1 -1 1 -1 -1 -1 -1 -1 -1 0 0 0 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 8 1 none
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Polytope 3243
Image of polytope 3243 PALP id: 3243
grdb id: 156909
Integer points: [ 1 0 0 -1 -1 -1 -2 -1 -2 -2 -2 -2 -1 -1 -1 -1 0 0]
[ 0 1 0 1 1 -2 1 -2 -3 -2 -1 0 -1 0 -1 0 -1 0]
[ 0 0 1 0 -1 0 -1 -1 -1 -1 -1 -1 0 0 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*y + x-1*y*z-1 + 2*y-1 + 3*x-1 + 3*x-1*z-1 + x-2*y*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + 4*x-2*z-1 + x-1*y-2 + x-1*y-2*z-1 + 6*x-2*y-1*z-1 + 4*x-2*y-2*z-1 + x-2*y-3*z-1
85 rank 3, number 8 x + y + z + x-1*y + x-1*y*z-1 + 2*y-1 + 4*x-1 + 3*x-1*z-1 + x-2*y*z-1 + 4*x-1*y-1 + 3*x-1*y-1*z-1 + 4*x-2*z-1 + x-1*y-2 + x-1*y-2*z-1 + 6*x-2*y-1*z-1 + 4*x-2*y-2*z-1 + x-2*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 93 1 Lattice Minkowski decompositions of facet 93
Polytope 3244
Image of polytope 3244 PALP id: 3244
grdb id: 161417
Integer points: [ 1 0 0 -1 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 1 0 -2 -1 -3 -2 -1 -2 -1 0 0 -1 -1 0]
[ 0 0 1 0 -1 1 1 -1 1 1 1 0 0 0 -1 1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3245
Image of polytope 3245 PALP id: 3245
grdb id: 161494
Integer points: [ 1 0 0 0 -1 0 -2 -1 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 -1 0 -2 -3 -1 -2 0 -1 0 -1 -2 0 -1]
[ 0 0 1 -1 0 1 1 0 1 1 1 0 0 1 1 1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
85 rank 3, number 8 x + y + z + x-1*y + y-1*z + 2*x-1*z + z-1 + 2*y-1 + 3*x-1 + 4*x-1*y-1*z + x-2*z + 4*x-1*y-1 + 2*x-1*y-2*z + 3*x-2*y-1*z + x-1*y-2 + 3*x-2*y-2*z + x-2*y-3*z
38 ? x + y + z + x-1*y + y-1*z + 2*x-1*z + z-1 + 2*y-1 + 2*x-1 + 4*x-1*y-1*z + x-2*z + 2*x-1*y-1 + 2*x-1*y-2*z + 3*x-2*y-1*z + x-1*y-2 + 3*x-2*y-2*z + x-2*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3246
Image of polytope 3246 PALP id: 3246
grdb id: 163474
Integer points: [ 1 0 0 0 0 -1 -1 -1 -3 -2 -1 -2 -1 0 -2 -1 0 0]
[ 0 1 0 1 -1 0 0 -2 -2 -1 -1 -2 0 0 -1 -1 -1 0]
[ 0 0 1 -1 1 0 -2 0 -2 -1 0 -1 -1 0 -2 -1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + y*z-1 + y-1*z + 2*z-1 + 2*y-1 + x-1 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*z-2 + 4*x-1*y-1*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + 2*x-2*y-1*z-2 + 2*x-2*y-2*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Polytope 3247
Image of polytope 3247 PALP id: 3247
grdb id: 161995
Integer points: [ 1 0 0 0 0 -1 0 -1 -3 -2 -1 -2 -1 -2 -1 0 -1 0]
[ 0 1 0 0 -1 1 -1 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
[ 0 0 1 -1 1 0 -1 -2 -2 -1 0 -1 0 -2 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y + y-1*z + z-1 + 2*y-1 + 3*x-1 + y-1*z-1 + 3*x-1*z-1 + 3*x-1*y-1 + 4*x-1*y-1*z-1 + 2*x-2*z-1 + x-1*y-1*z-2 + 3*x-2*y-1*z-1 + 2*x-2*y-1*z-2 + x-3*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3248
Image of polytope 3248 PALP id: 3248
grdb id: 161991
Integer points: [ 1 0 0 0 0 0 -1 -1 -3 -2 -1 0 -1 0 -2 -1 -2 -1]
[ 0 1 0 0 -1 -1 1 -1 -1 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 -1 1 -1 -1 1 -1 0 0 0 0 0 -1 -1 -1 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + y-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + 3*x-1*z-1 + 4*x-1*y-1 + 3*x-1*y-1*z-1 + 2*x-2*z-1 + 2*x-2*y-1 + 3*x-2*y-1*z-1 + x-3*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3249
Image of polytope 3249 PALP id: 3249
grdb id: 163471
Integer points: [ 1 0 0 1 -1 0 -1 -1 -3 -2 -1 -2 0 -1 0 -2 -1 0]
[ 0 1 0 -1 1 0 -1 -1 -1 -1 0 0 -1 -1 0 -1 0 -1]
[ 0 0 1 0 0 -1 0 -2 -2 -1 0 -1 0 -1 0 -2 -1 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*y-1 + x-1*y + z-1 + 2*y-1 + 2*x-1 + 2*y-1*z-1 + 3*x-1*z-1 + x-1*y-1 + 4*x-1*y-1*z-1 + 2*x-2*z-1 + x-1*y-1*z-2 + 2*x-2*y-1*z-1 + 2*x-2*y-1*z-2 + x-3*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3250
Image of polytope 3250 PALP id: 3250
grdb id: 163422
Integer points: [ 1 0 0 1 -1 0 -1 -1 -3 -2 -2 -1 -2 -1 0 -1 0 0]
[ 0 1 0 0 0 -1 0 -2 -2 -1 -1 0 -2 -1 0 -1 0 -1]
[ 0 0 1 -1 1 1 -1 1 1 0 1 0 1 0 -1 1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*z-1 + y-1*z + x-1*z + 2*z-1 + 2*y-1 + 2*x-1 + 3*x-1*y-1*z + x-1*z-1 + 4*x-1*y-1 + x-1*y-2*z + 2*x-2*y-1*z + 2*x-2*y-1 + 2*x-2*y-2*z + x-3*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3251
Image of polytope 3251 PALP id: 3251
grdb id: 161989
Integer points: [ 1 0 0 1 0 -1 -2 0 -3 -1 -2 0 -1 0 -1 -2 0 -1]
[ 0 1 0 -1 0 1 1 -2 1 -1 0 -1 0 -1 0 1 0 1]
[ 0 0 1 0 -1 -1 0 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + x*y-1 + 2*x-1*y + z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-2*y + 2*y-1*z-1 + 4*x-1*z-1 + 2*x-2*y*z-1 + y-2*z-1 + 3*x-1*y-1*z-1 + 3*x-2*z-1 + x-3*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3252
Image of polytope 3252 PALP id: 3252
grdb id: 161408
Integer points: [ 1 0 0 1 0 -1 0 -2 -3 -2 -1 0 -1 0 -2 -1 -1 0]
[ 0 1 0 0 -1 -1 -1 0 -1 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 -1 1 1 -1 -1 -1 0 0 0 0 0 -1 -1 -1 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*z-1 + y-1*z + 3*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + 3*x-1*z-1 + 4*x-1*y-1 + 3*x-1*y-1*z-1 + x-2*z-1 + 2*x-2*y-1 + 3*x-2*y-1*z-1 + x-3*y-1*z-1
39 ? x + y + z + x*z-1 + y-1*z + 3*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + 3*x-1*z-1 + 4*x-1*y-1 + 3*x-1*y-1*z-1 + x-2*z-1 + 2*x-2*y-1 + 3*x-2*y-1*z-1 + x-3*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 3253
Image of polytope 3253 PALP id: 3253
grdb id: 163000
Integer points: [ 1 0 0 1 1 1 -2 -2 -3 -1 0 -2 -1 0 -1 0 -1 0]
[ 0 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 1 -1 0 -1 -1 0 -1 0 0 -1 -1 -1 0 0 -1 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + x*z-1 + x*y-1 + x*y-1*z-1 + 3*z-1 + 3*y-1 + x-1 + 4*y-1*z-1 + 3*x-1*z-1 + 3*x-1*y-1 + 6*x-1*y-1*z-1 + x-2*z-1 + x-2*y-1 + 4*x-2*y-1*z-1 + x-3*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 90 2 Lattice Minkowski decompositions of facet 90
Polytope 3254
Image of polytope 3254 PALP id: 3254
grdb id: 160747
Integer points: [ 1 0 1 -1 0 -1 -1 -3 -3 -2 -3 -2 -1 -2 -1 0 -1 0]
[ 0 1 -1 1 0 1 -1 1 -1 -1 0 0 0 1 -1 -1 0 0]
[ 0 0 0 0 1 -1 0 -2 -2 -1 -2 -1 0 -1 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*y-1 + x-1*y + x-1*y*z-1 + 2*y-1 + 3*x-1 + 3*x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + 4*x-2*z-1 + x-3*y*z-2 + 2*x-2*y-1*z-1 + 2*x-3*z-2 + x-3*y-1*z-2
146 ? x + y + z + x*y-1 + x-1*y + x-1*y*z-1 + 2*y-1 + 4*x-1 + 3*x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1 + 2*x-1*y-1*z-1 + 5*x-2*z-1 + x-3*y*z-2 + 2*x-2*y-1*z-1 + 2*x-3*z-2 + x-3*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3255
Image of polytope 3255 PALP id: 3255
grdb id: 161488
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 2 -2 0 0 -2 -3 -1 -2 1 0 -1 1 -1 0 -1]
[ 0 0 1 -1 1 -1 1 0 1 1 1 0 0 0 -1 1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y2*z-1 + 2*x-1*y + 2*y-1*z + x-1*z + 2*x-1*y*z-1 + 2*y-1 + 5*x-1 + y-2*z + 3*x-1*y-1*z + x-1*z-1 + 4*x-1*y-1 + 3*x-1*y-2*z + x-1*y-2 + x-1*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3256
Image of polytope 3256 PALP id: 3256
grdb id: 160162
Integer points: [ 1 0 0 0 0 -2 -2 -3 -3 -1 -2 -1 -3 -2 -1 -1 0 -1]
[ 0 1 -1 0 -1 2 -1 0 2 1 1 0 1 0 -1 1 0 0]
[ 0 0 0 1 1 -1 -1 -2 -2 0 -1 0 -2 -1 0 -1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
3 ? x + y + z + 2*x-1*y + y-1*z + 2*x-1*y*z-1 + x-2*y2*z-1 + y-1 + 5*x-1 + 2*x-1*z-1 + 5*x-2*y*z-1 + 2*x-1*y-1 + x-3*y2*z-2 + 5*x-2*z-1 + 2*x-3*y*z-2 + x-2*y-1*z-1 + x-3*z-2
36 rank 3, number 7 x + y + z + 2*x-1*y + y-1*z + 2*x-1*y*z-1 + x-2*y2*z-1 + y-1 + 4*x-1 + 2*x-1*z-1 + 4*x-2*y*z-1 + 2*x-1*y-1 + x-3*y2*z-2 + 4*x-2*z-1 + 2*x-3*y*z-2 + x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 164 1 Lattice Minkowski decompositions of facet 164
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 3257
Image of polytope 3257 PALP id: 3257
grdb id: 157310
Integer points: [ 1 0 0 0 -1 0 -2 -2 -4 -3 -2 -1 -3 -2 -1 -1 -1 0]
[ 0 1 -1 0 1 -1 1 -1 -1 -1 -1 -1 0 0 0 -1 0 0]
[ 0 0 0 1 0 1 -1 -2 -3 -2 -1 0 -2 -1 0 -1 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y + y-1*z + y-1 + 4*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 4*x-1*y-1 + 2*x-1*y-1*z-1 + 5*x-2*z-1 + 6*x-2*y-1*z-1 + x-2*y-1*z-2 + 2*x-3*z-2 + 4*x-3*y-1*z-2 + x-4*y-1*z-3
36 rank 3, number 7 x + y + z + x-1*y + y-1*z + y-1 + 4*x-1 + 3*x-1*z-1 + x-2*y*z-1 + 4*x-1*y-1 + 2*x-1*y-1*z-1 + 5*x-2*z-1 + 6*x-2*y-1*z-1 + x-2*y-1*z-2 + 2*x-3*z-2 + 4*x-3*y-1*z-2 + x-4*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 3258
Image of polytope 3258 PALP id: 3258
grdb id: 162003
Integer points: [ 1 0 0 0 -1 0 -1 -2 -4 -2 -3 -1 -2 -3 -1 -2 0 -1]
[ 0 1 -1 0 -1 1 1 -1 1 1 1 0 0 0 1 1 0 0]
[ 0 0 0 1 0 -1 0 -1 -3 -1 -2 0 -1 -2 -1 -2 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + y*z-1 + x-1*y + 3*x-1*y*z-1 + y-1 + 3*x-1 + 3*x-1*z-1 + 3*x-2*y*z-1 + x-1*y-1 + 2*x-2*y*z-2 + 4*x-2*z-1 + 3*x-3*y*z-2 + x-2*y-1*z-1 + 2*x-3*z-2 + x-4*y*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3259
Image of polytope 3259 PALP id: 3259
grdb id: 161574
Integer points: [ 1 0 0 0 0 -1 -2 -2 -4 -2 -3 -1 -2 -3 -1 -1 0 -1]
[ 0 1 -1 0 -1 1 1 -1 1 1 1 0 0 0 -1 1 0 0]
[ 0 0 0 1 1 0 -2 -1 -3 -1 -2 0 -1 -2 0 -1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y + y-1*z + 2*x-1*y*z-1 + y-1 + 4*x-1 + 2*x-1*z-1 + 3*x-2*y*z-1 + 2*x-1*y-1 + x-2*y*z-2 + 5*x-2*z-1 + 3*x-3*y*z-2 + x-2*y-1*z-1 + 2*x-3*z-2 + x-4*y*z-3
36 rank 3, number 7 x + y + z + x-1*y + y-1*z + 2*x-1*y*z-1 + y-1 + 4*x-1 + 3*x-1*z-1 + 3*x-2*y*z-1 + 2*x-1*y-1 + x-2*y*z-2 + 5*x-2*z-1 + 3*x-3*y*z-2 + x-2*y-1*z-1 + 2*x-3*z-2 + x-4*y*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 3260
Image of polytope 3260 PALP id: 3260
grdb id: 176483
Integer points: [ 1 0 0 0 0 -1 0 -2 -2 -1 -2 -1 -1 0 -1 0 -1 0]
[ 0 1 0 1 -1 1 -1 1 -1 -1 0 0 -1 -1 0 0 1 0]
[ 0 0 1 -1 1 0 -1 -1 -1 0 -1 0 -1 0 -1 0 -1 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + y*z-1 + x-1*y + y-1*z + 2*z-1 + 2*x-1*y*z-1 + 2*y-1 + 3*x-1 + y-1*z-1 + 4*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3261
Image of polytope 3261 PALP id: 3261
grdb id: 625382
Integer points: [ 1 0 0 -1 0 2 1 2 -2 -1 1 -1 0 1 0 1 -1 0]
[ 0 1 0 1 1 -1 -2 -2 1 1 0 1 0 -1 0 -1 0 -1]
[ 0 0 1 1 -1 -1 0 -1 0 -1 -1 0 0 0 -1 -1 0 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
26 rank 2, number 8 x + y + z + x-1*y*z + x2*y-1*z-1 + 2*x*z-1 + y*z-1 + x*y-1 + x-1*y + x2*y-2*z-1 + 3*x*y-1*z-1 + 3*z-1 + x-1*y*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 10 2 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3262
Image of polytope 3262 PALP id: 3262
grdb id: 625383
Integer points: [ 1 0 1 0 0 -1 0 -1 1 1 1 0 0 1 0 0 0 -1]
[ 0 1 0 1 -1 0 -1 0 1 1 0 -1 0 1 0 0 1 0]
[ 0 0 2 2 -2 -2 0 0 1 3 1 -1 -1 2 0 1 1 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
26 rank 2, number 8 x*y*z3 + 2*x*y*z2 + x*y*z + x*z2 + y*z2 + 2*x*z + 2*y*z + x + y + z + z-1 + y-1 + x-1 + 2*y-1*z-1 + 2*x-1*z-1 + y-1*z-2 + x-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 10 2 Lattice Minkowski decompositions of facet 10
Image of facet 15 5 Lattice Minkowski decompositions of facet 15
Polytope 3263
Image of polytope 3263 PALP id: 3263
grdb id: 625376
Integer points: [ 1 0 0 -1 1 1 1 -1 -2 -2 -1 0 -1 0 -1 0 1 0]
[ 0 1 0 1 -1 -2 -2 1 1 1 0 -1 0 -1 1 0 -1 0]
[ 0 0 1 1 -1 0 -1 -1 0 -1 0 0 -1 -1 0 0 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + x-1*y*z + 2*x*y-1 + x-1*y + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + 3*y-1*z-1 + 3*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3264
Image of polytope 3264 PALP id: 3264
grdb id: 625356
Integer points: [ 1 0 0 1 -1 2 -2 -1 2 1 0 -1 1 0 1 0 -1 0]
[ 0 1 0 -1 1 -1 0 -1 -1 -1 -1 0 -1 0 0 -1 0 0]
[ 0 0 1 0 0 -1 1 0 -2 -2 0 1 -1 0 -1 -1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + x2*y-1*z-1 + 2*x*z-1 + x*y-1 + x-1*y + 2*x-1*z + x2*y-1*z-2 + 3*x*y-1*z-1 + 2*z-1 + 2*y-1 + 2*x-1 + x-2*z + x*y-1*z-2 + 2*y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3265
Image of polytope 3265 PALP id: 3265
grdb id: 625365
Integer points: [ 1 0 1 -1 -1 1 1 -2 0 0 0 -1 0 1 0 -1 0 1]
[ 0 1 0 0 0 -1 -1 1 -1 -1 -1 0 0 -1 0 1 0 0]
[ 0 0 2 0 -2 2 0 -2 -1 1 0 -1 -1 1 0 -1 1 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x*z2 + 2*x*z + x*y-1*z2 + x + y + 2*x*y-1*z + 2*z + x*y-1 + y-1*z + 2*z-1 + 2*x-1*y*z-1 + 2*y-1 + x-1 + y-1*z-1 + 2*x-1*z-1 + x-1*z-2 + x-2*y*z-2
51 rank 2, number 7 x*z2 + 2*x*z + x*y-1*z2 + x + y + 2*x*y-1*z + 2*z + x*y-1 + y-1*z + 2*z-1 + 2*x-1*y*z-1 + 2*y-1 + x-1 + y-1*z-1 + 3*x-1*z-1 + x-1*z-2 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 15 4 Lattice Minkowski decompositions of facet 15
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 3266
Image of polytope 3266 PALP id: 3266
grdb id: 625241
Integer points: [ 1 0 0 -1 1 -1 1 -2 1 -2 0 -1 0 -1 0 1 0 -1]
[ 0 1 0 1 -2 0 -2 1 -3 0 -2 -1 -1 0 -1 -1 0 1]
[ 0 0 1 1 -1 -1 0 0 -1 -1 -1 -1 0 0 -1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1 + x*y-3*z-1 + 3*y-2*z-1 + 3*x-1*y-1*z-1 + x-2*z-1
151 ? x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + x*y-2 + 4*y-1 + 4*x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1 + x*y-3*z-1 + 3*y-2*z-1 + 3*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 1 2 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Polytope 3267
Image of polytope 3267 PALP id: 3267
grdb id: 625031
Integer points: [ 1 0 0 -1 0 0 1 2 -1 -1 0 0 -1 1 1 0 -1 -1]
[ 0 1 0 1 -1 1 -1 -1 -1 1 0 -1 0 0 -1 0 1 0]
[ 0 0 1 1 1 -1 -1 -1 1 -1 -1 0 0 -1 0 0 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x-1*y*z + x2*y-1*z-1 + 2*x*z-1 + y*z-1 + 2*x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3268
Image of polytope 3268 PALP id: 3268
grdb id: 624171
Integer points: [ 1 0 1 -1 0 0 1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 -1 1 0 0 -1 0 -1 -1 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 1 -1 -1 -1 -1 2 0 1 0 1 -1 0 1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*y-1 + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + x*y-1*z-1 + z-1 + 4*y-1 + 3*x-1 + 3*x-1*y-1*z + 2*y-1*z-1 + x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3269
Image of polytope 3269 PALP id: 3269
grdb id: 622927
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 1 0 -1 -2 -1 -2 -1 -2 0 -1 0 -1 0 -1]
[ 0 0 1 -1 0 1 1 0 -2 -2 0 -1 0 -1 -1 0 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y + x-1*z + z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + 2*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + 4*x-1*y-1*z-1 + x-1*y-2 + x-1*y-1*z-2 + 2*x-1*y-2*z-1 + x-1*y-2*z-2
59 rank 2, number 16 x + y + z + x-1*y + x-1*z + z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + 2*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2 + x-1*y-1*z-2 + 2*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 143 1 Lattice Minkowski decompositions of facet 143
Polytope 3270
Image of polytope 3270 PALP id: 3270
grdb id: 623294
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 0 1 -1 -2 0 1 0 1 -1 0 -1 0 -1 0]
[ 0 0 1 -1 1 0 1 0 -2 -2 0 -1 0 -1 -1 0 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + y*z-1 + x-1*y + x-1*z + 2*z-1 + 2*x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + x-1*y*z-2 + 3*x-1*z-1 + 2*x-1*y-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
52 rank 2, number 52 x + y + z + y*z-1 + x-1*y + x-1*z + 2*z-1 + 2*x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + x-1*y*z-2 + 4*x-1*z-1 + 3*x-1*y-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 143 1 Lattice Minkowski decompositions of facet 143
Polytope 3271
Image of polytope 3271 PALP id: 3271
grdb id: 624138
Integer points: [ 1 0 0 0 0 -1 -1 -2 -1 -2 -2 -2 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 1 1 1 -2 -2 -1 0 -1 0 -1 0 -1 0]
[ 0 0 1 -1 1 0 -1 -1 0 -1 -1 -1 0 0 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y + y-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + 3*x-1*z-1 + x-2*y*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2 + 3*x-2*y-1*z-1 + x-2*y-2*z-1
146 ? x + y + z + x-1*y + y-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + 3*x-1*z-1 + x-2*y*z-1 + 4*x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2 + 3*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3272
Image of polytope 3272 PALP id: 3272
grdb id: 624170
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 1 1 -1 -2 -2 0 1 0 -1 0 -1 0 -1]
[ 0 0 1 -1 1 -1 1 -1 0 1 -1 0 0 0 1 1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + x-1*y*z + 2*x-1*y + y-1*z + 3*x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 5*x-1 + 3*x-1*y-1*z + 2*x-1*z-1 + 4*x-1*y-1 + x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3273
Image of polytope 3273 PALP id: 3273
grdb id: 624115
Integer points: [ 1 0 0 0 0 1 -1 -1 -2 -2 -1 -2 -1 0 -1 0 -1 0]
[ 0 1 0 1 -1 -1 -1 1 -1 1 1 0 0 0 0 0 -1 -1]
[ 0 0 1 -1 1 0 1 -2 0 -2 -1 -1 -1 -1 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + y*z-1 + x*y-1 + y-1*z + 2*z-1 + 2*x-1*y*z-1 + 3*y-1 + 3*x-1 + x-1*y-1*z + x-1*y*z-2 + 4*x-1*z-1 + 3*x-1*y-1 + x-2*y*z-2 + 2*x-2*z-1 + x-2*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3274
Image of polytope 3274 PALP id: 3274
grdb id: 624507
Integer points: [ 1 0 0 1 -1 0 -2 1 -1 1 0 -1 1 0 -1 0 1 0]
[ 0 1 0 0 0 -1 1 -2 0 -2 -1 0 -1 0 1 -1 -1 0]
[ 0 0 1 -1 1 1 0 0 -1 -1 0 0 0 0 0 -1 -1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 x + y + z + x*z-1 + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + 2*x*y-1*z-1 + 2*z-1 + x*y-2 + 4*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
62 rank 2, number 9 x + y + z + x*z-1 + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + 2*x*y-1*z-1 + 2*z-1 + x*y-2 + 2*y-1 + 2*x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3275
Image of polytope 3275 PALP id: 3275
grdb id: 624073
Integer points: [ 1 0 0 1 -1 0 -1 -1 0 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 -1 1 1 0 1 -2 -2 -1 0 -1 0 -1 0 -1 0]
[ 0 0 1 0 0 -1 1 -1 -1 -1 -1 -1 0 0 -1 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + z + y*z-1 + x*y-1 + x-1*y + x-1*z + 3*z-1 + x-1*y*z-1 + 3*y-1 + 3*x-1 + 3*y-1*z-1 + 3*x-1*z-1 + 2*x-1*y-1 + y-2*z-1 + 3*x-1*y-1*z-1 + x-1*y-2*z-1
10 rank 1, V18 x + y + z + y*z-1 + x*y-1 + x-1*y + x-1*z + 3*z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + 3*y-1*z-1 + 3*x-1*z-1 + 2*x-1*y-1 + y-2*z-1 + 3*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 3276
Image of polytope 3276 PALP id: 3276
grdb id: 624084
Integer points: [ 1 0 0 1 -1 1 0 -2 1 0 1 0 0 -1 0 0 -1 -1]
[ 0 1 0 0 1 -1 1 0 -2 -2 -1 -1 0 0 -1 0 -1 0]
[ 0 0 1 -1 0 0 -1 1 -1 -1 -1 0 0 1 -1 -1 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x*z-1 + y*z-1 + x*y-1 + x-1*y + 2*x-1*z + 2*x*y-1*z-1 + 3*z-1 + 3*y-1 + 3*x-1 + x-2*z + x*y-2*z-1 + 3*y-1*z-1 + 2*x-1*y-1 + y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3277
Image of polytope 3277 PALP id: 3277
grdb id: 624451
Integer points: [ 1 0 0 1 0 -1 0 -2 -1 -2 -2 -1 -1 0 -1 -1 0 0]
[ 0 1 0 -1 -1 0 -1 1 0 1 1 0 0 -1 1 1 0 0]
[ 0 0 1 0 1 1 -1 0 -2 -2 -1 0 -1 0 0 -1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + z + x*y-1 + 2*x-1*y + y-1*z + x-1*z + 2*z-1 + 2*x-1*y*z-1 + 2*y-1 + 4*x-1 + x-2*y + y-1*z-1 + 4*x-1*z-1 + 2*x-2*y*z-1 + x-1*z-2 + x-2*y*z-2
10 rank 1, V18 x + y + z + x*y-1 + 2*x-1*y + y-1*z + x-1*z + 2*z-1 + 2*x-1*y*z-1 + 2*y-1 + 3*x-1 + x-2*y + y-1*z-1 + 3*x-1*z-1 + 2*x-2*y*z-1 + x-1*z-2 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 96 1 Lattice Minkowski decompositions of facet 96
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3278
Image of polytope 3278 PALP id: 3278
grdb id: 624132
Integer points: [ 1 0 1 0 0 -1 -1 -1 0 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 -1 0 0 1 1 0 -2 -2 1 0 -1 0 -1 0 -1 -1]
[ 0 0 0 1 -1 1 -1 1 -1 -1 0 0 0 -1 -1 0 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + z + x-1*y*z + x*y-1 + 2*x-1*y + x-1*z + z-1 + x-1*y*z-1 + 3*y-1 + 4*x-1 + 2*y-1*z-1 + 3*x-1*z-1 + 2*x-1*y-1 + y-2*z-1 + 3*x-1*y-1*z-1 + x-1*y-2*z-1
10 rank 1, V18 x + y + z + x-1*y*z + x*y-1 + 2*x-1*y + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + 2*y-1*z-1 + 3*x-1*z-1 + 2*x-1*y-1 + y-2*z-1 + 3*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3279
Image of polytope 3279 PALP id: 3279
grdb id: 624186
Integer points: [ 1 0 1 0 1 -1 0 -2 -2 0 -1 -1 -1 -1 0 0 0 0]
[ 0 1 -1 0 -1 1 -1 1 1 -1 1 0 0 0 0 0 -1 -1]
[ 0 0 0 1 -1 1 1 1 0 -2 0 1 0 -1 0 -1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y*z + x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + x*y-1*z-1 + 2*z-1 + 3*y-1 + 4*x-1 + x-2*y + 3*y-1*z-1 + 2*x-1*z-1 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 3280
Image of polytope 3280 PALP id: 3280
grdb id: 624343
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1]
[ 0 1 -1 0 -2 2 0 2 0 -2 1 -1 0 1 -1 0 1 -1]
[ 0 0 0 1 1 -1 -1 -2 1 1 0 1 0 -1 1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + 2*y*z-1 + x-1*y2*z-1 + 2*x-1*y + 2*y-1*z + x-1*z + x-1*y2*z-2 + 3*x-1*y*z-1 + y-1 + 4*x-1 + y-2*z + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
31 rank 3, number 3 x + y + z + 2*y*z-1 + x-1*y2*z-1 + 2*x-1*y + 2*y-1*z + x-1*z + x-1*y2*z-2 + 4*x-1*y*z-1 + y-1 + 5*x-1 + y-2*z + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Polytope 3281
Image of polytope 3281 PALP id: 3281
grdb id: 624613
Integer points: [ 1 0 0 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 -1 0 -1 -1 0 -1 -1 -1 -1 0 0 -1 0 0]
[ 0 0 1 -1 1 1 -1 2 -2 -2 -1 0 1 -1 0 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
56 rank 2, number 11 x + y + z + y*z-1 + y-1*z + x-1*z + x-1*y-1*z2 + z-1 + 2*y-1 + 3*x-1 + 4*x-1*y-1*z + y-1*z-1 + 3*x-1*z-1 + 6*x-1*y-1 + x-1*z-2 + 4*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Polytope 3282
Image of polytope 3282 PALP id: 3282
grdb id: 625034
Integer points: [ 1 0 0 1 1 0 -2 1 -2 0 -1 0 -1 0 -1 1 0 -1]
[ 0 1 0 0 -1 -1 2 -1 1 -1 0 0 1 -1 0 -1 0 1]
[ 0 0 1 -1 0 1 1 -2 1 -1 0 -1 0 0 1 -1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*x-1*y*z + x-2*y2*z + x*z-1 + x*y-1 + 3*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + 2*x*y-1*z-1 + 3*z-1 + 2*y-1 + 2*x-1 + x*y-1*z-2 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3283
Image of polytope 3283 PALP id: 3283
grdb id: 624083
Integer points: [ 1 0 -1 0 1 -1 -2 1 -2 0 0 0 -1 -1 -1 -2 0 0]
[ 0 1 1 0 -1 0 1 -2 -1 -3 -1 -2 0 -1 -2 0 0 -1]
[ 0 0 0 1 1 -1 -1 1 -1 1 1 1 0 0 0 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + x*y-1*z + z + x-1*y + x*y-2*z + 3*y-1*z + 3*y-1 + 4*x-1 + 3*y-2*z + x-1*z-1 + x-2*y*z-1 + 5*x-1*y-1 + y-3*z + 2*x-2*z-1 + 2*x-1*y-2 + x-2*y-1*z-1
17 rank 1, V22 x + y + x*y-1*z + z + x-1*y + x*y-2*z + 3*y-1*z + 2*y-1 + 4*x-1 + 3*y-2*z + x-1*z-1 + x-2*y*z-1 + 5*x-1*y-1 + y-3*z + 2*x-2*z-1 + 2*x-1*y-2 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3284
Image of polytope 3284 PALP id: 3284
grdb id: 624143
Integer points: [ 1 0 0 0 -1 -1 -1 -1 0 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 1 0 0 -1 -2 -3 -2 -1 0 -2 -1 -1 0 -1]
[ 0 0 1 -1 0 -1 1 -1 1 1 0 0 0 1 1 0 0 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + x-1*y + 2*y-1*z + x-1*z + z-1 + 3*y-1 + 3*x-1 + y-2*z + 3*x-1*y-1*z + x-1*z-1 + 4*x-1*y-1 + 3*x-1*y-2*z + x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-3*z
17 rank 1, V22 x + y + z + x-1*y + 2*y-1*z + x-1*z + z-1 + 2*y-1 + 3*x-1 + y-2*z + 3*x-1*y-1*z + x-1*z-1 + 4*x-1*y-1 + 3*x-1*y-2*z + x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3285
Image of polytope 3285 PALP id: 3285
grdb id: 624136
Integer points: [ 1 0 1 -1 0 -1 1 -1 0 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 -1 1 0 1 -2 0 -3 -3 -1 -2 0 -1 -1 -2 0 -1]
[ 0 0 0 0 1 1 -1 1 -2 -2 0 -1 0 -1 0 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + x-1*y*z + x*y-1 + x-1*y + x-1*z + 4*y-1 + 3*x-1 + x*y-2*z-1 + 2*y-1*z-1 + 3*x-1*y-1 + 4*y-2*z-1 + 2*x-1*y-1*z-1 + 3*x-1*y-2*z-1 + y-3*z-2 + x-1*y-3*z-2
52 rank 2, number 52 x + y + z + x-1*y*z + x*y-1 + x-1*y + x-1*z + 3*y-1 + 3*x-1 + x*y-2*z-1 + 2*y-1*z-1 + 3*x-1*y-1 + 3*y-2*z-1 + 2*x-1*y-1*z-1 + 3*x-1*y-2*z-1 + y-3*z-2 + x-1*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3286
Image of polytope 3286 PALP id: 3286
grdb id: 637790
Integer points: [ 1 0 0 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 -1 1 -1 -1 1 -1 -1 0 0 0 1 -1 0 0]
[ 0 0 1 -1 1 1 -1 1 -1 -1 0 -1 0 1 0 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + y*z-1 + 2*x-1*y + y-1*z + 2*x-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + x-1*y-1*z + y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3287
Image of polytope 3287 PALP id: 3287
grdb id: 637785
Integer points: [ 1 0 0 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 0 0 -1 0]
[ 0 1 0 1 -1 0 0 -1 -2 -2 -1 -2 -1 0 -1 0 -1 0]
[ 0 0 1 -1 1 1 -1 -1 1 -1 1 0 0 0 0 0 -1 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + y*z-1 + y-1*z + x-1*z + 2*z-1 + 3*y-1 + 2*x-1 + 2*x-1*y-1*z + y-1*z-1 + x-1*z-1 + 4*x-1*y-1 + x-1*y-2*z + 2*x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-2*z-1
52 rank 2, number 52 x + y + z + y*z-1 + y-1*z + x-1*z + 2*z-1 + 2*y-1 + 2*x-1 + 2*x-1*y-1*z + y-1*z-1 + x-1*z-1 + 4*x-1*y-1 + x-1*y-2*z + 2*x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3288
Image of polytope 3288 PALP id: 3288
grdb id: 635393
Integer points: [ 1 0 0 0 0 -1 -1 0 -1 -1 -1 -1 -1 0 0 -1 -1 0]
[ 0 1 0 1 -1 1 -1 -1 -2 -2 0 -1 -2 0 -1 0 -1 0]
[ 0 0 1 -1 1 -1 1 -1 1 -1 0 0 0 0 0 -1 -1 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + y*z-1 + y-1*z + 2*z-1 + x-1*y*z-1 + 3*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + 3*x-1*z-1 + 4*x-1*y-1 + x-1*y-2*z + 3*x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-2*z-1
52 rank 2, number 52 x + y + z + y*z-1 + y-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + 3*x-1*z-1 + 4*x-1*y-1 + x-1*y-2*z + 3*x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3289
Image of polytope 3289 PALP id: 3289
grdb id: 635469
Integer points: [ 1 0 0 0 0 -1 0 -1 -1 -1 -1 -1 -1 0 0 -1 -1 0]
[ 0 1 0 1 0 1 -2 0 1 -2 -1 0 1 -1 0 -1 0 -1]
[ 0 0 1 -1 -1 0 1 1 -2 1 1 0 -1 1 0 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + y*z-1 + x-1*y + 2*y-1*z + x-1*z + z-1 + 2*x-1*y*z-1 + 2*y-1 + 4*x-1 + y-2*z + 2*x-1*y-1*z + x-1*y*z-2 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3290
Image of polytope 3290 PALP id: 3290
grdb id: 630597
Integer points: [ 1 0 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 1 -1 0 -1 1 1 -2 1 1 0 0 0 -1 -1 0]
[ 0 0 1 -1 1 -1 0 1 -2 1 0 -1 1 0 -1 1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + y*z-1 + 3*x-1*y + y-1*z + 3*x-1*z + z-1 + 3*x-1*y*z-1 + y-1 + 6*x-1 + 3*x-1*y-1*z + x-1*y*z-2 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 20 3 Lattice Minkowski decompositions of facet 20
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Polytope 3291
Image of polytope 3291 PALP id: 3291
grdb id: 635365
Integer points: [ 1 0 0 0 0 -1 -1 -1 -3 -3 -2 -1 -3 -2 -1 -2 -1 0]
[ 0 1 -1 0 -1 1 1 -1 1 -1 -1 -1 0 0 0 1 0 0]
[ 0 0 0 1 1 0 -1 -1 -2 -2 -1 0 -2 -1 0 -1 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*y + y-1*z + x-1*y*z-1 + y-1 + 4*x-1 + 3*x-1*z-1 + 2*x-2*y*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + 5*x-2*z-1 + x-3*y*z-2 + 3*x-2*y-1*z-1 + 2*x-3*z-2 + x-3*y-1*z-2
38 ? x + y + z + x-1*y + y-1*z + x-1*y*z-1 + y-1 + 4*x-1 + 2*x-1*z-1 + 2*x-2*y*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + 5*x-2*z-1 + x-3*y*z-2 + 3*x-2*y-1*z-1 + 2*x-3*z-2 + x-3*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 3292
Image of polytope 3292 PALP id: 3292
grdb id: 47445
Integer points: [ 1 0 1 0 0 -1 -1 0 0 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 0 1 1 -1 -1 -1 -1 -1 0 0 0 1 -1 0]
[ 0 0 0 1 -1 1 -1 1 -1 1 -1 0 -1 0 1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + x-1*y-1*z + y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
31 rank 3, number 3 x + y + z + x-1*y*z + x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + z-1 + x-1*y*z-1 + 3*y-1 + 4*x-1 + x-1*y-1*z + y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 3293
Image of polytope 3293 PALP id: 3293
grdb id: 47436
Integer points: [ 1 0 0 -1 1 0 -1 -1 1 -1 1 -1 -1 0 0 1 0 0]
[ 0 1 0 1 -1 -1 0 1 -2 0 -2 0 1 -1 0 -1 -1 0]
[ 0 0 1 1 -1 1 1 -1 0 -1 -1 0 0 0 0 0 -1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + x*y-2 + 3*y-1 + 2*x-1 + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 1 1 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3294
Image of polytope 3294 PALP id: 3294
grdb id: 47421
Integer points: [ 1 0 0 1 -1 0 1 -1 -1 1 -1 -1 0 0 -1 -1 0 0]
[ 0 1 0 -1 1 0 -1 0 0 -2 -2 -1 -2 -1 -1 0 -1 0]
[ 0 0 1 0 0 -1 -1 1 -1 -1 -1 0 -1 0 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*y-1 + x-1*y + x-1*z + x*y-1*z-1 + z-1 + 3*y-1 + 2*x-1 + x*y-2*z-1 + 3*y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + 2*y-2*z-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Polytope 3295
Image of polytope 3295 PALP id: 3295
grdb id: 47424
Integer points: [ 1 0 0 1 0 0 -1 -1 0 -1 -1 0 -1 -1 0 0 -1 -1]
[ 0 1 0 0 1 -1 1 1 -1 -2 -2 0 -1 0 -1 0 -1 0]
[ 0 0 1 -1 -1 1 1 0 -1 1 0 -1 0 0 0 0 1 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y*z + x*z-1 + y*z-1 + x-1*y + y-1*z + 3*x-1*z + 2*z-1 + 3*y-1 + 3*x-1 + 3*x-1*y-1*z + y-1*z-1 + 3*x-1*y-1 + x-1*y-2*z + x-1*y-2
62 rank 2, number 9 x + y + z + x-1*y*z + x*z-1 + y*z-1 + x-1*y + y-1*z + 3*x-1*z + 2*z-1 + 2*y-1 + 3*x-1 + 3*x-1*y-1*z + y-1*z-1 + 3*x-1*y-1 + x-1*y-2*z + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3296
Image of polytope 3296 PALP id: 3296
grdb id: 47429
Integer points: [ 1 0 1 0 1 -1 0 1 -2 0 -2 -1 0 -1 0 -1 0 -1]
[ 0 1 -1 0 -1 1 0 -2 1 -2 0 -1 -1 0 -1 0 0 1]
[ 0 0 0 1 -1 1 -1 -1 0 -1 -1 -1 0 0 -1 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + x*y-1 + 2*x-1*y + x*y-1*z-1 + z-1 + 2*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + 3*y-1*z-1 + 2*x-1*z-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3297
Image of polytope 3297 PALP id: 3297
grdb id: 47449
Integer points: [ 1 0 0 -1 1 0 0 -1 -2 1 1 1 0 -1 0 1 0 -1]
[ 0 1 0 1 -1 0 -1 0 1 -2 1 -1 -1 0 0 0 1 1]
[ 0 0 1 2 -2 -1 0 0 2 -2 0 -1 -1 1 0 -1 1 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x*y + 2*y*z + x-1*y*z2 + x + y + z + 2*x-1*y*z + x-2*y*z2 + 2*x*z-1 + 2*x-1*z + 2*x*y-1*z-1 + z-1 + y-1 + x-1 + x*y-1*z-2 + 2*y-1*z-1 + x*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 11 6 Lattice Minkowski decompositions of facet 11
Image of facet 15 3 Lattice Minkowski decompositions of facet 15
Polytope 3298
Image of polytope 3298 PALP id: 3298
grdb id: 52838
Integer points: [ 1 0 0 1 -1 -1 0 1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 -1 1 0 -1 -1 1 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 0 0 1 1 -1 -1 1 -1 0 -1 0 -1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*y-1 + x-1*y + y-1*z + x-1*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 3*y-1 + 3*x-1 + x-1*y-1*z + 2*y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 3299
Image of polytope 3299 PALP id: 3299
grdb id: 52868
Integer points: [ 1 0 0 -1 1 1 -1 -2 1 -2 -1 0 -1 0 -1 0 1 0]
[ 0 1 0 1 0 -1 0 1 -2 1 0 -1 0 0 1 -1 -1 0]
[ 0 0 1 1 -1 0 1 1 -1 0 -1 0 0 0 0 -1 -1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y*z + x*z-1 + x*y-1 + 2*x-1*y + x-1*z + x-2*y*z + 2*x*y-1*z-1 + 2*z-1 + 2*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3300
Image of polytope 3300 PALP id: 3300
grdb id: 51702
Integer points: [ 1 0 0 0 -1 -1 -1 0 -1 -1 -1 -1 -1 0 -1 -1 0 0]
[ 0 1 0 -1 1 0 1 -1 -1 0 -1 -1 -1 -1 0 0 0 0]
[ 0 0 1 1 0 1 -1 -1 1 -2 -2 0 -1 0 0 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y + y-1*z + x-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*z-2 + 3*x-1*y-1*z-1 + x-1*y-1*z-2
39 ? x + y + z + x-1*y + y-1*z + x-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + x-1*y-1*z + y-1*z-1 + 4*x-1*z-1 + 3*x-1*y-1 + x-1*z-2 + 3*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3301
Image of polytope 3301 PALP id: 3301
grdb id: 51708
Integer points: [ 1 0 0 0 -1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 -1]
[ 0 1 0 0 1 -1 -1 0 0 -2 -2 -1 -2 -1 0 -1 0 -1]
[ 0 0 1 -1 0 -1 1 -1 1 1 -1 1 0 0 0 0 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y + y-1*z + x-1*z + z-1 + 2*y-1 + 3*x-1 + 2*x-1*y-1*z + y-1*z-1 + x-1*z-1 + 4*x-1*y-1 + x-1*y-2*z + 2*x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-2*z-1
146 ? x + y + z + x-1*y + y-1*z + x-1*z + z-1 + 2*y-1 + 4*x-1 + 2*x-1*y-1*z + y-1*z-1 + x-1*z-1 + 5*x-1*y-1 + x-1*y-2*z + 2*x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-2*z-1
146 ? x + y + z + x-1*y + y-1*z + x-1*z + z-1 + 3*y-1 + 3*x-1 + 2*x-1*y-1*z + y-1*z-1 + x-1*z-1 + 4*x-1*y-1 + x-1*y-2*z + 2*x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-2*z-1
94 ? x + y + z + x-1*y + y-1*z + x-1*z + z-1 + 3*y-1 + 4*x-1 + 2*x-1*y-1*z + y-1*z-1 + x-1*z-1 + 5*x-1*y-1 + x-1*y-2*z + 2*x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Polytope 3302
Image of polytope 3302 PALP id: 3302
grdb id: 52267
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 -1 0 0]
[ 0 1 0 1 -1 -1 1 -2 1 0 -2 0 -1 0 0 -1 -1 0]
[ 0 0 1 -1 1 1 -1 1 -2 -2 0 0 0 -1 0 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + y*z-1 + y-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + x-1*y*z-2 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
52 rank 2, number 52 x + y + z + y*z-1 + y-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + x-1*y*z-2 + 4*x-1*z-1 + 4*x-1*y-1 + x-1*y-2*z + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 96 1 Lattice Minkowski decompositions of facet 96
Polytope 3303
Image of polytope 3303 PALP id: 3303
grdb id: 51803
Integer points: [ 1 0 0 0 0 -1 0 -1 -1 -2 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 1 -1 0 1 -1 1 -2 1 -2 0 -1 0 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*z + z-1 + y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + x-2*y-1*z + 3*x-1*y-1*z-1 + 3*x-2*y-1 + x-1*y-1*z-2 + 3*x-2*y-1*z-1 + x-2*y-1*z-2
36 rank 3, number 7 x + y + z + x-1*z + z-1 + y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + 2*x-1*z-1 + 4*x-1*y-1 + x-2*y-1*z + 4*x-1*y-1*z-1 + 3*x-2*y-1 + x-1*y-1*z-2 + 3*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3304
Image of polytope 3304 PALP id: 3304
grdb id: 52997
Integer points: [ 1 0 0 1 -1 1 -1 -1 -1 0 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 -1 1 -1 1 0 -1 -1 -1 0 0 -1 0 0 -1 -1]
[ 0 0 1 0 1 -1 0 1 0 -2 -2 -1 0 -1 -1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + x*y-1 + x-1*y + x-1*z + x*y-1*z-1 + 2*z-1 + 2*y-1 + 3*x-1 + 3*y-1*z-1 + 2*x-1*z-1 + x-1*y-1 + y-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3305
Image of polytope 3305 PALP id: 3305
grdb id: 50760
Integer points: [ 1 0 0 0 0 0 0 -1 -1 -1 -3 -2 -1 -2 -1 0 -2 -1]
[ 0 1 0 1 -1 -1 0 -1 1 -1 -1 -1 0 0 -1 0 -1 0]
[ 0 0 1 -1 1 0 -1 1 -1 -1 -1 0 0 -1 0 0 -1 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + y*z-1 + y-1*z + z-1 + x-1*y*z-1 + y-1 + 3*x-1 + x-1*y-1*z + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1 + 2*x-2*z-1 + 2*x-2*y-1 + 2*x-2*y-1*z-1 + x-3*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 7 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 30 3 Lattice Minkowski decompositions of facet 30
Polytope 3306
Image of polytope 3306 PALP id: 3306
grdb id: 11567
Integer points: [ 1 0 0 -1 1 -1 1 0 0 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 -1 1 -1 0 -1 0 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 1 1 0 0 -1 -1 1 -1 1 -1 0 0 1 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + x*y-1 + x-1*y + y-1*z + 2*x-1*z + x*y-1*z-1 + z-1 + 3*y-1 + 3*x-1 + x-1*y-1*z + 2*y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Polytope 3307
Image of polytope 3307 PALP id: 3307
grdb id: 11568
Integer points: [ 1 0 0 0 1 -1 0 -1 -1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 -1 1 -1 0 1 -1 -1 -1 -1 0 0 -1 0 0]
[ 0 0 1 -1 0 0 1 1 -1 1 -1 -1 0 -1 0 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + z + y*z-1 + x*y-1 + x-1*y + y-1*z + x-1*z + 2*z-1 + x-1*y*z-1 + 3*y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
10 rank 1, V18 x + y + z + y*z-1 + x*y-1 + x-1*y + y-1*z + x-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3308
Image of polytope 3308 PALP id: 3308
grdb id: 11546
Integer points: [ 1 0 0 -1 1 -1 -1 1 -2 1 1 1 -1 0 0 0 0 1]
[ 0 1 0 1 -1 1 0 0 1 -1 -2 -2 0 -1 0 -1 0 -1]
[ 0 0 1 1 0 0 1 -1 1 -2 -1 -2 0 -1 -1 0 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + x-1*y*z + x*z-1 + x*y-1 + x-1*y + x-1*z + x-2*y*z + 2*x*y-1*z-1 + 2*z-1 + 2*y-1 + 3*x-1 + x*y-1*z-2 + x*y-2*z-1 + 3*y-1*z-1 + x*y-2*z-2
20 rank 1, V16 x + y + z + x-1*y*z + x*z-1 + x*y-1 + x-1*y + x-1*z + x-2*y*z + 3*x*y-1*z-1 + 2*z-1 + 2*y-1 + 3*x-1 + x*y-1*z-2 + x*y-2*z-1 + 3*y-1*z-1 + x*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Polytope 3309
Image of polytope 3309 PALP id: 3309
grdb id: 11569
Integer points: [ 1 0 0 1 1 0 0 1 -1 -1 -2 -2 0 0 -1 0 -1 -1]
[ 0 1 0 0 -1 -1 1 -1 1 -1 0 1 -1 0 0 0 0 1]
[ 0 0 1 -1 0 1 -1 -1 -1 1 1 0 0 -1 0 0 1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x*z-1 + y*z-1 + x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-2*y + x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3310
Image of polytope 3310 PALP id: 3310
grdb id: 11035
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 0 -1 1 1 0 -1 -2 -2 0 -1 0 -1 -1 0]
[ 0 0 1 -1 -1 1 0 -1 1 -1 1 0 -1 0 0 1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + y*z-1 + x-1*y + y-1*z + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + 2*x-1*y-1*z + 2*x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
39 ? x + y + z + y*z-1 + x-1*y + y-1*z + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + 2*x-1*y-1*z + 2*x-1*z-1 + 4*x-1*y-1 + x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 96 1 Lattice Minkowski decompositions of facet 96
Polytope 3311
Image of polytope 3311 PALP id: 3311
grdb id: 1454
Integer points: [ 1 0 0 -1 1 0 -1 1 0 1 0 -1 -1 0 0 -1 0 -1]
[ 0 1 0 1 0 1 1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 1 1 -1 -1 0 0 1 -1 -1 1 0 0 -1 0 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + x-1*y*z + x*z-1 + y*z-1 + x*y-1 + x-1*y + y-1*z + 2*x-1*z + x*y-1*z-1 + 2*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + x-1*y-1
20 rank 1, V16 x + y + z + x-1*y*z + x*z-1 + y*z-1 + x*y-1 + x-1*y + y-1*z + 2*x-1*z + x*y-1*z-1 + 2*z-1 + 3*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 3 5 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3312
Image of polytope 3312 PALP id: 3312
grdb id: 547434
Integer points: [ 1 0 0 -4 -3 -2 -1 -3 -2 -1 0 -2 -1 0 -1 0 -1 0 0]
[ 0 1 1 -3 -2 -1 0 -2 -1 0 1 -1 0 1 0 1 -1 0 0]
[ 0 0 4 -4 -2 0 2 -3 -1 1 3 -2 0 2 -1 1 -1 1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 123 1 none
Image of facet 13 2 irreducible and admissible
Image of facet 206 1 Lattice Minkowski decompositions of facet 206
Polytope 3313
Image of polytope 3313 PALP id: 3313
grdb id: 547429
Integer points: [ 1 1 1 -3 -1 -2 0 -1 1 0 -1 1 0 1 -1 1 0 1 1]
[ 0 2 0 -2 -1 -1 0 0 1 1 -1 0 0 1 -1 0 0 1 0]
[ 0 0 4 -4 0 -3 1 -2 2 -1 -1 3 0 1 -2 2 -1 0 1]
Degree: 8
Hilbert function: 1 + 7 t + 25 t2 + 63 t3 + 129 t4 + 231 t5 + 377 t6 + 575 t7 + 833 t8 + 1159 t9 + 1561 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
5 rank 1, V8 x*z4 + 2*x*y*z2 + 4*x*z3 + x*y2 + 4*x*y*z + 6*x*z2 + 2*x*y + 4*x*z + x + 4*z + 4*y*z-1 + 4*z-1 + 2*x-1*y-1 + 6*x-1*z-2 + 4*x-1*y-1*z-1 + 2*x-1*y-1*z-2 + 4*x-2*y-1*z-3 + x-3*y-2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 4 Lattice Minkowski decompositions of facet 32
Polytope 3314
Image of polytope 3314 PALP id: 3314
grdb id: 547432
Integer points: [ 1 0 2 -6 1 0 -1 -2 -3 -4 -5 1 0 -1 -2 -3 1 0 -1]
[ 0 1 3 -5 2 1 0 -1 -2 -3 -4 2 1 0 -1 -2 1 0 -1]
[ 0 0 4 -4 3 2 1 0 -1 -2 -3 2 1 0 -1 -2 1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 208 1 Lattice Minkowski decompositions of facet 208
Image of facet 4 2 none
Image of facet 207 1 irreducible and admissible
Polytope 3315
Image of polytope 3315 PALP id: 3315
grdb id: 547433
Integer points: [ 1 1 1 -7 -1 -3 -5 0 -2 -4 1 -1 -3 0 1 -1 -3 0 1]
[ 0 2 0 -4 -1 -2 -3 0 -1 -2 1 0 -1 1 0 -1 -2 0 1]
[ 0 0 2 -2 1 0 -1 1 0 -1 1 0 -1 0 1 0 -1 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 209 1 none
Polytope 3316
Image of polytope 3316 PALP id: 3316
grdb id: 545136
Integer points: [ 1 1 -3 1 -3 1 0 0 -1 -1 -1 -2 -2 -3 1 1 0 -1 -1]
[ 0 2 -2 0 0 1 0 1 -1 0 1 -1 0 -1 0 1 0 -1 0]
[ 0 0 0 2 -2 1 1 0 1 0 -1 0 -1 -1 1 0 0 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 4 Lattice Minkowski decompositions of facet 16
Image of facet 210 1 none
Polytope 3317
Image of polytope 3317 PALP id: 3317
grdb id: 545228
Integer points: [ 1 1 -3 1 -1 0 1 0 -1 0 -1 -2 -1 -2 1 0 1 0 -1]
[ 0 2 -2 0 2 2 1 1 1 0 0 0 -1 -1 1 1 0 0 -1]
[ 0 0 0 2 -2 -1 1 0 -1 1 0 -1 1 0 0 -1 1 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 4 Lattice Minkowski decompositions of facet 16
Image of facet 211 1 none
Polytope 3318
Image of polytope 3318 PALP id: 3318
grdb id: 545139
Integer points: [ 1 1 1 -3 -3 -2 -1 0 -1 0 1 -3 -2 -1 -1 0 1 1 -1]
[ 0 2 0 -2 -2 -1 0 1 -1 0 1 -2 -1 0 -1 0 1 0 -1]
[ 0 0 2 -2 0 0 0 0 1 1 1 -1 -1 -1 0 0 0 1 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
11 rank 2, number 6 x*y2 + 2*x*y*z + x*z2 + 2*x*y + 2*x*z + x + 4*y + 4*z + 6*x-1 + 2*x-1*y-1*z + 2*x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-1*z-1 + 4*x-2*y-1 + 4*x-2*y-1*z-1 + x-3*y-2 + 2*x-3*y-2*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 32 2 Lattice Minkowski decompositions of facet 32
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Polytope 3319
Image of polytope 3319 PALP id: 3319
grdb id: 545211
Integer points: [ 1 0 0 -2 -2 0 -1 -1 -1 -1 -1 -2 -2 -2 -2 -2 0 0 0]
[ 0 1 1 -1 -1 1 0 0 0 0 0 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 2 2 -4 1 2 1 0 -1 -2 1 0 -1 -2 -3 1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 212 1 Lattice Minkowski decompositions of facet 212
Image of facet 53 1 irreducible and admissible
Image of facet 4 2 none
Polytope 3320
Image of polytope 3320 PALP id: 3320
grdb id: 545212
Integer points: [ 1 0 1 -1 -4 0 -1 0 -1 -2 -1 -2 -3 -2 -3 1 0 0 -1]
[ 0 1 0 -2 1 0 1 -1 0 1 -1 0 1 -1 0 0 0 -1 0]
[ 0 0 2 2 -4 1 -1 2 0 -2 1 -1 -3 0 -2 1 0 1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 14 1 none
Image of facet 213 1 Lattice Minkowski decompositions of facet 213
Polytope 3321
Image of polytope 3321 PALP id: 3321
grdb id: 545137
Integer points: [ 1 0 -2 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 1 -1 1 -1 -1 -1 -1 0 0 0 0 0 1 1 1 0 0 0]
[ 0 0 0 4 -4 -3 -2 -1 -2 -1 0 1 2 1 2 3 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 4 2 none
Image of facet 13 2 irreducible and admissible
Image of facet 214 1 Lattice Minkowski decompositions of facet 214
Polytope 3322
Image of polytope 3322 PALP id: 3322
grdb id: 545196
Integer points: [ 1 0 0 -2 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -4 3 2 1 0 -1 -2 -3 2 1 0 -1 -2 1 0 -1]
[ 0 0 1 3 -4 -3 -2 -1 0 1 2 -2 -1 0 1 2 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 4 2 none
Image of facet 196 1 irreducible and admissible
Image of facet 215 1 Lattice Minkowski decompositions of facet 215
Polytope 3323
Image of polytope 3323 PALP id: 3323
grdb id: 545229
Integer points: [ 1 0 0 -2 -2 0 0 -1 -1 -1 -1 -1 -2 -2 -2 -2 0 0 0]
[ 0 1 1 -1 -1 1 1 0 0 0 0 0 -1 -1 -1 -1 0 0 0]
[ 0 0 3 1 -4 2 1 2 1 0 -1 -2 0 -1 -2 -3 1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 216 1 Lattice Minkowski decompositions of facet 216
Image of facet 9 1 irreducible and admissible
Image of facet 43 1 irreducible and admissible
Image of facet 4 2 none
Polytope 3324
Image of polytope 3324 PALP id: 3324
grdb id: 545223
Integer points: [ 1 0 0 -1 -4 -3 -2 -1 -3 -2 -1 -2 -1 -2 -1 0 -1 0 0]
[ 0 1 1 -2 1 1 1 1 0 0 0 -1 -1 1 1 1 0 0 -1]
[ 0 0 2 -2 4 3 2 1 2 1 0 0 -1 3 2 1 1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 121 1 none
Polytope 3325
Image of polytope 3325 PALP id: 3325
grdb id: 545199
Integer points: [ 1 0 1 -5 -1 -2 -3 -4 0 -1 -2 -3 0 -1 0 -1 -2 1 0]
[ 0 1 0 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
[ 0 0 2 -2 2 1 0 -1 2 1 0 -1 1 0 1 0 -1 1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 217 1 none
Polytope 3326
Image of polytope 3326 PALP id: 3326
grdb id: 545188
Integer points: [ 1 0 0 -1 -6 -2 -3 -4 -5 -1 -2 -3 -4 -1 -2 0 -1 -2 0]
[ 0 1 0 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 1 2 -3 1 0 -1 -2 1 0 -1 -2 0 -1 1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 218 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 73 1 none
Polytope 3327
Image of polytope 3327 PALP id: 3327
grdb id: 545227
Integer points: [ 1 1 0 -7 -9 -8 -6 -5 -4 -3 -3 -2 -1 0 -4 -3 -1 0 1]
[ 0 2 0 -4 -6 -5 -4 -3 -2 -1 -2 -1 0 1 -3 -2 -1 0 1]
[ 0 0 1 -2 -2 -2 -1 -1 -1 -1 0 0 0 0 -1 -1 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 219 1 none
Image of facet 14 1 none
Polytope 3328
Image of polytope 3328 PALP id: 3328
grdb id: 545072
Integer points: [ 1 1 -1 1 -3 0 -1 -2 1 0 -1 0 -1 -2 1 0 -1 1 0]
[ 0 2 -2 0 0 0 0 0 1 1 1 -1 -1 -1 0 0 0 1 -1]
[ 0 0 0 2 -2 1 0 -1 1 0 -1 1 0 -1 1 0 -1 0 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
22 ? x*y2 + 2*x*y*z + x*z2 + 2*x*y + 2*x*z + x + 4*y + 4*z + 2*y-1*z + 2*x-1*y*z-1 + 2*y-1 + 6*x-1 + 2*x-1*z-1 + 4*x-1*y-1 + 4*x-2*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 4 Lattice Minkowski decompositions of facet 16
Image of facet 32 2 Lattice Minkowski decompositions of facet 32
Polytope 3329
Image of polytope 3329 PALP id: 3329
grdb id: 526889
Integer points: [ 1 1 0 -2 0 -4 -3 -2 -1 -3 -2 -1 0 -2 -1 0 -1 0 1]
[ 0 2 0 -2 2 -2 -1 0 1 -2 -1 0 1 -1 0 1 -1 0 1]
[ 0 0 1 -1 1 1 1 1 1 0 0 0 0 1 1 1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
24 ? x*y2 + y2*z + 2*x*y + 2*y*z + x + 4*y + z + 4*x-1*y*z + 4*x-1*z + 6*x-1 + 6*x-2*z + 2*x-1*y-1 + 2*x-2*y-1*z + 4*x-2*y-1 + 4*x-3*y-1*z + x-2*y-2*z-1 + 2*x-3*y-2 + x-4*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 1 irreducible and admissible
Image of facet 133 1 Lattice Minkowski decompositions of facet 133
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3330
Image of polytope 3330 PALP id: 3330
grdb id: 526891
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0]
[ 0 1 1 0 0 -2 0 0 0 -1 -1 -1 1 1 1 0 0 0 -1]
[ 0 0 4 2 -2 -4 1 0 -1 -1 -2 -3 3 2 1 1 0 -1 -2]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
11 rank 2, number 6 y*z4 + 4*y*z3 + 6*y*z2 + 4*y*z + x + y + 2*z + x-1*z2 + 4*x-1*z + 2*z-1 + 6*x-1 + 4*x-1*z-1 + 2*y-1*z-2 + x-1*z-2 + 2*x-1*y-1*z-1 + 4*x-1*y-1*z-2 + 2*x-1*y-1*z-3 + x-1*y-2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 13 1 irreducible and admissible
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Image of facet 134 1 Lattice Minkowski decompositions of facet 134
Polytope 3331
Image of polytope 3331 PALP id: 3331
grdb id: 526296
Integer points: [ 1 0 0 -1 -3 -3 -2 -3 -2 -1 -3 -2 -1 -2 -1 -1 0 -1 0]
[ 0 1 0 -2 -2 1 -2 -1 -1 -1 0 0 0 1 1 -1 -1 0 0]
[ 0 0 1 2 0 -3 1 -1 0 1 -2 -1 0 -2 -1 0 1 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 220 1 Lattice Minkowski decompositions of facet 220
Image of facet 14 1 none
Polytope 3332
Image of polytope 3332 PALP id: 3332
grdb id: 526278
Integer points: [ 1 0 0 2 -3 0 0 0 -1 -1 -1 -2 -2 1 1 0 0 -1 1]
[ 0 1 0 -1 0 -3 -2 -1 -2 -1 0 -1 0 -2 -1 -1 0 0 0]
[ 0 0 1 -2 1 -2 -1 0 -1 0 1 0 1 -2 -1 -1 0 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + 2*x*z-1 + 3*x-1*z + x2*y-1*z-2 + 3*x*y-1*z-1 + 3*y-1 + 2*x-1 + 3*x-2*z + 4*y-1*z-1 + 6*x-1*y-1 + x-3*z + 2*x*y-2*z-2 + 3*y-2*z-1 + 3*x-2*y-1 + 3*x-1*y-2*z-1 + y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Polytope 3333
Image of polytope 3333 PALP id: 3333
grdb id: 526321
Integer points: [ 1 0 1 -3 -3 -1 -2 0 -1 -2 -3 0 -1 -2 0 -1 1 0 -1]
[ 0 1 0 0 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 0 0 0]
[ 0 0 2 -2 0 2 1 2 1 0 -1 1 0 -1 1 0 1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x*z2 + 2*x*z + x + y + 2*z + 2*y-1*z2 + 2*y-1*z + x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-2*z-1 + 5*x-2*y-1 + 2*x-2*y-2*z + x-3*z-2 + 2*x-3*y-1*z-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 3 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 221 1 Lattice Minkowski decompositions of facet 221
Polytope 3334
Image of polytope 3334 PALP id: 3334
grdb id: 526350
Integer points: [ 1 0 1 1 -3 -1 0 -2 -1 0 1 -2 -1 0 0 1 -1 0 1]
[ 0 1 0 -2 0 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 0 0 0]
[ 0 0 2 0 -2 -2 -1 -2 -1 0 1 -1 0 1 -1 0 -1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x*z2 + 2*x*z + x + y + 2*x*y-1*z + 4*z + 2*x*y-1 + x*y-2 + 6*y-1 + 6*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + 2*y-2*z-1 + 6*x-1*y-1*z-1 + 4*x-2*z-1 + x-1*y-2*z-2 + 2*x-2*y-1*z-2 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3335
Image of polytope 3335 PALP id: 3335
grdb id: 526359
Integer points: [ 1 1 -1 0 -1 -3 -2 -1 -2 -1 0 0 -2 -1 -1 0 0 1 0]
[ 0 2 -2 0 2 0 0 0 1 1 1 2 -1 -1 0 0 1 1 -1]
[ 0 0 0 1 -2 -2 -1 0 -2 -1 0 -1 -1 0 -1 0 -1 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 14 1 none
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Polytope 3336
Image of polytope 3336 PALP id: 3336
grdb id: 526335
Integer points: [ 1 0 0 0 -2 -4 -3 -2 -1 -3 -2 -1 0 -1 -2 -1 0 -1 0]
[ 0 1 -1 1 -1 1 1 1 1 0 0 0 0 -1 1 1 1 0 0]
[ 0 0 0 2 -2 -2 -1 0 1 -2 -1 0 1 -1 -1 0 1 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 y*z2 + 2*y*z + x + y + 2*z + 4*x-1*y*z + 4*x-1*y + y-1 + 6*x-1 + 6*x-2*y + 2*x-1*z-1 + 2*x-2*y*z-1 + 2*x-1*y-1*z-1 + 6*x-2*z-1 + 4*x-3*y*z-1 + x-2*y-1*z-2 + 2*x-3*z-2 + x-4*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 3 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3337
Image of polytope 3337 PALP id: 3337
grdb id: 526881
Integer points: [ 1 0 1 -3 -1 1 0 -2 -1 0 1 -2 -1 0 0 1 -1 0 1]
[ 0 1 0 0 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 0 0 0]
[ 0 0 2 -2 2 4 3 0 1 2 3 -1 0 1 1 2 -1 0 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 3 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 222 1 none
Polytope 3338
Image of polytope 3338 PALP id: 3338
grdb id: 526791
Integer points: [ 1 1 -3 0 -4 1 1 0 -1 0 -1 -2 -1 -2 -3 1 1 0 -1]
[ 0 2 -2 0 -4 4 3 1 -1 2 0 -2 1 -1 -3 1 2 0 -1]
[ 0 0 0 1 1 -2 -1 0 1 -1 0 1 -1 0 1 0 -1 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x*y4*z-2 + 2*x*y3*z-1 + x*y2 + 2*x*y2*z-1 + 2*x*y + 4*y2*z-1 + x + 5*y + z + 2*x-1*y*z-1 + 8*x-1 + 4*x-1*y-1*z + 2*x-1*y-1 + 5*x-2*y-1 + 6*x-2*y-2*z + x-3*y-2 + 4*x-3*y-3*z + x-4*y-4*z
40 rank 2, number 10 x*y4*z-2 + 2*x*y3*z-1 + x*y2 + 2*x*y2*z-1 + 2*x*y + 5*y2*z-1 + x + 6*y + z + 2*x-1*y*z-1 + 10*x-1 + 4*x-1*y-1*z + 2*x-1*y-1 + 6*x-2*y-1 + 6*x-2*y-2*z + x-3*y-2 + 4*x-3*y-3*z + x-4*y-4*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 223 1 Lattice Minkowski decompositions of facet 223
Polytope 3339
Image of polytope 3339 PALP id: 3339
grdb id: 526756
Integer points: [ 1 0 0 -4 -5 -1 -2 -3 -4 -1 -2 -3 0 -1 -2 0 -1 -2 0]
[ 0 1 1 -3 -4 0 -1 -2 -3 0 -1 -2 1 0 -1 0 -1 -2 0]
[ 0 0 2 -2 -2 2 1 0 -1 1 0 -1 1 0 -1 1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
32 ? y*z2 + 2*y*z + x + y + 2*z + x-1*z2 + 6*x-1*z + 5*x-1 + 4*x-1*y-1 + 4*x-2*y-1*z + 10*x-2*y-1 + 2*x-2*y-1*z-1 + 2*x-2*y-2*z-1 + 6*x-3*y-2 + 6*x-3*y-2*z-1 + 4*x-4*y-3*z-1 + x-4*y-3*z-2 + x-5*y-4*z-2
8 ? y*z2 + 2*y*z + x + y + 2*z + x-1*z2 + 5*x-1*z + 4*x-1 + 4*x-1*y-1 + 4*x-2*y-1*z + 8*x-2*y-1 + 2*x-2*y-1*z-1 + 2*x-2*y-2*z-1 + 6*x-3*y-2 + 5*x-3*y-2*z-1 + 4*x-4*y-3*z-1 + x-4*y-3*z-2 + x-5*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 4 irreducible and admissible
Image of facet 223 1 Lattice Minkowski decompositions of facet 223
Polytope 3340
Image of polytope 3340 PALP id: 3340
grdb id: 526273
Integer points: [ 1 0 0 -2 -2 -5 -4 -3 -4 -3 -2 -3 -2 -1 -1 -2 -1 -1 0]
[ 0 1 0 -1 -1 -4 -3 -2 -3 -2 -1 -2 -1 0 0 -2 -1 -1 0]
[ 0 0 1 -1 2 2 1 0 2 1 0 2 1 0 1 1 0 1 0]
Degree: 40
Hilbert function: 1 + 23 t + 105 t2 + 287 t3 + 609 t4 + 1111 t5 + 1833 t6 + 2815 t7 + 4097 t8 + 5719 t9 + 7721 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 194 1 Lattice Minkowski decompositions of facet 194
Image of facet 14 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3341
Image of polytope 3341 PALP id: 3341
grdb id: 526344
Integer points: [ 1 0 1 -3 -3 -5 0 -1 -2 -1 -2 -3 -4 -4 1 0 -1 -1 -2]
[ 0 1 0 0 -2 -2 0 0 0 -1 -1 -1 -1 -2 0 0 0 -1 -1]
[ 0 0 2 -2 -2 -4 1 0 -1 0 -1 -2 -3 -3 1 0 -1 -1 -2]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x*z2 + 2*x*z + x + y + 4*z + 6*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 4*x-2*z-1 + 6*x-2*y-1*z-1 + 2*x-2*y-1*z-2 + x-3*z-2 + 6*x-3*y-1*z-2 + x-3*y-2*z-2 + 2*x-4*y-1*z-3 + 2*x-4*y-2*z-3 + x-5*y-2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3342
Image of polytope 3342 PALP id: 3342
grdb id: 526281
Integer points: [ 1 0 0 -1 -4 -7 -5 -3 -6 -4 -2 -5 -3 -1 -2 -3 -1 -2 0]
[ 0 1 0 -1 -1 -4 -3 -2 -3 -2 -1 -2 -1 0 0 -2 -1 -1 0]
[ 0 0 1 1 -2 -2 -1 0 -2 -1 0 -2 -1 0 -1 -1 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 220 1 Lattice Minkowski decompositions of facet 220
Image of facet 14 2 none
Polytope 3343
Image of polytope 3343 PALP id: 3343
grdb id: 526648
Integer points: [ 1 0 0 -1 -2 -6 -5 -4 -3 -4 -3 -2 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 -1 -2 -2 -2 -2 -2 -1 -1 -1 0 0 -1 -1 -1 0 0]
[ 0 0 1 -1 -1 3 2 1 0 2 1 0 1 0 2 1 0 1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 80 1 none
Image of facet 148 1 none
Image of facet 14 1 none
Polytope 3344
Image of polytope 3344 PALP id: 3344
grdb id: 526650
Integer points: [ 1 0 1 0 -2 -8 -6 -4 -2 -5 -3 -1 -2 0 -5 -3 -1 -2 0]
[ 0 1 -1 0 0 -4 -3 -2 -1 -3 -2 -1 -2 -1 -2 -1 0 -1 0]
[ 0 0 0 1 -1 -3 -2 -1 0 -2 -1 0 -1 0 -2 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 80 1 none
Image of facet 121 1 none
Polytope 3345
Image of polytope 3345 PALP id: 3345
grdb id: 526843
Integer points: [ 1 0 0 -2 -4 -10 -2 -4 -6 -8 -1 -3 -5 -1 -3 -5 -7 0 -2]
[ 0 1 0 -2 -3 -5 -1 -2 -3 -4 0 -1 -2 -1 -2 -3 -4 0 -1]
[ 0 0 1 -1 -2 -4 0 -1 -2 -3 0 -1 -2 0 -1 -2 -3 0 -1]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 73 1 none
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Polytope 3346
Image of polytope 3346 PALP id: 3346
grdb id: 525719
Integer points: [ 1 0 0 0 -2 -2 0 -1 -1 -1 -1 -2 -2 -2 0 0 -1 -1 -1]
[ 0 1 -1 1 -3 1 0 1 0 -1 -2 0 -1 -2 1 0 1 0 -1]
[ 0 0 0 2 -2 2 1 2 1 0 -1 1 0 -1 1 0 1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 y*z2 + 2*y*z + 2*x-1*y*z2 + x + y + 2*z + 2*x-1*y*z + x-2*y*z2 + 6*x-1*z + y-1 + 4*x-1 + 4*x-2*z + 6*x-1*y-1 + 2*x-1*y-1*z-1 + 6*x-2*y-1 + 2*x-1*y-2*z-1 + 4*x-2*y-2*z-1 + x-2*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 4 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3347
Image of polytope 3347 PALP id: 3347
grdb id: 525733
Integer points: [ 1 0 1 -3 -1 1 0 -1 -2 1 0 -1 -2 1 0 -1 0 1 0]
[ 0 1 0 0 -2 -2 0 0 0 -1 -1 -1 -1 0 0 0 -2 -1 -1]
[ 0 0 2 -2 0 2 1 0 -1 2 1 0 -1 1 0 -1 1 1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? x*z2 + 2*x*z + 2*x*y-1*z2 + x + y + 2*x*y-1*z + 4*z + x*y-2*z2 + 6*y-1*z + 2*y-1 + 6*x-1 + 2*y-2*z + 2*x-1*z-1 + 6*x-1*y-1 + 4*x-2*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 3 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3348
Image of polytope 3348 PALP id: 3348
grdb id: 525745
Integer points: [ 1 1 -1 -1 1 -3 0 0 -1 -2 -2 1 0 1 0 -1 0 -1 1]
[ 0 2 0 -2 0 -2 -1 0 -1 -2 -1 0 -1 1 0 -1 1 0 1]
[ 0 0 0 0 2 -2 1 1 0 -1 -1 1 0 1 0 -1 0 -1 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
11 rank 2, number 6 x*y2 + 2*x*y*z + x*z2 + 2*x*y + 2*x*z + x + 2*y + 2*z + 2*y-1*z + 2*y-1 + x-1 + 2*x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + 2*x-2*y-2*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 6 Lattice Minkowski decompositions of facet 16
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Polytope 3349
Image of polytope 3349 PALP id: 3349
grdb id: 525553
Integer points: [ 1 1 1 -1 -1 -1 0 0 1 -1 0 -1 0 1 0 1 -1 0 0]
[ 0 2 0 0 -2 0 1 0 1 0 1 -1 0 1 -1 0 -1 0 -1]
[ 0 0 2 -2 0 0 -1 -1 0 -1 0 -1 0 1 0 1 0 1 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
22 ? x*y2 + 2*x*y*z + x*z2 + 2*x*y + 2*x*z + x + 2*y + 2*z + 2*y*z-1 + 2*y-1*z + 2*z-1 + 2*y-1 + x-1 + 2*x-1*z-1 + 2*x-1*y-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 8 Lattice Minkowski decompositions of facet 16
Polytope 3350
Image of polytope 3350 PALP id: 3350
grdb id: 458642
Integer points: [ 1 0 -2 1 -1 0 -2 -1 -2 -1 0 -1 0 -1 0 -1 0 1 0]
[ 0 1 1 0 -2 1 -1 1 0 0 0 -1 -1 1 1 0 0 0 -1]
[ 0 0 0 2 -2 2 -2 1 -1 0 1 -1 0 0 1 -1 0 1 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x*z2 + y*z2 + 2*x*z + 2*y*z + x + y + 4*z + 2*x-1*y*z + 2*x-1*y + 2*y-1 + 6*x-1 + x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + 4*x-1*y-1*z-1 + 2*x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
26 rank 2, number 8 x*z2 + y*z2 + 2*x*z + 2*y*z + x + y + 2*z + 2*x-1*y*z + 2*x-1*y + 2*y-1 + 3*x-1 + x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 3 Lattice Minkowski decompositions of facet 16
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Image of facet 135 1 Lattice Minkowski decompositions of facet 135
Polytope 3351
Image of polytope 3351 PALP id: 3351
grdb id: 458556
Integer points: [ 1 0 1 0 -2 -1 -2 -2 -1 0 -2 -1 0 -1 -1 0 -1 0 1]
[ 0 1 -2 0 2 -2 -1 0 -1 -2 1 0 -1 1 0 -1 1 0 -1]
[ 0 0 0 1 1 -2 -2 -1 -1 -1 0 0 0 1 -1 -1 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 155 1 Lattice Minkowski decompositions of facet 155
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3352
Image of polytope 3352 PALP id: 3352
grdb id: 458617
Integer points: [ 1 0 0 -1 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 2 -2 -1 3 0 1 2 -1 0 1 0 1 2 -1 0 1]
[ 0 0 1 2 -2 -2 2 -1 0 1 -1 0 1 -1 0 1 -1 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
101 ? x-1*y2*z2 + x-2*y3*z2 + 2*y*z + 2*x-1*y2*z + x + y + z + 5*x-1*y*z + 4*x-2*y2*z + 4*x-1*y + 6*x-1 + 6*x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + 4*x-1*y-1*z-1 + 4*x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
52 rank 2, number 52 x-1*y2*z2 + x-2*y3*z2 + 2*y*z + 2*x-1*y2*z + x + y + z + 2*x-1*y*z + 4*x-2*y2*z + 4*x-1*y + 3*x-1 + 6*x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1*z-1 + 4*x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 2 irreducible and admissible
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Image of facet 137 1 Lattice Minkowski decompositions of facet 137
Polytope 3353
Image of polytope 3353 PALP id: 3353
grdb id: 458586
Integer points: [ 1 0 0 0 -1 -1 -4 -3 -2 -3 -2 -1 -2 -1 -2 -1 -1 0 0]
[ 0 1 -1 0 1 -2 1 1 1 0 0 0 -1 -1 1 1 0 0 -1]
[ 0 0 0 1 1 -2 -2 -1 0 -2 -1 0 -2 -1 -1 0 -1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 153 1 Lattice Minkowski decompositions of facet 153
Image of facet 14 1 none
Polytope 3354
Image of polytope 3354 PALP id: 3354
grdb id: 458626
Integer points: [ 1 0 0 1 -3 -4 0 -1 -2 -3 0 -1 -2 0 -1 -2 1 0 -1]
[ 0 1 -1 0 0 1 1 1 1 1 0 0 0 1 1 1 0 0 0]
[ 0 0 0 2 -2 -2 2 1 0 -1 1 0 -1 1 0 -1 1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
75 ? x*z2 + y*z2 + 2*x*z + 2*y*z + x + y + 4*z + 4*x-1*y*z + 4*x-1*y + y-1 + 7*x-1 + 6*x-2*y + 2*x-1*z-1 + 2*x-2*y*z-1 + 4*x-2*z-1 + 4*x-3*y*z-1 + x-3*z-2 + x-4*y*z-2
13 rank 2, number 12 x*z2 + y*z2 + 2*x*z + 2*y*z + x + y + 2*z + 4*x-1*y*z + 4*x-1*y + y-1 + 2*x-1 + 6*x-2*y + 2*x-1*z-1 + 2*x-2*y*z-1 + 2*x-2*z-1 + 4*x-3*y*z-1 + x-3*z-2 + x-4*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 2 irreducible and admissible
Image of facet 139 1 Lattice Minkowski decompositions of facet 139
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3355
Image of polytope 3355 PALP id: 3355
grdb id: 458803
Integer points: [ 1 0 0 1 -2 1 -4 -1 0 -1 -2 -3 0 -1 -2 -3 1 0 -1]
[ 0 1 0 -2 2 -3 2 1 -1 0 1 2 -2 -1 0 1 -1 0 1]
[ 0 0 1 2 -1 2 -3 0 1 0 -1 -2 1 0 -1 -2 1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 1 none
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 43 1 irreducible and admissible
Image of facet 201 1 Lattice Minkowski decompositions of facet 201
Polytope 3356
Image of polytope 3356 PALP id: 3356
grdb id: 458619
Integer points: [ 1 0 0 -2 -2 2 2 -1 0 1 -1 0 1 -1 0 1 -1 0 1]
[ 0 1 0 1 0 -3 -4 -1 -2 -3 0 -1 -2 0 -1 -2 1 0 -1]
[ 0 0 1 -2 -1 2 3 0 1 2 -1 0 1 0 1 2 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 x + y + 3*x*y-1*z + z + x2*y-3*z2 + 2*x*y-2*z2 + x2*y-4*z3 + 4*x*y-2*z + 4*y-1*z + 4*x*y-3*z2 + 2*x-1*y*z-1 + 6*y-1 + 2*x-1 + 6*y-2*z + 4*x-1*z-1 + 4*x-1*y-1 + x-2*y*z-2 + x-2*z-1
20 rank 1, V16 x + y + 2*x*y-1*z + z + x2*y-3*z2 + 2*x*y-2*z2 + x2*y-4*z3 + 4*x*y-2*z + 4*y-1*z + 4*x*y-3*z2 + 2*x-1*y*z-1 + 6*y-1 + 2*x-1 + 6*y-2*z + 4*x-1*z-1 + 4*x-1*y-1 + x-2*y*z-2 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 1 irreducible and admissible
Image of facet 134 1 Lattice Minkowski decompositions of facet 134
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 13 1 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3357
Image of polytope 3357 PALP id: 3357
grdb id: 457578
Integer points: [ 1 0 0 -1 -1 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 0 1 1 1 -3 0 -1 -2 1 0 -1 -2 0 -1 0 -1 0]
[ 0 0 1 0 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 64 1 none
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Polytope 3358
Image of polytope 3358 PALP id: 3358
grdb id: 456770
Integer points: [ 1 0 0 -1 0 -3 -3 -2 -1 -3 -2 -1 0 -2 -1 -1 0 -1 0]
[ 0 1 0 1 -2 0 -2 0 0 -1 -1 -1 -1 -2 -2 0 0 -1 -1]
[ 0 0 1 -1 1 -2 -2 -1 0 -2 -1 0 1 -1 0 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Image of facet 14 1 none
Polytope 3359
Image of polytope 3359 PALP id: 3359
grdb id: 456289
Integer points: [ 1 0 0 -1 1 0 -3 -1 -2 0 -1 -2 0 -1 -1 -2 0 -1 0]
[ 0 1 0 1 -1 -3 -3 -1 -2 -1 -2 -3 -2 -3 0 -1 0 -1 -1]
[ 0 0 1 0 -1 -2 -2 0 -1 0 -1 -2 -1 -2 0 -1 0 -1 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 14 1 none
Polytope 3360
Image of polytope 3360 PALP id: 3360
grdb id: 456303
Integer points: [ 1 0 0 0 -1 0 -3 -2 -1 -2 -1 0 -1 0 -2 -1 0 -1 0]
[ 0 1 0 1 1 -2 1 0 -1 1 0 -1 1 0 1 0 -1 1 0]
[ 0 0 1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + y*z-1 + 3*x-1*y + 3*z-1 + 3*x-1*y*z-1 + 2*y-1 + 4*x-1 + 2*x-2*y + 3*y-1*z-1 + 6*x-1*z-1 + 3*x-2*y*z-1 + y-2*z-1 + 3*x-1*y-1*z-1 + 3*x-2*z-1 + x-3*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Polytope 3361
Image of polytope 3361 PALP id: 3361
grdb id: 456569
Integer points: [ 1 0 -1 0 0 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0 0]
[ 0 1 1 1 -3 1 -3 0 -1 -2 0 -1 -2 1 0 -1 1 0 -1]
[ 0 0 0 2 -2 2 -2 1 0 -1 1 0 -1 1 0 -1 1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 y*z2 + 2*y*z + x-1*y*z2 + x + y + 4*z + 2*x-1*y*z + x-1*y + 4*x-1*z + 6*y-1 + 4*x-1 + 2*y-1*z-1 + 6*x-1*y-1 + 4*y-2*z-1 + 2*x-1*y-1*z-1 + 4*x-1*y-2*z-1 + y-3*z-2 + x-1*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 2 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 134 1 Lattice Minkowski decompositions of facet 134
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3362
Image of polytope 3362 PALP id: 3362
grdb id: 456388
Integer points: [ 1 0 0 -2 -3 -1 -3 -3 -2 -2 -2 -1 -1 -1 0 -1 -1 0 0]
[ 0 1 1 -1 -2 0 -2 -2 -1 -1 -1 0 0 0 1 -1 -1 0 0]
[ 0 0 2 -2 -2 2 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 y*z2 + 2*y*z + x + y + 2*z + x-1*z2 + 4*x-1*z + 5*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-2*y-1*z + 2*x-1*y-1*z-1 + 5*x-2*y-1 + 4*x-2*y-1*z-1 + x-2*y-1*z-2 + x-3*y-2 + 2*x-3*y-2*z-1 + x-3*y-2*z-2
17 rank 1, V22 y*z2 + 2*y*z + x + y + 2*z + x-1*z2 + 5*x-1*z + 6*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-2*y-1*z + 2*x-1*y-1*z-1 + 6*x-2*y-1 + 5*x-2*y-1*z-1 + x-2*y-1*z-2 + x-3*y-2 + 2*x-3*y-2*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 4 irreducible and admissible
Image of facet 224 1 Lattice Minkowski decompositions of facet 224
Polytope 3363
Image of polytope 3363 PALP id: 3363
grdb id: 457407
Integer points: [ 1 0 0 -1 -2 -3 -3 -3 -3 -3 -2 -2 -2 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 -2 -2 -2 -2 -2 -1 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 1 -1 2 -2 2 1 0 -1 1 0 -1 1 0 1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 202 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 3364
Image of polytope 3364 PALP id: 3364
grdb id: 456230
Integer points: [ 1 0 0 -2 0 -1 -4 -2 -1 0 -3 -2 -1 -3 0 -1 0 -2 -1]
[ 0 1 0 1 -2 -2 1 -1 -1 -1 0 0 0 1 -1 0 0 1 1]
[ 0 0 1 0 -1 -2 -2 -2 -1 0 -2 -1 0 -1 -1 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + 2*x-1*y + 2*y-1 + 3*x-1 + x-2*y + 2*y-1*z-1 + 4*x-1*z-1 + 2*x-2*y*z-1 + y-2*z-1 + 4*x-1*y-1*z-1 + 5*x-2*z-1 + 2*x-3*y*z-1 + x-1*y-2*z-2 + 3*x-2*y-1*z-2 + 3*x-3*z-2 + x-4*y*z-2
17 rank 1, V22 x + y + z + 2*x-1*y + 2*y-1 + 4*x-1 + x-2*y + 2*y-1*z-1 + 4*x-1*z-1 + 2*x-2*y*z-1 + y-2*z-1 + 5*x-1*y-1*z-1 + 6*x-2*z-1 + 2*x-3*y*z-1 + x-1*y-2*z-2 + 3*x-2*y-1*z-2 + 3*x-3*z-2 + x-4*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 155 1 Lattice Minkowski decompositions of facet 155
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 3365
Image of polytope 3365 PALP id: 3365
grdb id: 456769
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 -1 -2 -4 0 -1 0 -1 -2 -3 -2 -3 0 -1 -1 -2]
[ 0 0 1 1 1 -2 -2 0 -1 1 0 -1 -2 0 -1 0 -1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y*z + 2*x-1*z + 3*y-1 + 3*x-1 + x-1*y-1*z + 2*y-1*z-1 + 6*x-1*y-1 + 2*y-2*z-1 + 3*x-1*y-1*z-1 + 3*x-1*y-2 + 6*x-1*y-2*z-1 + x-1*y-2*z-2 + 3*x-1*y-3*z-1 + 2*x-1*y-3*z-2 + x-1*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Polytope 3366
Image of polytope 3366 PALP id: 3366
grdb id: 456529
Integer points: [ 1 0 0 0 -2 -1 -2 0 -1 -1 -1 -1 -2 -2 -2 0 0 -1 -1]
[ 0 1 0 -2 0 -2 -4 -1 -3 -2 -1 0 -3 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 1 -2 -3 0 -2 -1 0 1 -2 -1 0 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 64 1 none
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3367
Image of polytope 3367 PALP id: 3367
grdb id: 457562
Integer points: [ 1 0 0 0 -1 -2 -4 -1 -2 -3 -1 -2 -3 -1 -2 -1 0 -1 0]
[ 0 1 0 1 -2 1 1 1 1 1 0 0 0 -1 -1 1 0 0 -1]
[ 0 0 1 1 0 -2 -3 0 -1 -2 0 -1 -2 0 -1 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 148 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3368
Image of polytope 3368 PALP id: 3368
grdb id: 456285
Integer points: [ 1 0 0 0 -1 -1 -4 -3 -2 -3 -2 -1 -2 -1 -2 -1 -1 0 0]
[ 0 1 0 0 1 -2 -2 -1 0 -2 -1 0 -2 -1 -1 0 -1 0 -1]
[ 0 0 1 -1 0 0 -3 -2 -1 -2 -1 0 -1 0 -2 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y + z-1 + 2*y-1 + 2*x-1 + 3*x-1*z-1 + 2*x-1*y-1 + 4*x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2 + 5*x-2*y-1*z-1 + 2*x-2*y-1*z-2 + 3*x-2*y-2*z-1 + 3*x-3*y-1*z-2 + 3*x-3*y-2*z-2 + x-4*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 132 1 Lattice Minkowski decompositions of facet 132
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3369
Image of polytope 3369 PALP id: 3369
grdb id: 456284
Integer points: [ 1 0 0 0 -1 -1 -4 -2 -1 -3 -2 -1 -3 -2 -1 0 -2 -1 0]
[ 0 1 0 1 1 -2 1 1 0 1 0 -1 0 -1 1 0 1 0 -1]
[ 0 0 1 -1 0 0 -3 -1 0 -2 -1 0 -2 -1 -1 0 -2 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 124 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3370
Image of polytope 3370 PALP id: 3370
grdb id: 456302
Integer points: [ 1 0 1 0 -1 -1 -4 -3 -2 -3 -2 -1 -2 -1 -2 -1 -1 0 0]
[ 0 1 -1 0 1 -2 -2 -1 0 -2 -1 0 -2 -1 -1 0 -1 0 -1]
[ 0 0 0 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*y-1 + x-1*y*z-1 + 3*y-1 + 3*x-1 + 3*x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + 3*x-2*z-1 + 2*x-2*y-1 + x-1*y-2*z-1 + 6*x-2*y-1*z-1 + 3*x-2*y-2*z-1 + 3*x-3*y-1*z-1 + 3*x-3*y-2*z-1 + x-4*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 56 1 Lattice Minkowski decompositions of facet 56
Polytope 3371
Image of polytope 3371 PALP id: 3371
grdb id: 457568
Integer points: [ 1 0 0 -1 -1 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 1 -1 2 -1 3 2 1 0 2 1 0 -1 1 0 1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 64 1 none
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Polytope 3372
Image of polytope 3372 PALP id: 3372
grdb id: 455988
Integer points: [ 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 -1 2 -3 -4 0 1 -2 -1 0 -3 -2 -1 0 1 -2 -1]
[ 0 0 1 1 -2 1 1 0 -1 1 0 -1 1 0 1 0 -1 1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + 2*y*z-1 + 3*y-1*z + x-1*y2*z-2 + 3*x-1*y*z-1 + 3*y-1 + 3*x-1 + 3*y-2*z + x-1*y-1*z + 3*x-1*z-1 + 6*x-1*y-1 + y-3*z + 3*x-1*y-2*z + 3*x-1*y-2 + 3*x-1*y-3*z + x-1*y-4*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Polytope 3373
Image of polytope 3373 PALP id: 3373
grdb id: 456763
Integer points: [ 1 0 0 0 -1 -1 -3 -2 -1 -2 -1 0 -2 -1 0 -1 0 0 0]
[ 0 1 -1 1 -2 0 -2 -1 0 -2 -1 0 -1 0 1 -1 0 -1 0]
[ 0 0 0 2 -2 -2 -4 -2 0 -3 -1 1 -3 -1 1 -2 0 -1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 y*z2 + 2*y*z + x + y + 2*z + 2*z-1 + y-1 + 3*x-1 + 2*y-1*z-1 + 4*x-1*z-1 + x-1*z-2 + 4*x-1*y-1*z-1 + 4*x-1*y-1*z-2 + x-1*y-2*z-2 + 3*x-2*y-1*z-2 + 2*x-2*y-1*z-3 + 2*x-2*y-2*z-3 + x-3*y-2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Polytope 3374
Image of polytope 3374 PALP id: 3374
grdb id: 456807
Integer points: [ 1 0 0 0 0 -2 -2 -1 -2 -1 0 -1 -1 0 -1 0 -1 0 0]
[ 0 1 1 -1 -1 -1 -3 0 -2 -1 0 -2 0 1 -1 0 -2 -1 0]
[ 0 0 2 0 -2 -2 -4 0 -3 -1 1 -2 -1 1 -2 0 -3 -1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 y*z2 + 2*y*z + x + y + 2*z + 2*z-1 + y-1 + 2*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + y-1*z-2 + 4*x-1*y-1*z-1 + 4*x-1*y-1*z-2 + 2*x-1*y-2*z-2 + x-2*y-1*z-2 + 2*x-1*y-2*z-3 + 2*x-2*y-2*z-3 + x-2*y-3*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 3 irreducible and admissible
Image of facet 36 2 Lattice Minkowski decompositions of facet 36
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 3375
Image of polytope 3375 PALP id: 3375
grdb id: 456805
Integer points: [ 1 1 -1 -1 0 -3 -3 -2 -3 -2 -1 -2 -1 0 -1 0 -1 0 1]
[ 0 2 -2 0 0 -2 -4 -3 -3 -2 -1 -1 -2 -1 -1 0 0 1 1]
[ 0 0 0 0 1 -2 -2 -1 -2 -1 0 -1 -1 0 -1 0 -1 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x*y2 + 2*x*y + x + 2*y + z + 2*y-1 + x-1 + 2*x-1*z-1 + 3*x-1*y-1 + 4*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 2*x-2*y-1*z-1 + 4*x-2*y-2*z-1 + 2*x-2*y-3*z-1 + x-3*y-2*z-2 + 2*x-3*y-3*z-2 + x-3*y-4*z-2
40 rank 2, number 10 x*y2 + 2*x*y + x + 2*y + z + 2*y-1 + x-1 + 2*x-1*z-1 + 4*x-1*y-1 + 4*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 2*x-2*y-1*z-1 + 5*x-2*y-2*z-1 + 2*x-2*y-3*z-1 + x-3*y-2*z-2 + 2*x-3*y-3*z-2 + x-3*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 3 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Polytope 3376
Image of polytope 3376 PALP id: 3376
grdb id: 457565
Integer points: [ 1 0 -1 0 0 -2 -4 -3 -2 -1 -3 -2 -1 -2 -1 -1 0 -1 0]
[ 0 1 1 0 -1 -3 -5 -4 -3 -2 -3 -2 -1 -1 0 -2 -1 -1 0]
[ 0 0 0 1 1 -2 -3 -2 -1 0 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 148 1 none
Image of facet 64 1 none
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3377
Image of polytope 3377 PALP id: 3377
grdb id: 456198
Integer points: [ 1 0 0 -1 -3 -2 -5 -4 -3 -4 -3 -2 -1 -2 -1 -2 -1 -1 0]
[ 0 1 0 1 0 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 -1 -2 1 -2 -1 0 -2 -1 0 1 -1 0 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 14 1 none
Image of facet 225 1 Lattice Minkowski decompositions of facet 225
Polytope 3378
Image of polytope 3378 PALP id: 3378
grdb id: 456281
Integer points: [ 1 0 0 -1 0 -1 -4 -2 -1 -3 -2 -1 -3 -2 0 -1 0 -2 -1]
[ 0 1 0 1 -1 -2 -5 -3 -1 -4 -2 0 -3 -1 -1 -2 0 -3 -1]
[ 0 0 1 0 -1 0 -3 -1 0 -2 -1 0 -2 -1 0 -1 0 -2 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 124 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3379
Image of polytope 3379 PALP id: 3379
grdb id: 456347
Integer points: [ 1 0 0 0 -3 -2 -5 -1 -3 -2 -1 -4 -3 -2 -4 -1 0 -2 -1]
[ 0 1 0 -1 0 -2 -2 -1 -2 -1 0 -2 -1 0 -1 -1 0 -1 0]
[ 0 0 1 1 -2 1 -2 1 0 0 0 -1 -1 -1 -2 0 0 -1 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
159 ? x + y + z + y-1*z + 5*x-1 + 2*x-1*y-1*z + 2*x-1*z-1 + 3*x-1*y-1 + 3*x-2*z-1 + 7*x-2*y-1 + x-2*y-2*z + 2*x-2*y-1*z-1 + x-3*z-2 + 6*x-3*y-1*z-1 + 3*x-3*y-2 + 2*x-4*y-1*z-2 + 3*x-4*y-2*z-1 + x-5*y-2*z-2
107 rank 3, number 11 x + y + z + y-1*z + 3*x-1 + 2*x-1*y-1*z + 2*x-1*z-1 + 3*x-1*y-1 + 2*x-2*z-1 + 5*x-2*y-1 + x-2*y-2*z + 2*x-2*y-1*z-1 + x-3*z-2 + 5*x-3*y-1*z-1 + 3*x-3*y-2 + 2*x-4*y-1*z-2 + 3*x-4*y-2*z-1 + x-5*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 199 1 Lattice Minkowski decompositions of facet 199
Polytope 3380
Image of polytope 3380 PALP id: 3380
grdb id: 456300
Integer points: [ 1 0 1 0 -1 -2 -5 -3 -4 -1 -2 -3 0 -1 -1 -2 -3 0 -1]
[ 0 1 -1 0 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 0 0 1 -1 0 -3 -1 -2 0 -1 -2 0 -1 0 -1 -2 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*y-1 + x-1*y*z-1 + 3*y-1 + 3*x-1 + 3*x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + 4*x-2*z-1 + x-2*y-1 + 6*x-2*y-1*z-1 + 2*x-3*z-2 + 3*x-3*y-1*z-1 + 3*x-3*y-1*z-2 + 3*x-4*y-1*z-2 + x-5*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3381
Image of polytope 3381 PALP id: 3381
grdb id: 456371
Integer points: [ 1 0 0 -1 -3 -2 -5 -3 -4 -1 -2 -3 -4 -1 -2 -1 -2 0 -1]
[ 0 1 0 0 -2 -1 -4 -2 -3 0 -1 -2 -3 0 -1 -1 -2 0 -1]
[ 0 0 1 -1 0 2 2 2 2 1 1 1 1 0 0 1 1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
119 ? x + y + z + 2*x-1*z + 2*x-1 + 3*x-1*y-1*z + x-2*y-1*z2 + x-1*z-1 + 2*x-1*y-1 + 5*x-2*y-1*z + 3*x-2*y-1 + 2*x-2*y-2*z + 3*x-3*y-2*z2 + 5*x-3*y-2*z + x-3*y-2 + 3*x-4*y-3*z2 + 2*x-4*y-3*z + x-5*y-4*z2
126 ? x + y + z + 2*x-1*z + 3*x-1 + 3*x-1*y-1*z + x-2*y-1*z2 + x-1*z-1 + 2*x-1*y-1 + 6*x-2*y-1*z + 5*x-2*y-1 + 2*x-2*y-2*z + 3*x-3*y-2*z2 + 7*x-3*y-2*z + x-3*y-2 + 3*x-4*y-3*z2 + 2*x-4*y-3*z + x-5*y-4*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 199 1 Lattice Minkowski decompositions of facet 199
Polytope 3382
Image of polytope 3382 PALP id: 3382
grdb id: 458286
Integer points: [ 1 0 0 -1 0 -3 -5 -1 -2 -3 -4 -1 -2 0 -1 -2 -3 0 -1]
[ 0 1 0 -1 2 -2 -3 1 0 -1 -2 0 -1 1 0 -1 -2 0 -1]
[ 0 0 1 0 1 -3 -4 0 -1 -2 -3 -1 -2 1 0 -1 -2 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 146 1 Lattice Minkowski decompositions of facet 146
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Image of facet 8 1 none
Image of facet 9 1 irreducible and admissible
Polytope 3383
Image of polytope 3383 PALP id: 3383
grdb id: 456760
Integer points: [ 1 0 0 0 -2 -3 -5 -1 -2 -1 -2 -3 -4 -3 -4 0 -1 -1 -2]
[ 0 1 -1 0 2 0 2 0 0 1 1 1 1 2 2 0 0 1 1]
[ 0 0 0 1 -1 -2 -4 0 -1 0 -1 -2 -3 -2 -3 0 -1 -1 -2]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + 2*x-1*y + 3*x-1*y*z-1 + x-2*y2*z-1 + y-1 + 3*x-1 + 2*x-1*z-1 + 6*x-2*y*z-1 + 2*x-2*y*z-2 + 3*x-3*y2*z-2 + 3*x-2*z-1 + 6*x-3*y*z-2 + 3*x-4*y2*z-3 + x-3*z-2 + 2*x-4*y*z-3 + x-5*y2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Polytope 3384
Image of polytope 3384 PALP id: 3384
grdb id: 458268
Integer points: [ 1 0 0 0 -1 -4 -6 -5 -4 -3 -2 -3 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 1 1 -3 -4 -3 -2 -1 0 -2 -1 0 -2 -1 0 -1 0]
[ 0 0 1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 8 1 none
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 13 1 irreducible and admissible
Image of facet 157 1 Lattice Minkowski decompositions of facet 157
Polytope 3385
Image of polytope 3385 PALP id: 3385
grdb id: 456296
Integer points: [ 1 0 0 0 -1 -3 -6 -4 -2 -5 -3 -1 -4 -2 -3 -1 -2 0 -1]
[ 0 1 -1 0 -1 0 3 2 1 2 1 0 1 0 2 1 1 0 0]
[ 0 0 0 1 -1 -2 -2 -1 0 -2 -1 0 -2 -1 -1 0 -1 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 14 1 none
Image of facet 153 1 Lattice Minkowski decompositions of facet 153
Polytope 3386
Image of polytope 3386 PALP id: 3386
grdb id: 454052
Integer points: [ 1 0 0 0 0 -2 -2 -1 -2 -1 0 -1 -1 0 -1 0 -1 0 0]
[ 0 1 1 -1 -1 1 1 0 1 0 -1 0 1 0 1 0 1 0 1]
[ 0 0 2 -2 0 2 0 -1 1 0 -1 1 0 -1 1 0 2 1 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 y*z2 + 2*y*z + 2*x-1*y*z2 + x + y + 2*z + 4*x-1*y*z + x-2*y*z2 + 2*x-1*y + 2*x-1*z + 2*x-2*y*z + 2*z-1 + y-1 + 4*x-1 + x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 4 irreducible and admissible
Image of facet 36 2 Lattice Minkowski decompositions of facet 36
Polytope 3387
Image of polytope 3387 PALP id: 3387
grdb id: 453160
Integer points: [ 1 0 0 0 -1 0 -3 -2 -1 -2 -1 0 -1 0 -2 -1 -1 0 0]
[ 0 1 0 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 0 1 1 0 -2 -2 -1 0 -2 -1 0 -2 -1 -1 0 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + x-1*y + y-1*z + 2*z-1 + 3*y-1 + 3*x-1 + 3*y-1*z-1 + 4*x-1*z-1 + 3*x-1*y-1 + y-1*z-2 + 6*x-1*y-1*z-1 + 2*x-2*z-1 + 3*x-1*y-1*z-2 + 3*x-2*y-1*z-1 + 3*x-2*y-1*z-2 + x-3*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Polytope 3388
Image of polytope 3388 PALP id: 3388
grdb id: 321878
Integer points: [ 1 0 0 1 -1 -1 0 -3 -2 -1 -2 -1 0 -2 -1 0 -1 0 0]
[ 0 1 0 -1 1 1 -2 1 0 -1 1 0 -1 1 0 -1 1 0 0]
[ 0 0 1 -1 1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
23 ? x + y + z + x-1*y*z + 2*x-1*y + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + 2*x-2*y + 2*y-1*z-1 + 4*x-1*z-1 + 2*x-2*y*z-1 + y-2*z-1 + 3*x-1*y-1*z-1 + 3*x-2*z-1 + x-3*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Polytope 3389
Image of polytope 3389 PALP id: 3389
grdb id: 321877
Integer points: [ 1 0 0 -2 1 -2 3 2 -1 1 2 -1 0 1 0 1 2 -1 0]
[ 0 1 0 2 -2 1 -2 -1 1 0 -1 1 0 -1 0 -1 -2 0 -1]
[ 0 0 1 1 0 0 -2 -2 1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
11 rank 2, number 6 x + y + z + 2*x-1*y*z + x-2*y2*z + 2*x2*y-1*z-1 + 2*x*z-1 + 2*x*y-1 + 2*x-1*y + x3*y-2*z-2 + x2*y-1*z-2 + 2*x2*y-2*z-1 + 4*x*y-1*z-1 + 2*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3390
Image of polytope 3390 PALP id: 3390
grdb id: 321866
Integer points: [ 1 0 0 -1 0 -2 -2 2 -1 -2 -1 0 1 -1 0 1 -1 0 1]
[ 0 1 0 1 -1 1 1 -3 0 1 0 -1 -2 1 0 -1 0 -1 -2]
[ 0 0 1 1 1 1 -1 -1 1 0 0 0 0 0 0 0 -1 -1 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 2 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3391
Image of polytope 3391 PALP id: 3391
grdb id: 321874
Integer points: [ 1 1 0 0 -1 -1 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 1]
[ 0 2 0 1 -3 0 -4 -1 -2 -3 0 -1 -2 -1 -2 1 0 -1 1]
[ 0 0 1 1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 0 0 0 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 2 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 3392
Image of polytope 3392 PALP id: 3392
grdb id: 321879
Integer points: [ 1 1 0 0 -1 -1 -1 -3 -2 -1 0 -1 0 1 0 1 -2 -2 -1]
[ 0 3 0 1 -3 -1 -1 -5 -3 -1 1 -2 0 2 -1 1 -3 -4 -2]
[ 0 0 1 1 -1 -1 1 -1 0 0 0 0 0 0 0 0 -1 -1 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
22 ? x*y3 + 3*x*y2 + 3*x*y + y*z + x + 3*y + z + 3*y-1 + x-1*y-1*z + 3*x-1*y-1 + x-1*y-1*z-1 + 3*x-1*y-2 + 2*x-1*y-2*z-1 + x-1*y-3*z-1 + 2*x-2*y-3 + 2*x-2*y-3*z-1 + 2*x-2*y-4*z-1 + x-3*y-5*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 65 2 Lattice Minkowski decompositions of facet 65
Polytope 3393
Image of polytope 3393 PALP id: 3393
grdb id: 320569
Integer points: [ 1 0 0 0 1 0 -2 -2 -2 -2 -1 -1 -1 0 -1 -1 -1 0 0]
[ 0 1 0 0 -1 -2 1 -2 -1 0 -2 -1 0 -1 -1 0 1 -1 0]
[ 0 0 1 -1 0 1 -2 1 0 -1 1 0 -1 0 1 0 -1 1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*y-1 + 2*y-1*z + z-1 + 2*x-1*y*z-1 + 4*y-1 + 4*x-1 + y-2*z + 2*x-1*y-1*z + 3*x-1*z-1 + 5*x-1*y-1 + 2*x-1*y-2*z + x-2*y*z-2 + 3*x-2*z-1 + 3*x-2*y-1 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 138 1 Lattice Minkowski decompositions of facet 138
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Polytope 3394
Image of polytope 3394 PALP id: 3394
grdb id: 320563
Integer points: [ 1 0 0 1 -1 -1 -2 -2 -1 0 -2 -1 0 -2 -1 -1 0 -1 0]
[ 0 1 0 -1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 1 1 1 -2 1 -2 1 1 0 0 0 -1 -1 0 0 -1 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + x*y-1*z + z + 3*y-1*z + x-1*z + 2*z-1 + 3*y-1 + 4*x-1 + 3*x-1*y-1*z + 3*x-1*z-1 + 6*x-1*y-1 + x-2*y-1*z + x-1*z-2 + 3*x-1*y-1*z-1 + 3*x-2*y-1 + 3*x-2*y-1*z-1 + x-2*y-1*z-2
56 rank 2, number 11 x + y + x*y-1*z + z + 3*y-1*z + x-1*z + 2*z-1 + 3*y-1 + 2*x-1 + 3*x-1*y-1*z + 2*x-1*z-1 + 6*x-1*y-1 + x-2*y-1*z + x-1*z-2 + 3*x-1*y-1*z-1 + 3*x-2*y-1 + 3*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3395
Image of polytope 3395 PALP id: 3395
grdb id: 321327
Integer points: [ 1 0 0 1 1 -2 0 -2 -1 0 -2 -1 -1 0 1 -1 0 -1 0]
[ 0 1 0 -1 -1 1 -1 -1 -1 -1 0 0 -1 -1 -1 0 0 1 0]
[ 0 0 1 1 -1 0 -2 -2 -1 0 -1 0 -2 -1 0 -1 0 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + x*y-1*z + z + 2*x*y-1 + 2*x-1*y + x*y-1*z-1 + 2*z-1 + 3*y-1 + 3*x-1 + x-2*y + 4*y-1*z-1 + 4*x-1*z-1 + y-1*z-2 + 3*x-1*y-1*z-1 + 2*x-2*z-1 + 2*x-1*y-1*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3396
Image of polytope 3396 PALP id: 3396
grdb id: 321233
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 -1 0 0 -1 -1 -1 0 0 0 0]
[ 0 1 1 1 -2 1 0 -2 -1 0 -1 0 -1 0 1 -1 0 1 0]
[ 0 0 2 1 -1 -1 -2 -2 -1 0 0 1 -2 -1 0 -1 0 1 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 y*z2 + 2*y*z + x + y + 3*z + x-1*y*z + 2*x-1*y + 2*z-1 + x-1*y*z-1 + 3*y-1 + 3*x-1 + 2*y-1*z-1 + 4*x-1*z-1 + x-1*z-2 + y-2*z-1 + 3*x-1*y-1*z-1 + 2*x-1*y-1*z-2 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3397
Image of polytope 3397 PALP id: 3397
grdb id: 320955
Integer points: [ 1 0 0 0 0 -2 -1 -2 -2 -2 -2 -1 -1 -1 0 -1 -1 -1 0]
[ 0 1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 1 -1 1 -2 2 2 1 0 -1 1 0 -1 0 1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 226 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 3398
Image of polytope 3398 PALP id: 3398
grdb id: 321301
Integer points: [ 1 0 0 1 -2 -2 1 0 1 0 -1 0 -1 1 0 1 0 -1 -1]
[ 0 1 0 -2 2 1 -2 -1 -2 -1 0 -1 0 -1 0 -1 0 1 1]
[ 0 0 1 0 1 0 -2 -2 -1 -1 -1 0 0 -1 -1 0 0 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*x-1*y*z + x-2*y2*z + 2*x*y-1 + 2*x-1*y + 2*x*y-1*z-1 + 2*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + 2*x*y-2*z-1 + 4*y-1*z-1 + 2*x-1*z-1 + x*y-2*z-2 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3399
Image of polytope 3399 PALP id: 3399
grdb id: 321302
Integer points: [ 1 0 0 1 1 0 -2 -2 -1 0 -1 -2 0 -1 0 -1 1 0 -1]
[ 0 1 0 0 -1 1 -1 1 1 0 0 0 -1 -1 1 1 0 0 0]
[ 0 0 1 -2 -1 -2 2 0 -1 -1 0 1 0 1 -1 0 -1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*x*z-1 + 2*y*z-1 + 2*x-1*y + 2*x-1*z + x*z-2 + y*z-2 + x*y-1*z-1 + 4*z-1 + 2*x-1*y*z-1 + 3*y-1 + 5*x-1 + x-2*y + 3*x-1*y-1*z + 2*x-2*z + x-2*y-1*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3400
Image of polytope 3400 PALP id: 3400
grdb id: 321353
Integer points: [ 1 0 1 -1 0 -2 0 -2 -1 -2 -1 0 -1 0 -1 0 1 -1 0]
[ 0 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 0 2 -2 0 -2 2 0 -1 -1 0 1 1 -1 -1 0 1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x*z2 + 2*x*z + x + y + 2*z + y-1*z2 + 2*y-1*z + 2*z-1 + y-1 + 2*x-1 + 2*x-1*y-1*z + 2*x-1*z-1 + 4*x-1*y-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-2*y-1 + 2*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3401
Image of polytope 3401 PALP id: 3401
grdb id: 321330
Integer points: [ 1 0 0 0 -1 0 -2 -2 -2 -2 -1 -1 -1 0 -1 -1 -1 0 0]
[ 0 1 0 0 1 -2 1 -2 -1 0 -2 -1 0 -1 -1 0 1 -1 0]
[ 0 0 1 -1 -1 1 0 3 2 1 2 1 0 0 2 1 0 1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + 2*x-1*y + 2*y-1*z + 4*x-1*z + 2*x-1*y-1*z2 + z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + x-2*y + y-2*z + 5*x-1*y-1*z + 3*x-2*z + 2*x-1*y-2*z2 + 3*x-2*y-1*z2 + x-2*y-2*z3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3402
Image of polytope 3402 PALP id: 3402
grdb id: 320953
Integer points: [ 1 0 0 0 0 -2 -1 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 -1 2 3 2 1 0 2 1 0 1 0 -1 1 0]
[ 0 0 1 -1 0 -2 2 2 1 0 -1 1 0 -1 1 0 -1 1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 80 1 none
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3403
Image of polytope 3403 PALP id: 3403
grdb id: 321254
Integer points: [ 1 0 0 -1 -2 2 0 2 -1 0 -1 1 0 -1 1 0 1 0 1]
[ 0 1 0 1 0 -1 -2 -2 -1 -1 0 -2 -1 0 -1 0 -1 0 0]
[ 0 0 1 0 1 -2 -1 -3 0 0 1 -2 -1 0 -1 0 -2 -1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + 2*x*z-1 + x-1*y + 2*x-1*z + x2*y-1*z-2 + 3*x*y-1*z-1 + 3*z-1 + 2*y-1 + 2*x-1 + x-2*z + 3*x*y-1*z-2 + 4*y-1*z-1 + 2*x-1*y-1 + x2*y-2*z-3 + 2*x*y-2*z-2 + y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Polytope 3404
Image of polytope 3404 PALP id: 3404
grdb id: 320907
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 2 2 -3 -1 0 1 -2 -1 0 1 -2 -1 -1 0 1]
[ 0 0 1 -1 -2 -1 2 2 1 0 2 1 0 -1 1 0 1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 178 1 Lattice Minkowski decompositions of facet 178
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 8 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3405
Image of polytope 3405 PALP id: 3405
grdb id: 321303
Integer points: [ 1 0 0 0 2 -1 -2 -3 -1 -1 -2 1 0 0 -1 -1 -2 1 0]
[ 0 1 0 1 -1 -1 1 1 1 1 1 0 0 0 0 0 0 -1 -1]
[ 0 0 1 1 -2 1 0 1 1 0 1 -1 0 -1 1 0 1 -1 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 y*z + x + y + z + 3*x-1*y*z + 2*x*z-1 + 2*x-1*y + 3*x-1*z + 3*x-2*y*z + x2*y-1*z-2 + 3*x*y-1*z-1 + 2*z-1 + 3*y-1 + 4*x-1 + x-2*y + x-1*y-1*z + 2*x-2*z + x-3*y*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3406
Image of polytope 3406 PALP id: 3406
grdb id: 320465
Integer points: [ 1 0 0 1 0 0 -2 -3 -2 -1 -2 -1 0 -1 0 -1 0 -1 0]
[ 0 1 0 -1 1 -2 1 1 0 -1 1 0 -1 1 0 0 -1 1 0]
[ 0 0 1 0 -1 -1 2 2 1 0 1 0 -1 0 -1 1 0 1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 66 1 none
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3407
Image of polytope 3407 PALP id: 3407
grdb id: 320927
Integer points: [ 1 0 -1 1 -2 0 -2 -4 -1 -2 -3 0 -1 -2 -3 -1 1 0 -1]
[ 0 1 -1 0 -1 1 1 1 1 1 1 0 0 0 0 1 0 0 0]
[ 0 0 0 2 -1 1 -2 -3 0 -1 -2 1 0 -1 -2 -1 1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 162 1 Lattice Minkowski decompositions of facet 162
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3408
Image of polytope 3408 PALP id: 3408
grdb id: 321054
Integer points: [ 1 0 0 -2 1 -2 1 0 -1 -1 -1 0 0 1 -1 0 0 1 1]
[ 0 1 0 2 -2 1 -4 -3 -1 0 1 -2 -1 -3 1 -1 0 -2 -1]
[ 0 0 1 1 0 0 -2 -2 -1 0 1 -1 0 -1 0 -1 0 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 x + y + z + 2*x-1*y*z + x-2*y2*z + 2*x*y-1 + 2*x-1*y + x*y-2 + 5*y-1 + 5*x-1 + x-2*y + 2*x*y-2*z-1 + 2*y-1*z-1 + 2*x*y-3*z-1 + 5*y-2*z-1 + 2*x-1*y-1*z-1 + x*y-4*z-2 + y-3*z-2
20 rank 1, V16 x + y + z + 2*x-1*y*z + x-2*y2*z + 2*x*y-1 + 2*x-1*y + x*y-2 + 4*y-1 + 4*x-1 + x-2*y + 2*x*y-2*z-1 + 2*y-1*z-1 + 2*x*y-3*z-1 + 4*y-2*z-1 + 2*x-1*y-1*z-1 + x*y-4*z-2 + y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 164 1 Lattice Minkowski decompositions of facet 164
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3409
Image of polytope 3409 PALP id: 3409
grdb id: 321331
Integer points: [ 1 0 0 -1 1 -2 -1 -4 -2 -3 0 -1 -2 -1 -2 -3 1 0 -1]
[ 0 1 0 1 -2 2 -1 2 0 1 -1 0 1 0 1 2 -1 0 1]
[ 0 0 1 -1 0 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + z + 2*x*y-1 + 2*x-1*y + x-1*y*z-1 + x-2*y2*z-1 + x*y-2 + 3*y-1 + 3*x-1 + 2*x-2*y + 2*x-1*z-1 + 4*x-2*y*z-1 + 2*x-3*y2*z-1 + x-1*y-1*z-1 + 3*x-2*z-1 + 3*x-3*y*z-1 + x-4*y2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 56 1 Lattice Minkowski decompositions of facet 56
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3410
Image of polytope 3410 PALP id: 3410
grdb id: 320929
Integer points: [ 1 0 0 1 0 0 -3 -4 -3 -2 -1 -2 -1 0 -2 -1 -1 0 1]
[ 0 1 0 -2 -1 -2 2 2 1 0 -1 1 0 -1 1 0 1 0 -1]
[ 0 0 1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 8 1 none
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Polytope 3411
Image of polytope 3411 PALP id: 3411
grdb id: 320962
Integer points: [ 1 0 0 0 -1 -1 -1 -5 -4 -3 -2 -3 -2 -1 -3 -2 -1 -1 0]
[ 0 1 -1 0 1 -1 1 1 1 1 1 0 0 0 1 1 1 0 0]
[ 0 0 0 1 -1 -1 1 -3 -2 -1 0 -2 -1 0 -2 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 80 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Polytope 3412
Image of polytope 3412 PALP id: 3412
grdb id: 320445
Integer points: [ 1 0 0 1 0 -1 -3 -4 -2 -3 -1 -2 0 -1 -1 -2 0 -1 1]
[ 0 1 0 -2 -1 0 2 3 1 2 0 1 -1 0 1 2 0 1 -1]
[ 0 0 1 0 1 1 -2 -2 0 -1 0 -1 0 -1 0 -1 0 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 136 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3413
Image of polytope 3413 PALP id: 3413
grdb id: 314406
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 1 -2 -1 -2 -2 -2 -1 -1 -1 0 0 0 -1 -1 0]
[ 0 0 1 0 -1 -1 2 2 1 0 1 0 -1 1 0 -1 1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Image of facet 174 1 Lattice Minkowski decompositions of facet 174
Polytope 3414
Image of polytope 3414 PALP id: 3414
grdb id: 314193
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 2 -1 -2 -1 -2 -2 -1 0 -1 0 1 0 1 -1 -1 0]
[ 0 0 1 -1 -1 0 2 2 1 0 -1 1 0 -1 1 0 0 1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y2*z-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + 3*x-1*y*z-1 + 2*y-1 + 7*x-1 + 5*x-1*y-1*z + x-1*y-2*z2 + 3*x-1*z-1 + 5*x-1*y-1 + 2*x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 174 1 Lattice Minkowski decompositions of facet 174
Polytope 3415
Image of polytope 3415 PALP id: 3415
grdb id: 317924
Integer points: [ 1 0 0 -1 0 -1 -1 2 0 1 -1 0 -1 0 1 0 1 -1 0]
[ 0 1 -1 0 1 0 -2 1 -1 0 -1 0 -1 0 1 0 1 0 1]
[ 0 0 0 0 2 -2 -2 2 -1 1 -1 1 -2 0 2 -1 1 -1 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
11 rank 2, number 6 x2*y*z2 + 2*x*y*z2 + 2*x*y*z + y*z2 + 2*x*z + 2*y*z + x + y + 2*z + 2*z-1 + y-1 + x-1 + 2*y-1*z-1 + 2*x-1*z-1 + x-1*z-2 + 2*x-1*y-1*z-1 + 2*x-1*y-1*z-2 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 4 Lattice Minkowski decompositions of facet 16
Image of facet 15 4 Lattice Minkowski decompositions of facet 15
Polytope 3416
Image of polytope 3416 PALP id: 3416
grdb id: 315922
Integer points: [ 1 0 0 0 0 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 1 0 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 0 1 0 -1 -2 2 -2 -1 0 1 -1 0 1 -1 0 1 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + y*z-1 + 2*x-1*z + 2*z-1 + y-1 + 5*x-1 + 2*x-1*y-1*z + x-2*y-1*z2 + 4*x-1*z-1 + 4*x-1*y-1 + 4*x-2*y-1*z + x-1*z-2 + 2*x-1*y-1*z-1 + 6*x-2*y-1 + 4*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3417
Image of polytope 3417 PALP id: 3417
grdb id: 315610
Integer points: [ 1 0 1 0 -1 -2 -1 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 2 2 -2 -2 -1 0 1 -1 0 1 -1 0 1 -1 0]
[ 0 0 0 1 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 134 1 Lattice Minkowski decompositions of facet 134
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3418
Image of polytope 3418 PALP id: 3418
grdb id: 315744
Integer points: [ 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 1 -2 -1 -3 -2 -1 0 -2 -1 0 1 0 -1 -1 0]
[ 0 0 1 -1 1 1 -1 1 1 1 1 0 0 0 0 -1 1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3419
Image of polytope 3419 PALP id: 3419
grdb id: 315934
Integer points: [ 1 0 0 -1 0 0 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -1 -1 1 -3 -2 -1 0 -2 -1 0 -2 -1 0 -1 0]
[ 0 0 1 0 -1 1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y + y-1*z + 2*y-1 + 4*x-1 + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1 + 5*x-1*y-1 + 4*x-1*y-1*z-1 + 4*x-2*z-1 + 2*x-1*y-2 + 2*x-1*y-2*z-1 + 6*x-2*y-1*z-1 + 4*x-2*y-2*z-1 + x-2*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Polytope 3420
Image of polytope 3420 PALP id: 3420
grdb id: 314336
Integer points: [ 1 0 0 1 -1 -1 -2 -2 -1 0 -2 -1 0 -2 -1 -1 0 -1 0]
[ 0 1 0 -1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 1 0 1 -2 0 -3 0 0 -1 -1 -1 -2 -2 0 0 -1 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + x*y-1 + x-1*z + 2*z-1 + 3*y-1 + 2*x-1 + 3*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + x-1*z-2 + 6*x-1*y-1*z-1 + x-2*y-1 + 3*x-1*y-1*z-2 + 3*x-2*y-1*z-1 + 3*x-2*y-1*z-2 + x-2*y-1*z-3
39 ? x + y + z + x*y-1 + x-1*z + 2*z-1 + 3*y-1 + 3*x-1 + 3*y-1*z-1 + 4*x-1*z-1 + 3*x-1*y-1 + x-1*z-2 + 6*x-1*y-1*z-1 + x-2*y-1 + 3*x-1*y-1*z-2 + 3*x-2*y-1*z-1 + 3*x-2*y-1*z-2 + x-2*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3421
Image of polytope 3421 PALP id: 3421
grdb id: 317606
Integer points: [ 1 0 0 1 0 -2 0 -2 0 -1 -1 -1 -2 -2 0 0 -1 -1 -1]
[ 0 1 0 -1 0 1 -2 -2 -1 -2 -1 0 -1 0 -1 0 -1 0 1]
[ 0 0 1 0 -1 0 -1 -3 0 -2 -1 0 -2 -1 -1 0 -2 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*y-1 + 2*x-1*y + z-1 + 2*y-1 + 2*x-1 + x-2*y + 3*y-1*z-1 + 4*x-1*z-1 + y-2*z-1 + 4*x-1*y-1*z-1 + 3*x-2*z-1 + 2*x-1*y-1*z-2 + 2*x-1*y-2*z-2 + 3*x-2*y-1*z-2 + x-2*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Polytope 3422
Image of polytope 3422 PALP id: 3422
grdb id: 317467
Integer points: [ 1 0 0 0 0 -1 -2 -2 -1 -1 -1 0 0 0 -2 -2 -1 -1 -1]
[ 0 1 -1 0 -2 2 3 0 0 1 2 -1 0 1 1 2 -1 0 1]
[ 0 0 0 1 1 -2 -2 1 1 0 -1 1 0 -1 0 -1 1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + 2*y*z-1 + 2*x-1*y2*z-1 + 4*x-1*y + 2*y-1*z + 2*x-1*z + x-1*y2*z-2 + x-2*y3*z-2 + 3*x-1*y*z-1 + 3*x-2*y2*z-1 + y-1 + 4*x-1 + 3*x-2*y + y-2*z + 2*x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3423
Image of polytope 3423 PALP id: 3423
grdb id: 320054
Integer points: [ 1 0 0 -1 -1 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -2 -2 2 -3 1 0 -1 -2 1 0 -1 0 -1 0 -1]
[ 0 0 1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + 2*x-1*y + x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 5*x-1 + 3*x-1*z-1 + 5*x-2*y*z-1 + 4*x-1*y-1 + 3*x-1*y-1*z-1 + 10*x-2*z-1 + x-1*y-2 + x-1*y-2*z-1 + 10*x-2*y-1*z-1 + 5*x-2*y-2*z-1 + x-2*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 146 1 Lattice Minkowski decompositions of facet 146
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3424
Image of polytope 3424 PALP id: 3424
grdb id: 317702
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 2 -2 0 -1 -3 -2 -1 -2 -1 0 1 0 1 -1 -1 0]
[ 0 0 1 -1 1 1 -1 1 1 1 0 0 0 0 -1 -1 1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 8 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Polytope 3425
Image of polytope 3425 PALP id: 3425
grdb id: 316454
Integer points: [ 1 0 0 0 -1 -2 -3 -3 -1 -2 -1 -3 -2 -1 -2 -1 0 -1 0]
[ 0 1 0 -1 -2 2 2 0 1 1 0 1 0 -1 -1 1 0 0 -1]
[ 0 0 1 1 0 -1 -2 -2 0 -1 0 -2 -1 0 -1 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + 2*x-1*y + y-1*z + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 5*x-1 + 2*x-1*z-1 + 5*x-2*y*z-1 + 3*x-1*y-1 + x-3*y2*z-2 + 5*x-2*z-1 + x-1*y-2 + 2*x-3*y*z-2 + 2*x-2*y-1*z-1 + x-3*z-2
59 rank 2, number 16 x + y + z + 2*x-1*y + y-1*z + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 3*x-1 + 2*x-1*z-1 + 3*x-2*y*z-1 + 2*x-1*y-1 + x-3*y2*z-2 + 4*x-2*z-1 + x-1*y-2 + 2*x-3*y*z-2 + 2*x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 203 1 Lattice Minkowski decompositions of facet 203
Polytope 3426
Image of polytope 3426 PALP id: 3426
grdb id: 314791
Integer points: [ 1 0 -1 0 -2 0 -3 -3 -2 -1 -3 -2 -1 -2 -1 -1 0 -1 0]
[ 0 1 1 0 0 -1 -2 -4 -3 -2 -3 -2 -1 -1 0 -2 -1 -1 0]
[ 0 0 0 1 -1 1 -2 -2 -1 0 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 204 1 Lattice Minkowski decompositions of facet 204
Image of facet 14 1 none
Polytope 3427
Image of polytope 3427 PALP id: 3427
grdb id: 320067
Integer points: [ 1 0 -1 0 -1 -2 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 1 0 0 1 -3 -4 -3 -2 -1 0 -2 -1 0 -2 -1 -1 0]
[ 0 0 0 1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 146 1 Lattice Minkowski decompositions of facet 146
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 8 1 none
Image of facet 9 1 irreducible and admissible
Polytope 3428
Image of polytope 3428 PALP id: 3428
grdb id: 314752
Integer points: [ 1 0 0 -1 -2 -1 -3 -3 -2 -3 -2 -1 -3 -2 -1 -1 0 -1 0]
[ 0 1 0 0 0 -2 -1 -4 -3 -3 -2 -1 -2 -1 0 -2 -1 -1 0]
[ 0 0 1 -1 -1 0 -2 -2 -1 -2 -1 0 -2 -1 0 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + 2*y-1 + 2*x-1 + x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + x-2*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 4*x-2*y-1*z-1 + 5*x-2*y-2*z-1 + x-3*y-1*z-2 + 2*x-2*y-3*z-1 + 3*x-3*y-2*z-2 + 3*x-3*y-3*z-2 + x-3*y-4*z-2
144 rank 3, number 12 x + y + z + 2*y-1 + 2*x-1 + x-1*z-1 + 4*x-1*y-1 + 3*x-1*y-1*z-1 + x-2*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 5*x-2*y-1*z-1 + 6*x-2*y-2*z-1 + x-3*y-1*z-2 + 2*x-2*y-3*z-1 + 3*x-3*y-2*z-2 + 3*x-3*y-3*z-2 + x-3*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 155 1 Lattice Minkowski decompositions of facet 155
Polytope 3429
Image of polytope 3429 PALP id: 3429
grdb id: 314488
Integer points: [ 1 0 0 -1 0 -1 -2 -4 -3 -2 -3 -2 -1 -2 -1 -1 -1 0 0]
[ 0 1 0 1 -1 -2 -1 -2 -1 0 -2 -1 0 -2 -1 0 -1 0 -1]
[ 0 0 1 0 1 0 -2 -3 -2 -1 -2 -1 0 -1 0 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*y + y-1*z + 2*y-1 + 3*x-1 + 2*x-1*z-1 + 4*x-1*y-1 + 3*x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2 + 6*x-2*y-1*z-1 + x-2*y-1*z-2 + 3*x-2*y-2*z-1 + 3*x-3*y-1*z-2 + 3*x-3*y-2*z-2 + x-4*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 153 1 Lattice Minkowski decompositions of facet 153
Polytope 3430
Image of polytope 3430 PALP id: 3430
grdb id: 315935
Integer points: [ 1 0 0 -1 0 0 -2 -4 -3 -2 -1 -3 -2 -1 -2 -1 0 -1 0]
[ 0 1 0 1 -1 -1 1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 0 1 0 -1 1 -1 -3 -2 -1 0 -2 -1 0 -2 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y + y-1*z + 2*y-1 + 4*x-1 + y-1*z-1 + 3*x-1*z-1 + x-2*y*z-1 + 4*x-1*y-1 + 4*x-1*y-1*z-1 + 5*x-2*z-1 + 6*x-2*y-1*z-1 + 2*x-2*y-1*z-2 + 2*x-3*z-2 + 4*x-3*y-1*z-2 + x-4*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 3431
Image of polytope 3431 PALP id: 3431
grdb id: 314507
Integer points: [ 1 0 0 0 -1 -1 -2 -4 -2 -1 -3 -2 -1 -3 -2 -1 0 -1 0]
[ 0 1 0 -1 1 -2 1 1 1 0 1 0 -1 0 -1 1 0 0 -1]
[ 0 0 1 1 0 0 -2 -3 -1 0 -2 -1 0 -2 -1 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y + y-1*z + 2*x-1*y*z-1 + 2*y-1 + 4*x-1 + 3*x-1*z-1 + 3*x-2*y*z-1 + 3*x-1*y-1 + x-2*y*z-2 + 6*x-2*z-1 + x-1*y-2 + 3*x-3*y*z-2 + 3*x-2*y-1*z-1 + 3*x-3*z-2 + x-4*y*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 153 1 Lattice Minkowski decompositions of facet 153
Polytope 3432
Image of polytope 3432 PALP id: 3432
grdb id: 315929
Integer points: [ 1 0 0 0 -1 0 -2 -4 -1 -2 -3 0 -1 -2 -1 -2 -3 0 -1]
[ 0 1 0 -1 1 -1 1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 0 1 -1 1 1 1 1 1 1 1 0 0 0 1 1 1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y*z + y-1*z + 4*x-1*z + x-2*y*z + 2*y-1 + 2*x-1 + 4*x-1*y-1*z + 5*x-2*z + y-1*z-1 + 4*x-1*y-1 + 6*x-2*y-1*z + 2*x-3*z + 2*x-2*y-1 + 4*x-3*y-1*z + x-4*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Polytope 3433
Image of polytope 3433 PALP id: 3433
grdb id: 317608
Integer points: [ 1 0 0 0 0 -2 -1 -4 -1 -3 -2 -1 -3 -2 -1 0 -2 -1 0]
[ 0 1 0 0 -1 0 -2 -2 0 -1 -1 -1 -2 -2 0 0 -1 -1 -1]
[ 0 0 1 -1 1 -1 0 -3 0 -2 -1 0 -2 -1 -1 0 -2 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + y-1*z + z-1 + 2*y-1 + 2*x-1 + 2*x-1*z-1 + 4*x-1*y-1 + 4*x-1*y-1*z-1 + x-2*z-1 + x-1*y-2 + 5*x-2*y-1*z-1 + 2*x-2*y-1*z-2 + 3*x-2*y-2*z-1 + 2*x-3*y-1*z-2 + 3*x-3*y-2*z-2 + x-4*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 3434
Image of polytope 3434 PALP id: 3434
grdb id: 314779
Integer points: [ 1 0 0 0 0 -1 -2 -4 -2 -3 -1 -2 -3 0 -1 -1 -2 0 -1]
[ 0 1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 1 -1 1 1 -2 -2 0 -1 0 -1 -2 0 -1 0 -1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + y-1*z + 2*y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + 2*x-1*z-1 + 5*x-1*y-1 + 4*x-1*y-1*z-1 + 2*x-2*z-1 + 3*x-2*y-1 + 6*x-2*y-1*z-1 + x-2*y-1*z-2 + 3*x-3*y-1*z-1 + 2*x-3*y-1*z-2 + x-4*y-1*z-2
38 ? x + y + z + y-1*z + 2*y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + 2*x-1*z-1 + 4*x-1*y-1 + 3*x-1*y-1*z-1 + 2*x-2*z-1 + 3*x-2*y-1 + 5*x-2*y-1*z-1 + x-2*y-1*z-2 + 3*x-3*y-1*z-1 + 2*x-3*y-1*z-2 + x-4*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 155 1 Lattice Minkowski decompositions of facet 155
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3435
Image of polytope 3435 PALP id: 3435
grdb id: 315883
Integer points: [ 1 0 1 -1 0 0 -2 -4 -3 -2 -1 -3 -2 -1 -2 -1 0 -1 0]
[ 0 1 -1 1 0 -2 0 -4 -3 -2 -1 -2 -1 0 -3 -2 -1 -1 0]
[ 0 0 0 0 1 -1 -1 -3 -2 -1 0 -2 -1 0 -2 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 80 2 none
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3436
Image of polytope 3436 PALP id: 3436
grdb id: 318502
Integer points: [ 1 0 0 -1 -2 -3 -1 -3 -3 -3 -3 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 0 -1 -1 -2 -1 -2 -2 -2 -2 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 1 -1 -1 -1 2 3 0 1 2 0 1 2 0 1 0 1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 148 1 none
Image of facet 93 1 Lattice Minkowski decompositions of facet 93
Polytope 3437
Image of polytope 3437 PALP id: 3437
grdb id: 314493
Integer points: [ 1 0 0 0 -1 -2 -3 -3 -2 -1 -3 -2 -1 -3 -2 -1 -1 0 -1]
[ 0 1 0 -1 2 -1 0 3 2 1 2 1 0 1 0 -1 1 0 0]
[ 0 0 1 1 -1 -1 -2 -2 -1 0 -2 -1 0 -2 -1 0 -1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y2*z-1 + 3*x-1*y + y-1*z + 3*x-1*y*z-1 + 3*x-2*y2*z-1 + 5*x-1 + x-3*y3*z-2 + 2*x-1*z-1 + 7*x-2*y*z-1 + 2*x-1*y-1 + 3*x-3*y2*z-2 + 5*x-2*z-1 + 3*x-3*y*z-2 + x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 174 1 Lattice Minkowski decompositions of facet 174
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3438
Image of polytope 3438 PALP id: 3438
grdb id: 314702
Integer points: [ 1 0 0 0 -1 0 -1 -4 -3 -2 -3 -2 -1 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 0 1 -1 1 2 2 1 0 2 1 0 2 1 1 0 1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 14 1 none
Image of facet 153 1 Lattice Minkowski decompositions of facet 153
Polytope 3439
Image of polytope 3439 PALP id: 3439
grdb id: 315731
Integer points: [ 1 0 0 0 0 -2 -2 -4 -1 -2 -3 -1 0 -1 -2 -3 0 -1 -1]
[ 0 1 -1 0 2 -2 -1 -2 1 0 -1 0 1 0 -1 -2 0 -1 -1]
[ 0 0 0 1 1 -1 -2 -3 0 -1 -2 -1 1 0 -1 -2 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 y2*z + 2*y*z + x + y + z + 4*x-1*y + y-1 + 6*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + 6*x-2*z-1 + 6*x-2*y-1*z-1 + x-2*y-1*z-2 + x-2*y-2*z-1 + 4*x-3*y-1*z-2 + 2*x-3*y-2*z-2 + x-4*y-2*z-3
13 rank 2, number 12 y2*z + 2*y*z + x + y + z + 4*x-1*y + y-1 + 6*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 6*x-2*z-1 + 6*x-2*y-1*z-1 + x-2*y-1*z-2 + x-2*y-2*z-1 + 4*x-3*y-1*z-2 + 2*x-3*y-2*z-2 + x-4*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3440
Image of polytope 3440 PALP id: 3440
grdb id: 314609
Integer points: [ 1 0 0 -1 -1 -2 -3 -5 -3 -4 -2 -3 -4 -1 -2 -1 -2 0 -1]
[ 0 1 0 0 0 -1 -2 -4 -2 -3 -1 -2 -3 0 -1 -1 -2 0 -1]
[ 0 0 1 -1 1 1 -2 -2 0 -1 0 -1 -2 0 -1 0 -1 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + x-1*z + 3*x-1 + x-1*z-1 + 3*x-1*y-1 + x-2*y-1*z + 2*x-1*y-1*z-1 + 4*x-2*y-1 + 4*x-2*y-1*z-1 + 2*x-2*y-2*z-1 + 3*x-3*y-2 + 5*x-3*y-2*z-1 + x-3*y-2*z-2 + 3*x-4*y-3*z-1 + 2*x-4*y-3*z-2 + x-5*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 204 1 Lattice Minkowski decompositions of facet 204
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3441
Image of polytope 3441 PALP id: 3441
grdb id: 315887
Integer points: [ 1 0 0 -1 0 -1 -1 -5 -4 -3 -2 -3 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 0 -1 0 -2 -4 -3 -2 -1 -2 -1 0 -3 -2 -1 -1 0]
[ 0 0 1 -1 1 1 1 1 1 1 1 0 0 0 1 1 1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + y-1*z + x-1*z + 3*x-1 + 4*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z + 4*x-2*y-1*z + 4*x-2*y-1 + 5*x-2*y-2*z + 6*x-3*y-2*z + 2*x-3*y-2 + 2*x-3*y-3*z + 4*x-4*y-3*z + x-5*y-4*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 3442
Image of polytope 3442 PALP id: 3442
grdb id: 315886
Integer points: [ 1 0 0 0 -1 -1 -1 -5 -4 -3 -2 -3 -2 -1 -3 -2 -1 -1 0]
[ 0 1 -1 0 0 0 -2 -4 -3 -2 -1 -3 -2 -1 -2 -1 0 -1 0]
[ 0 0 0 1 -1 1 -1 -3 -2 -1 0 -2 -1 0 -2 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 80 1 none
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 3443
Image of polytope 3443 PALP id: 3443
grdb id: 308301
Integer points: [ 1 0 1 -1 0 1 -2 -2 -2 -2 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 1 -1 1 0 -2 1 -2 -1 0 -2 -1 0 -2 -1 -1 0 -1 0]
[ 0 0 0 0 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*y-1 + x-1*y + 3*y-1 + 3*x-1 + x*y-2*z-1 + 3*y-1*z-1 + 3*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + 3*y-2*z-1 + 6*x-1*y-1*z-1 + 3*x-2*z-1 + 3*x-1*y-2*z-1 + 3*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Polytope 3444
Image of polytope 3444 PALP id: 3444
grdb id: 308463
Integer points: [ 1 0 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 0 -2 0 -3 -1 0 -2 -1 0 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 1 1 -2 1 1 0 1 0 -1 0 -1 1 0 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + z + y*z-1 + 2*y-1*z + x-1*z + 2*z-1 + 3*y-1 + 3*x-1 + y-2*z + 3*x-1*y-1*z + 3*x-1*z-1 + 6*x-1*y-1 + 3*x-1*y-2*z + x-1*z-2 + 3*x-1*y-1*z-1 + 3*x-1*y-2 + x-1*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Polytope 3445
Image of polytope 3445 PALP id: 3445
grdb id: 147462
Integer points: [ 1 0 0 -1 -1 0 0 -1 -1 -1 -1 -1 0 0 -1 -1 0 0 0]
[ 0 1 0 2 -1 1 -2 -2 2 1 0 -1 0 -1 1 0 1 0 -1]
[ 0 0 1 -1 2 -2 1 2 -2 -1 0 1 -1 0 0 1 -1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
26 rank 2, number 8 x + y + z + y*z-1 + x-1*y2*z-1 + 3*x-1*y + y-1*z + 3*x-1*z + x-1*y-1*z2 + y*z-2 + x-1*y2*z-2 + 3*z-1 + 4*x-1*y*z-1 + 3*y-1 + 6*x-1 + y-2*z + 4*x-1*y-1*z + x-1*y-2*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 10 2 Lattice Minkowski decompositions of facet 10
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 90 2 Lattice Minkowski decompositions of facet 90
Polytope 3446
Image of polytope 3446 PALP id: 3446
grdb id: 147470
Integer points: [ 1 0 0 2 -1 -2 1 0 -2 0 -1 1 0 -1 1 0 -1 0 -1]
[ 0 1 0 -1 2 1 -2 -2 0 -1 0 -1 0 1 0 1 -1 -1 0]
[ 0 0 1 -1 -1 0 0 1 1 1 1 0 0 0 -1 -1 1 0 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
22 ? x + y + z + x2*y-1*z-1 + 3*x*z-1 + 3*y*z-1 + x-1*y2*z-1 + 3*x*y-1 + 3*x-1*y + 2*y-1*z + 2*x-1*z + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + y-2*z + 2*x-1*y-1*z + x-2*z
7 rank 1, V12 x + y + z + x2*y-1*z-1 + 3*x*z-1 + 3*y*z-1 + x-1*y2*z-1 + 2*x*y-1 + 3*x-1*y + 2*y-1*z + 2*x-1*z + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + y-2*z + 2*x-1*y-1*z + x-2*z
7 rank 1, V12 x + y + z + x2*y-1*z-1 + 3*x*z-1 + 3*y*z-1 + x-1*y2*z-1 + 3*x*y-1 + 2*x-1*y + 2*y-1*z + 2*x-1*z + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + y-2*z + 2*x-1*y-1*z + x-2*z
11 rank 2, number 6 x + y + z + x2*y-1*z-1 + 3*x*z-1 + 3*y*z-1 + x-1*y2*z-1 + 2*x*y-1 + 2*x-1*y + 2*y-1*z + 2*x-1*z + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + y-2*z + 2*x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 23 2 Lattice Minkowski decompositions of facet 23
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3447
Image of polytope 3447 PALP id: 3447
grdb id: 147436
Integer points: [ 1 0 1 -1 0 -1 -1 0 -1 -1 -1 0 0 -1 -1 0 0 0 1]
[ 0 1 0 0 -1 1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 0 2 -2 -1 -1 -2 2 1 -1 0 0 1 -1 0 -1 0 1 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x*z2 + 2*x*z + x + y + 2*z + y-1*z2 + 3*y-1*z + 2*z-1 + x-1*y*z-1 + 3*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*z-2 + 3*x-1*y-1*z-1 + x-1*y-1*z-2
51 rank 2, number 7 x*z2 + 2*x*z + x + y + 3*z + y-1*z2 + 3*y-1*z + 2*z-1 + x-1*y*z-1 + 3*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*z-2 + 3*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 3448
Image of polytope 3448 PALP id: 3448
grdb id: 147317
Integer points: [ 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 -1 2 -2 1 3 2 1 2 1 0 -1 0 1 0 -1]
[ 0 0 1 -1 0 1 -2 2 2 1 0 2 1 0 -1 1 1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? x-1*y3*z2 + y2*z + 2*x-1*y2*z2 + 3*y*z + 3*x-1*y2*z + x-1*y*z2 + x + y + z + 5*x-1*y*z + 3*x-1*y + 2*x-1*z + 6*x-1 + 2*y-1*z-1 + x-1*z-1 + x-1*y-1 + 4*x-1*y-1*z-1 + x-1*y-2*z-2
31 rank 3, number 3 x-1*y3*z2 + y2*z + 2*x-1*y2*z2 + 2*y*z + 3*x-1*y2*z + x-1*y*z2 + x + y + z + 5*x-1*y*z + 3*x-1*y + 2*x-1*z + 6*x-1 + 2*y-1*z-1 + x-1*z-1 + x-1*y-1 + 4*x-1*y-1*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 158 1 Lattice Minkowski decompositions of facet 158
Polytope 3449
Image of polytope 3449 PALP id: 3449
grdb id: 147431
Integer points: [ 1 0 0 0 1 -2 1 -2 1 -1 0 -1 0 1 -1 0 -1 0 1]
[ 0 1 0 0 -1 1 -2 0 -3 -1 -2 0 -1 -2 0 -1 1 0 -1]
[ 0 0 1 -1 0 -2 2 -1 2 0 1 -1 0 1 0 1 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + 2*x*y-1*z + z + x*y-2*z2 + x*y-1 + 2*x*y-2*z + 3*y-1*z + x*y-3*z2 + z-1 + 2*x-1*y*z-1 + 4*y-1 + 2*x-1 + 3*y-2*z + 3*x-1*z-1 + 3*x-1*y-1 + x-2*y*z-2 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3450
Image of polytope 3450 PALP id: 3450
grdb id: 147434
Integer points: [ 1 0 0 1 1 -2 -1 0 -3 -2 -1 -2 -1 0 0 -1 -1 0 1]
[ 0 1 0 -2 -2 2 0 -1 2 1 0 1 0 -1 -1 1 1 0 -1]
[ 0 0 1 0 -1 1 -1 1 1 1 1 0 0 0 -1 1 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 1 none
Image of facet 1 1 irreducible and admissible
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3451
Image of polytope 3451 PALP id: 3451
grdb id: 147467
Integer points: [ 1 0 0 0 2 -3 3 -2 2 1 -1 0 1 2 -1 0 1 -2 -1]
[ 0 1 -1 0 1 -3 3 -1 3 2 0 1 1 2 -1 0 1 -2 -1]
[ 0 0 0 1 -1 1 -2 0 -2 -1 0 -1 0 -1 1 0 -1 1 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x3*y3*z-2 + x2*y3*z-2 + 3*x2*y2*z-1 + x2*y*z-1 + 2*x*y2*z-1 + 3*x*y + 2*x*y*z-1 + x + y + z + 2*y*z-1 + y-1 + 2*x-1 + 3*x-1*y-1*z + 2*x-1*y-1 + x-2*y-1 + 3*x-2*y-2*z + x-3*y-3*z
34 rank 2, number 5 x3*y3*z-2 + x2*y3*z-2 + 3*x2*y2*z-1 + x2*y*z-1 + 2*x*y2*z-1 + 3*x*y + 4*x*y*z-1 + x + y + z + 2*y*z-1 + y-1 + 2*x-1 + 3*x-1*y-1*z + 3*x-1*y-1 + x-2*y-1 + 3*x-2*y-2*z + x-3*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 72 1 Lattice Minkowski decompositions of facet 72
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Polytope 3452
Image of polytope 3452 PALP id: 3452
grdb id: 146786
Integer points: [ 1 0 0 2 -1 -1 -1 -1 1 0 0 -1 1 0 1 0 -1 0 -1]
[ 0 1 0 -1 2 -1 1 -1 -1 -1 0 0 -1 -1 0 0 0 1 1]
[ 0 0 1 -1 -1 2 -1 1 -1 0 -1 0 0 1 -1 0 1 -1 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
34 rank 2, number 5 x + y + z + x2*y-1*z-1 + 3*x*z-1 + 3*y*z-1 + x-1*y2*z-1 + 3*x*y-1 + 3*x-1*y + 3*y-1*z + 3*x-1*z + x-1*y-1*z2 + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 20 3 Lattice Minkowski decompositions of facet 20
Image of facet 44 3 Lattice Minkowski decompositions of facet 44
Polytope 3453
Image of polytope 3453 PALP id: 3453
grdb id: 144213
Integer points: [ 1 0 0 -1 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 1 0 -1 -2 -2 0 0 -1 -1 -1 -2 -2 0 -1 -1]
[ 0 0 1 1 0 -1 1 -2 1 1 0 1 0 -1 0 -1 0 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y*z + x-1*y + y-1*z + 3*x-1*z + 3*y-1 + 4*x-1 + 3*x-1*y-1*z + 2*y-1*z-1 + x-1*z-1 + 6*x-1*y-1 + x-1*y-2*z + 3*x-1*y-1*z-1 + 3*x-1*y-2 + 3*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 153 1 Lattice Minkowski decompositions of facet 153
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3454
Image of polytope 3454 PALP id: 3454
grdb id: 145662
Integer points: [ 1 0 0 0 -1 -2 1 0 1 0 1 -1 0 -1 1 0 1 -1 0]
[ 0 1 0 -1 0 1 -2 -1 -2 -1 -2 0 -1 0 -1 0 -1 1 0]
[ 0 0 1 1 1 0 0 -2 -2 0 -1 0 -1 -1 0 0 -1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + 2*x*y-1*z-1 + 2*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + 2*x*y-2*z-1 + 4*y-1*z-1 + 2*x-1*z-1 + x*y-2*z-2 + y-1*z-2
62 rank 2, number 9 x + y + z + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + 2*x*y-1*z-1 + 2*z-1 + x*y-2 + 3*y-1 + 2*x-1 + x-2*y + 2*x*y-2*z-1 + 3*y-1*z-1 + 2*x-1*z-1 + x*y-2*z-2 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 143 1 Lattice Minkowski decompositions of facet 143
Polytope 3455
Image of polytope 3455 PALP id: 3455
grdb id: 144137
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 -1 1 -2 0 1 1 1 0 0 0 -1 -1 0 0 -1]
[ 0 0 1 -1 1 1 0 -2 -2 0 -1 1 0 -1 0 -1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + y*z-1 + 3*x-1*y + 2*x-1*z + 2*z-1 + 3*x-1*y*z-1 + 2*y-1 + 5*x-1 + x-1*y-1*z + x-1*y*z-2 + 4*x-1*z-1 + 3*x-1*y-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
31 rank 3, number 3 x + y + z + x-1*y*z + y*z-1 + 3*x-1*y + 2*x-1*z + 2*z-1 + 3*x-1*y*z-1 + 2*y-1 + 6*x-1 + x-1*y-1*z + x-1*y*z-2 + 5*x-1*z-1 + 4*x-1*y-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 155 1 Lattice Minkowski decompositions of facet 155
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 3456
Image of polytope 3456 PALP id: 3456
grdb id: 146567
Integer points: [ 1 0 0 0 -1 0 -2 -1 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 1 -1 1 0 1 1 1 1 1 0 0 0 0 0 -1]
[ 0 0 1 1 1 -1 1 -2 -2 0 -1 0 -1 1 0 -1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + 3*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + 2*z-1 + 2*x-1*y*z-1 + 2*y-1 + 5*x-1 + 3*x-2*y + y-1*z-1 + 4*x-1*z-1 + 3*x-2*y*z-1 + x-1*z-2 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3457
Image of polytope 3457 PALP id: 3457
grdb id: 146344
Integer points: [ 1 0 0 0 1 1 1 -2 -2 -1 0 -2 -1 0 -1 -1 0 -1 0]
[ 0 1 0 0 -1 -1 -2 0 -2 -2 -2 -1 -1 -1 0 -1 -1 0 0]
[ 0 0 1 -1 0 -1 -1 1 -1 -1 -1 0 0 0 1 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*y-1 + 2*x-1*z + x*y-1*z-1 + z-1 + 4*y-1 + 2*x-1 + x-2*z + x*y-2*z-1 + 3*y-1*z-1 + 5*x-1*y-1 + 3*y-2*z-1 + 2*x-1*y-1*z-1 + 2*x-2*y-1 + 3*x-1*y-2*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3458
Image of polytope 3458 PALP id: 3458
grdb id: 144273
Integer points: [ 1 0 -1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 1 0 -1 0 -2 -1 -2 -2 -2 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 0 1 -1 -1 -1 2 2 0 1 -1 0 1 0 1 0 1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + 3*y-1 + 3*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + y-1*z-1 + x-1*z-1 + 5*x-1*y-1 + 3*x-1*y-2*z + 2*x-1*y-1*z-1 + 3*x-1*y-2 + x-1*y-2*z-1
146 ? x + y + z + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + 3*y-1 + 4*x-1 + 5*x-1*y-1*z + x-1*y-2*z2 + y-1*z-1 + x-1*z-1 + 6*x-1*y-1 + 3*x-1*y-2*z + 2*x-1*y-1*z-1 + 3*x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 155 1 Lattice Minkowski decompositions of facet 155
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 3459
Image of polytope 3459 PALP id: 3459
grdb id: 145359
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 2 -2 1 -2 2 1 0 1 0 -1 0 -1 1 0 -1]
[ 0 0 1 2 -2 2 -2 1 -1 0 1 -1 0 1 -1 0 -1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + z + 2*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + x-1*y2*z-2 + 4*x-1*y*z-1 + 6*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + x-1*y*z-2 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z
151 ? x + y + z + 2*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + x-1*y2*z-2 + 5*x-1*y*z-1 + 8*x-1 + 5*x-1*y-1*z + x-1*y-2*z2 + x-1*y*z-2 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 188 1 Lattice Minkowski decompositions of facet 188
Polytope 3460
Image of polytope 3460 PALP id: 3460
grdb id: 146429
Integer points: [ 1 0 0 0 2 -2 -1 1 -2 0 -1 1 0 -1 -2 1 0 -1 -1]
[ 0 1 0 0 -2 1 0 -2 1 -1 0 -1 -1 0 1 -1 0 1 1]
[ 0 0 1 -1 -1 0 -1 -1 2 0 1 0 -1 0 1 -1 0 1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*x-1*y*z + x-2*y*z2 + 2*x*y-1 + 2*x-1*y + 3*x-1*z + 2*x-2*y*z + x2*y-2*z-1 + 2*x*y-1*z-1 + z-1 + 3*y-1 + 4*x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3461
Image of polytope 3461 PALP id: 3461
grdb id: 145189
Integer points: [ 1 0 0 1 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 0 -1 1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 0 0]
[ 0 0 1 -1 1 0 2 -2 -2 -1 0 1 -1 0 1 -1 0 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + x*z-1 + x-1*y + y-1*z + 2*x-1*z + x-1*y-1*z2 + 2*z-1 + 3*y-1 + 4*x-1 + 4*x-1*y-1*z + 3*y-1*z-1 + 2*x-1*z-1 + 6*x-1*y-1 + y-1*z-2 + 4*x-1*y-1*z-1 + x-1*y-1*z-2
20 rank 1, V16 x + y + z + x*z-1 + x-1*y + y-1*z + 2*x-1*z + x-1*y-1*z2 + 3*z-1 + 3*y-1 + 4*x-1 + 4*x-1*y-1*z + 3*y-1*z-1 + 2*x-1*z-1 + 6*x-1*y-1 + y-1*z-2 + 4*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3462
Image of polytope 3462 PALP id: 3462
grdb id: 146358
Integer points: [ 1 0 1 0 0 0 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 0 -1 -1 2 -1 1 0 1 0 -1 1 0 -1 0 -1]
[ 0 0 0 1 -1 1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*y-1 + 2*x-1*y + y-1*z + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 4*x-1 + y-1*z-1 + 4*x-1*z-1 + 3*x-2*y*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3463
Image of polytope 3463 PALP id: 3463
grdb id: 146791
Integer points: [ 1 0 0 -1 1 -1 1 1 -1 -1 0 0 -1 -1 0 0 1 1 0]
[ 0 1 0 1 -1 1 -2 -3 -1 0 -2 -1 0 1 -1 0 -2 -1 0]
[ 0 0 1 1 -1 -1 0 -1 -1 0 -1 0 -1 0 -1 0 -1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + x*y-2 + 3*y-1 + 2*x-1 + 2*x*y-2*z-1 + 4*y-1*z-1 + 2*x-1*z-1 + x*y-3*z-1 + 2*y-2*z-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3464
Image of polytope 3464 PALP id: 3464
grdb id: 146362
Integer points: [ 1 0 0 0 0 -1 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 1 -1 0 -3 -1 -2 0 -1 -2 0 -1 -2 0 -1]
[ 0 0 1 -1 1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + y-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + y-1*z-1 + 3*x-1*z-1 + 4*x-1*y-1 + 4*x-1*y-1*z-1 + x-2*z-1 + 2*x-1*y-2 + 2*x-1*y-2*z-1 + 3*x-2*y-1*z-1 + 3*x-2*y-2*z-1 + x-2*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3465
Image of polytope 3465 PALP id: 3465
grdb id: 146307
Integer points: [ 1 0 0 0 1 -2 1 -2 1 0 -1 0 -1 1 0 -1 1 0 -1]
[ 0 1 0 0 -1 1 -2 0 -3 -2 -1 -1 0 -2 -1 0 -1 0 1]
[ 0 0 1 -1 -1 0 0 -1 -1 -1 -1 0 0 -1 -1 -1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + 2*x*y-1 + 2*x-1*y + x*y-1*z-1 + z-1 + x*y-2 + 2*y-1 + 2*x-1 + x-2*y + 2*x*y-2*z-1 + 4*y-1*z-1 + 2*x-1*z-1 + x*y-3*z-1 + 3*y-2*z-1 + 3*x-1*y-1*z-1 + x-2*z-1
151 ? x + y + z + 2*x*y-1 + 2*x-1*y + x*y-1*z-1 + z-1 + x*y-2 + 4*y-1 + 3*x-1 + x-2*y + 2*x*y-2*z-1 + 4*y-1*z-1 + 2*x-1*z-1 + x*y-3*z-1 + 3*y-2*z-1 + 3*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3466
Image of polytope 3466 PALP id: 3466
grdb id: 145002
Integer points: [ 1 0 0 1 -2 -2 1 -3 1 0 -1 -2 0 -1 0 -1 1 0 -1]
[ 0 1 0 -2 1 1 -2 1 -3 -2 -1 0 -1 0 -1 0 -1 0 1]
[ 0 0 1 0 0 -1 -1 -1 -1 -1 -1 -1 0 0 -1 -1 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? x + y + z + 2*x*y-1 + 2*x-1*y + x*y-2 + 4*y-1 + 4*x-1 + x-2*y + x*y-2*z-1 + 3*y-1*z-1 + 3*x-1*z-1 + x-2*y*z-1 + x*y-3*z-1 + 4*y-2*z-1 + 6*x-1*y-1*z-1 + 4*x-2*z-1 + x-3*y*z-1
31 rank 3, number 3 x + y + z + 2*x*y-1 + 2*x-1*y + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + 3*y-1*z-1 + 3*x-1*z-1 + x-2*y*z-1 + x*y-3*z-1 + 4*y-2*z-1 + 6*x-1*y-1*z-1 + 4*x-2*z-1 + x-3*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 93 1 Lattice Minkowski decompositions of facet 93
Polytope 3467
Image of polytope 3467 PALP id: 3467
grdb id: 146348
Integer points: [ 1 0 0 1 -1 0 -1 -1 -1 -1 -1 0 0 -1 -1 -1 0 0 -1]
[ 0 1 0 -1 1 0 0 -1 -3 -2 -1 -2 -1 -2 -1 0 -1 0 0]
[ 0 0 1 0 0 -1 1 -2 -2 -1 0 -1 0 -2 -1 0 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*y-1 + x-1*y + x-1*z + z-1 + 3*y-1 + 2*x-1 + 3*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + 2*y-2*z-1 + 4*x-1*y-1*z-1 + x-1*y-1*z-2 + 3*x-1*y-2*z-1 + 2*x-1*y-2*z-2 + x-1*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Polytope 3468
Image of polytope 3468 PALP id: 3468
grdb id: 146336
Integer points: [ 1 0 1 -1 0 1 -1 1 -1 -1 -1 0 0 0 1 -1 -1 0 0]
[ 0 1 -1 1 0 -1 0 -3 -3 -2 -1 -3 -2 -1 -2 -1 0 -1 0]
[ 0 0 0 0 1 -1 1 -2 -2 -1 0 -2 -1 0 -1 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 14 1 none
Polytope 3469
Image of polytope 3469 PALP id: 3469
grdb id: 146566
Integer points: [ 1 0 1 0 -1 1 -2 0 -2 0 0 -1 -1 -1 -2 0 0 -1 -1]
[ 0 1 -1 0 1 -2 1 -3 -1 -2 -1 -2 -1 0 0 -1 0 0 1]
[ 0 0 0 1 1 -1 0 -2 -2 -1 0 -2 -1 0 -1 -1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + x*y-1 + 2*x-1*y + 3*y-1 + 4*x-1 + x-2*y + x*y-2*z-1 + 3*y-1*z-1 + 2*x-1*z-1 + 3*y-2*z-1 + 5*x-1*y-1*z-1 + 2*x-2*z-1 + y-3*z-2 + 2*x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3470
Image of polytope 3470 PALP id: 3470
grdb id: 146472
Integer points: [ 1 0 0 0 -1 1 -2 -1 -2 0 -1 0 -1 -2 1 0 -1 0 -1]
[ 0 1 0 1 1 0 0 -2 -2 0 0 -1 -1 -1 0 0 0 -1 -1]
[ 0 0 1 -1 0 -2 1 2 3 -1 0 0 1 2 -1 0 1 1 2]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*x*z-1 + y*z-1 + x-1*y + 2*y-1*z + 3*x-1*z + 2*x-1*y-1*z2 + x*z-2 + 3*z-1 + 2*y-1 + 3*x-1 + 4*x-1*y-1*z + x-2*z + x-1*y-2*z2 + 2*x-2*y-1*z2 + x-2*y-2*z3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3471
Image of polytope 3471 PALP id: 3471
grdb id: 145029
Integer points: [ 1 0 0 -1 -1 -1 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 1 2 -2 -2 2 -1 0 1 -1 0 1 0 -1 0 1]
[ 0 0 1 0 -2 -2 2 1 -3 0 -1 -2 1 0 -1 -1 1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 3*x-1*y*z-1 + 4*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + x-1*y*z-2 + 2*x-1*z-1 + x-1*y-1 + x-2*y2*z-3 + 4*x-2*y*z-2 + 6*x-2*z-1 + 4*x-2*y-1 + x-2*y-2*z
109 ? x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 5*x-1*y*z-1 + 7*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + x-1*y*z-2 + 2*x-1*z-1 + x-1*y-1 + x-2*y2*z-3 + 4*x-2*y*z-2 + 6*x-2*z-1 + 4*x-2*y-1 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 165 1 Lattice Minkowski decompositions of facet 165
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Polytope 3472
Image of polytope 3472 PALP id: 3472
grdb id: 146294
Integer points: [ 1 0 0 0 -1 -1 -1 0 -1 -1 -1 0 0 -1 -1 -1 0 0 0]
[ 0 1 0 1 0 -1 0 -2 -3 -1 -2 0 -1 0 -1 -2 1 0 -1]
[ 0 0 1 -2 1 2 -1 1 2 0 1 -1 0 0 1 2 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + 2*y*z-1 + 2*y-1*z + x-1*z + x-1*y-1*z2 + y*z-2 + 3*z-1 + 3*y-1 + 2*x-1 + y-2*z + 4*x-1*y-1*z + 2*x-1*y-2*z2 + x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-2*z + x-1*y-3*z2
40 rank 2, number 10 x + y + z + 2*y*z-1 + 3*y-1*z + x-1*z + x-1*y-1*z2 + y*z-2 + 3*z-1 + 3*y-1 + 2*x-1 + y-2*z + 4*x-1*y-1*z + 2*x-1*y-2*z2 + x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-2*z + x-1*y-3*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 3473
Image of polytope 3473 PALP id: 3473
grdb id: 146438
Integer points: [ 1 0 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 -1 0 -1 0 -1 -1 -1 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 1 1 -2 -2 2 -3 1 0 -1 -2 0 -1 0 -1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
56 rank 2, number 11 x + y + z + y-1*z + x-1*z + x-1*y-1*z2 + z-1 + 3*y-1 + 3*x-1 + 5*x-1*y-1*z + 3*y-1*z-1 + 3*x-1*z-1 + 10*x-1*y-1 + y-1*z-2 + x-1*z-2 + 10*x-1*y-1*z-1 + 5*x-1*y-1*z-2 + x-1*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 9 2 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 146 2 Lattice Minkowski decompositions of facet 146
Polytope 3474
Image of polytope 3474 PALP id: 3474
grdb id: 146747
Integer points: [ 1 0 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 1 1 -2 1 -2 -3 0 -1 -2 0 -1 0 -1 1 0 -1]
[ 0 0 1 -2 -1 1 -2 2 2 -1 0 1 0 1 -1 0 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + 2*y*z-1 + y-1*z + y*z-2 + 3*z-1 + x-1*y*z-1 + 3*y-1 + 3*x-1 + y-2*z + 3*x-1*y-1*z + x-1*y-2*z2 + x-1*y*z-2 + 4*x-1*z-1 + 6*x-1*y-1 + 4*x-1*y-2*z + x-1*y-3*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 9 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 90 2 Lattice Minkowski decompositions of facet 90
Polytope 3475
Image of polytope 3475 PALP id: 3475
grdb id: 146675
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 0 -2 2 1 -2 -3 0 -1 -2 1 0 -1 -1 1 0 -1]
[ 0 0 1 -1 1 -2 -2 2 2 -1 0 1 -1 0 1 0 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + 2*y*z-1 + y-1*z + x-1*y2*z-2 + z-1 + 4*x-1*y*z-1 + 2*y-1 + 6*x-1 + y-2*z + 4*x-1*y-1*z + x-1*y-2*z2 + x-1*y*z-2 + 4*x-1*z-1 + 6*x-1*y-1 + 4*x-1*y-2*z + x-1*y-3*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 134 1 Lattice Minkowski decompositions of facet 134
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3476
Image of polytope 3476 PALP id: 3476
grdb id: 146798
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 0 -1 0 -1 0 -1 0 -1 0]
[ 0 1 1 -1 -1 0 0 -2 -2 -1 0 0 1 -1 0 -2 -1 -1 0]
[ 0 0 2 -2 0 1 -1 -3 -1 0 1 0 1 -1 0 -2 -1 -2 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 y*z2 + 2*y*z + x + y + 2*z + x-1*z + 2*z-1 + y-1 + 2*x-1 + 2*y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + y-1*z-2 + 4*x-1*y-1*z-1 + 2*x-1*y-1*z-2 + x-1*y-2*z-1 + 2*x-1*y-2*z-2 + x-1*y-2*z-3
40 rank 2, number 10 y*z2 + 2*y*z + x + y + 2*z + x-1*z + 2*z-1 + y-1 + 2*x-1 + 3*y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + y-1*z-2 + 4*x-1*y-1*z-1 + 2*x-1*y-1*z-2 + x-1*y-2*z-1 + 2*x-1*y-2*z-2 + x-1*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 15 3 Lattice Minkowski decompositions of facet 15
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 3477
Image of polytope 3477 PALP id: 3477
grdb id: 145166
Integer points: [ 1 0 0 -1 -1 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 1 0 0 -3 -4 -1 -2 -3 0 -1 -2 -1 -2 0 -1]
[ 0 0 1 1 0 -1 1 -2 -3 0 -1 -2 0 -1 -2 0 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y*z + x-1*y + x-1*z + 3*y-1 + 4*x-1 + 3*y-1*z-1 + x-1*z-1 + 4*x-1*y-1 + 3*y-2*z-1 + 5*x-1*y-1*z-1 + 6*x-1*y-2*z-1 + y-3*z-2 + 2*x-1*y-2*z-2 + 4*x-1*y-3*z-2 + x-1*y-4*z-3
13 rank 2, number 12 x + y + z + x-1*y*z + x-1*y + x-1*z + 3*y-1 + 4*x-1 + 2*y-1*z-1 + x-1*z-1 + 4*x-1*y-1 + 3*y-2*z-1 + 5*x-1*y-1*z-1 + 6*x-1*y-2*z-1 + y-3*z-2 + 2*x-1*y-2*z-2 + 4*x-1*y-3*z-2 + x-1*y-4*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 9 1 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Polytope 3478
Image of polytope 3478 PALP id: 3478
grdb id: 134479
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 1 -1 -1 2 -1 -1 -1 0 0 0 1 1 -1 0 0]
[ 0 0 1 1 -1 -1 2 -1 -1 0 1 -1 0 1 -1 0 0 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + y*z-1 + x-1*y2*z-1 + 3*x-1*y + y-1*z + 3*x-1*z + x-1*y-1*z2 + 2*z-1 + 3*x-1*y*z-1 + 2*y-1 + 6*x-1 + 3*x-1*y-1*z + y-1*z-1 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Polytope 3479
Image of polytope 3479 PALP id: 3479
grdb id: 140654
Integer points: [ 1 0 0 1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 -1 1 -1 1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 0 1 0 0 -1 -1 -1 2 0 1 -1 0 1 -1 0 1 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + x*y-1 + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 4*y-1 + 4*x-1 + 3*x-1*y-1*z + 2*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Polytope 3480
Image of polytope 3480 PALP id: 3480
grdb id: 140115
Integer points: [ 1 0 0 -1 -1 0 0 -1 -1 -1 -1 -1 0 0 0 -1 -1 0 0]
[ 0 1 0 0 1 1 -2 1 -2 -1 0 1 -1 0 1 -1 0 -1 0]
[ 0 0 1 1 0 -2 1 -2 1 1 0 -1 1 0 -1 0 -1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 x + y + z + 2*y*z-1 + x-1*y + 2*y-1*z + x-1*z + y*z-2 + 3*z-1 + 2*x-1*y*z-1 + 3*y-1 + 4*x-1 + y-2*z + 2*x-1*y-1*z + x-1*y*z-2 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 9 1 irreducible and admissible
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3481
Image of polytope 3481 PALP id: 3481
grdb id: 140254
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 -1 0 0]
[ 0 1 0 1 -1 1 0 -2 -2 -1 0 -2 -1 0 -1 0 -1 -1 0]
[ 0 0 1 0 1 -1 -2 0 -2 0 0 -1 -1 -1 0 0 -2 -1 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y + y-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + 2*y-1*z-1 + 4*x-1*z-1 + 3*x-1*y-1 + x-1*z-2 + 5*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-1*z-2 + 2*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3482
Image of polytope 3482 PALP id: 3482
grdb id: 140624
Integer points: [ 1 0 0 0 -1 -1 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 0 -1 -1 -1 -1 -1 -1 0 0 -1 -1 -1 0 0 -1]
[ 0 0 1 0 1 1 -2 1 -2 0 -1 0 -1 0 -1 -2 0 -1 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*z + 2*z-1 + y-1 + 3*x-1 + x-1*y-1*z + 2*y-1*z-1 + 2*x-1*z-1 + 4*x-1*y-1 + x-2*y-1*z + y-1*z-2 + 5*x-1*y-1*z-1 + 3*x-2*y-1 + 2*x-1*y-1*z-2 + 3*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3483
Image of polytope 3483 PALP id: 3483
grdb id: 140735
Integer points: [ 1 0 0 1 1 0 0 -2 -2 -1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 1 0 0 -1 -2 1 0 1 0 1 -1 0 1 -1 0 1 -1 0]
[ 0 0 1 -1 0 1 -2 1 0 1 0 1 0 -1 1 0 -1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
51 rank 2, number 7 x + y + z + x*z-1 + 2*y*z-1 + x*y-1 + 2*x-1*y + 2*y-1*z + 2*x-1*z + y*z-2 + 3*z-1 + 2*x-1*y*z-1 + 3*y-1 + 4*x-1 + x-2*y + y-2*z + 2*x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3484
Image of polytope 3484 PALP id: 3484
grdb id: 136440
Integer points: [ 1 0 0 0 -1 -1 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 2 -1 -2 2 -2 1 0 -1 1 0 -1 1 0 0 -1]
[ 0 0 1 1 -1 -1 0 -1 -1 -1 -1 -1 0 0 0 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y2*z-1 + 2*x-1*y + y-1*z + 3*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 5*x-1 + 3*x-1*z-1 + 4*x-2*y*z-1 + 4*x-1*y-1 + x-1*y-1*z-1 + 6*x-2*z-1 + x-1*y-2 + 4*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 9 1 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Polytope 3485
Image of polytope 3485 PALP id: 3485
grdb id: 140871
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 0 -1 0 -2 -2 0 0 -1 -1 -1 -2 0 0 -1 -1]
[ 0 0 1 -1 1 2 -2 2 0 -1 0 -1 0 1 1 -1 0 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + y*z-1 + 2*y-1*z + x-1*z + x-1*y-1*z2 + 2*z-1 + 2*y-1 + 3*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + 3*x-1*z-1 + 5*x-1*y-1 + 2*x-1*y-2*z + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3486
Image of polytope 3486 PALP id: 3486
grdb id: 142082
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 1 -1 -1 -1 1 1 -1 -1 0 0 0 1 -1 0 0 0 1]
[ 0 0 2 -2 0 0 2 0 -2 -1 -1 0 1 1 -1 -1 0 1 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 y*z2 + 2*y*z + x-1*y*z2 + x + y + 2*z + 2*x-1*y*z + x-1*y + 2*x-1*z + 2*z-1 + y-1 + 4*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + x-1*y-1 + y-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 15 4 Lattice Minkowski decompositions of facet 15
Polytope 3487
Image of polytope 3487 PALP id: 3487
grdb id: 136237
Integer points: [ 1 0 0 0 0 0 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 1 -1 0 1 2 2 -2 -1 0 1 -1 0 1 -1 0 1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + y-1*z + 2*x-1*z + x-1*y-1*z2 + z-1 + y-1 + 4*x-1 + 4*x-1*y-1*z + x-2*y-1*z2 + 2*x-1*z-1 + 5*x-1*y-1 + 4*x-2*y-1*z + 2*x-1*y-1*z-1 + 6*x-2*y-1 + 4*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Polytope 3488
Image of polytope 3488 PALP id: 3488
grdb id: 136447
Integer points: [ 1 0 0 -1 -1 0 -2 -1 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 1 -1 1 -2 -3 -2 -1 0 -2 -1 0 -1 0 -1 0]
[ 0 0 1 -1 0 1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 8 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Polytope 3489
Image of polytope 3489 PALP id: 3489
grdb id: 135822
Integer points: [ 1 0 0 -1 0 -2 -1 -3 -3 -2 -3 -2 -1 -2 -1 -1 0 -1 0]
[ 0 1 0 1 -1 1 -2 0 -2 -2 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 0 1 -1 0 -2 -2 -1 -2 -1 0 -1 0 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
3 ? x + y + z + x-1*y + y-1*z + 2*y-1 + 4*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 4*x-1*y-1 + 2*x-1*y-1*z-1 + 5*x-2*z-1 + x-1*y-2 + 6*x-2*y-1*z-1 + x-3*z-2 + 2*x-2*y-2*z-1 + 2*x-3*y-1*z-2 + x-3*y-2*z-2
38 ? x + y + z + x-1*y + y-1*z + 2*y-1 + 3*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2 + 4*x-2*y-1*z-1 + x-3*z-2 + 2*x-2*y-2*z-1 + 2*x-3*y-1*z-2 + x-3*y-2*z-2
36 rank 3, number 7 x + y + z + x-1*y + y-1*z + 2*y-1 + 3*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 4*x-1*y-1 + 2*x-1*y-1*z-1 + 4*x-2*z-1 + x-1*y-2 + 5*x-2*y-1*z-1 + x-3*z-2 + 2*x-2*y-2*z-1 + 2*x-3*y-1*z-2 + x-3*y-2*z-2
85 rank 3, number 8 x + y + z + x-1*y + y-1*z + 2*y-1 + 4*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 5*x-1*y-1 + 2*x-1*y-1*z-1 + 4*x-2*z-1 + x-1*y-2 + 6*x-2*y-1*z-1 + x-3*z-2 + 2*x-2*y-2*z-1 + 2*x-3*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 205 1 Lattice Minkowski decompositions of facet 205
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 3490
Image of polytope 3490 PALP id: 3490
grdb id: 134595
Integer points: [ 1 0 0 0 -1 -1 -2 -3 -3 -2 -1 -3 -2 -1 -3 -2 -1 0 -1]
[ 0 1 -1 0 1 -2 1 0 -3 -2 -1 -2 -1 0 -1 0 -1 0 0]
[ 0 0 0 1 0 -1 -1 -2 -2 -1 0 -2 -1 0 -2 -1 -1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y + y-1 + 3*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + 4*x-2*z-1 + x-1*y-2*z-1 + 6*x-2*y-1*z-1 + x-3*z-2 + 3*x-2*y-2*z-1 + 3*x-3*y-1*z-2 + 3*x-3*y-2*z-2 + x-3*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 153 1 Lattice Minkowski decompositions of facet 153
Polytope 3491
Image of polytope 3491 PALP id: 3491
grdb id: 134607
Integer points: [ 1 0 0 0 -1 -1 -2 -3 -3 -3 -2 -1 -3 -2 -1 -2 -1 -1 0]
[ 0 1 -1 0 1 1 -2 1 -2 -1 -1 -1 0 0 0 1 -1 0 0]
[ 0 0 0 1 0 -1 -1 -2 -2 -2 -1 0 -2 -1 0 -1 -1 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + x-1*y + x-1*y*z-1 + y-1 + 4*x-1 + 3*x-1*z-1 + 2*x-2*y*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 6*x-2*z-1 + x-3*y*z-2 + 5*x-2*y-1*z-1 + 3*x-3*z-2 + x-2*y-2*z-1 + 3*x-3*y-1*z-2 + x-3*y-2*z-2
46 ? x + y + z + x-1*y + x-1*y*z-1 + y-1 + 3*x-1 + 3*x-1*z-1 + 2*x-2*y*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 5*x-2*z-1 + x-3*y*z-2 + 4*x-2*y-1*z-1 + 3*x-3*z-2 + x-2*y-2*z-1 + 3*x-3*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 155 1 Lattice Minkowski decompositions of facet 155
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3492
Image of polytope 3492 PALP id: 3492
grdb id: 140571
Integer points: [ 1 0 0 0 -1 0 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 -1 -1 0 -3 -2 -1 -2 -1 0 -2 -1 0 -1 0]
[ 0 0 1 -1 0 -1 1 1 1 1 1 0 0 0 1 1 1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y + y-1*z + 2*x-1*z + z-1 + 2*y-1 + 3*x-1 + 4*x-1*y-1*z + x-2*z + y-1*z-1 + 4*x-1*y-1 + 2*x-1*y-2*z + 3*x-2*y-1*z + 2*x-1*y-2 + 3*x-2*y-2*z + x-2*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 3493
Image of polytope 3493 PALP id: 3493
grdb id: 140188
Integer points: [ 1 0 0 0 0 -1 -1 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 -1 -1 0 -1 -1 -1 -1 0 0 -1 -1 -1 0 0 -1]
[ 0 0 1 1 -1 1 -2 0 -3 -1 -2 0 -1 0 -1 -2 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + y-1*z + 2*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + y-1*z-1 + 3*x-1*z-1 + 4*x-1*y-1 + x-1*z-2 + 5*x-1*y-1*z-1 + x-2*y-1 + 2*x-1*y-1*z-2 + 3*x-2*y-1*z-1 + 3*x-2*y-1*z-2 + x-2*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3494
Image of polytope 3494 PALP id: 3494
grdb id: 134327
Integer points: [ 1 0 1 -1 0 -2 1 0 -3 0 0 -1 -1 -1 -2 -2 0 0 -1]
[ 0 1 -1 1 0 1 -2 -3 0 -1 -2 0 -1 -2 0 -1 0 -1 0]
[ 0 0 0 0 1 -1 -1 -2 -2 0 -1 0 -1 -2 -1 -2 0 -1 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*y-1 + x-1*y + 3*y-1 + 3*x-1 + x*y-2*z-1 + 4*y-1*z-1 + 4*x-1*z-1 + x-2*y*z-1 + 3*y-2*z-1 + 6*x-1*y-1*z-1 + 3*x-2*z-1 + y-3*z-2 + 3*x-1*y-2*z-2 + 3*x-2*y-1*z-2 + x-3*z-2
13 rank 2, number 12 x + y + z + x*y-1 + x-1*y + 3*y-1 + 3*x-1 + x*y-2*z-1 + 3*y-1*z-1 + 3*x-1*z-1 + x-2*y*z-1 + 3*y-2*z-1 + 6*x-1*y-1*z-1 + 3*x-2*z-1 + y-3*z-2 + 3*x-1*y-2*z-2 + 3*x-2*y-1*z-2 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Polytope 3495
Image of polytope 3495 PALP id: 3495
grdb id: 140548
Integer points: [ 1 0 0 0 0 -1 0 -1 -3 -1 -2 0 -1 -2 0 -1 -2 0 -1]
[ 0 1 0 1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 0 1 -1 1 0 -1 2 2 0 1 0 1 2 -1 0 1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + y*z-1 + x-1*y + y-1*z + 3*x-1*z + x-1*y-1*z2 + 2*z-1 + 2*y-1 + 4*x-1 + 4*x-1*y-1*z + 2*x-2*z + 2*x-2*y-1*z2 + y-1*z-1 + 3*x-1*y-1 + 3*x-2*y-1*z + x-3*y-1*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Polytope 3496
Image of polytope 3496 PALP id: 3496
grdb id: 140565
Integer points: [ 1 0 0 0 0 0 -2 -1 -4 -3 -2 -2 -1 -3 -2 -1 -1 0 -1]
[ 0 1 0 0 -1 -1 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 0 1 1 1 1 1 1 0 0 1 1 1 0 0 1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + y-1*z + 2*x-1*z + z-1 + y-1 + 2*x-1 + 4*x-1*y-1*z + x-2*z + 3*x-1*y-1 + x-1*y-2*z + 5*x-2*y-1*z + 2*x-2*y-1 + 3*x-2*y-2*z + 2*x-3*y-1*z + 3*x-3*y-2*z + x-4*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3497
Image of polytope 3497 PALP id: 3497
grdb id: 140568
Integer points: [ 1 0 0 0 0 0 -1 -2 -4 -2 -3 -1 -2 -1 -2 -3 0 -1 -1]
[ 0 1 0 -1 0 -1 -1 -1 -1 -1 -1 0 0 -1 -1 -1 0 0 -1]
[ 0 0 1 0 -1 1 1 -2 -2 0 -1 0 -1 0 -1 -2 0 -1 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + y-1*z + z-1 + y-1 + 3*x-1 + x-1*y-1*z + 2*x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-1*z-1 + 2*x-2*z-1 + 3*x-2*y-1 + 5*x-2*y-1*z-1 + x-2*y-1*z-2 + 3*x-3*y-1*z-1 + 2*x-3*y-1*z-2 + x-4*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 3498
Image of polytope 3498 PALP id: 3498
grdb id: 140567
Integer points: [ 1 0 0 0 0 0 -1 -2 -4 -2 -3 -1 -2 -3 -1 -1 -2 0 -1]
[ 0 1 0 0 -1 1 1 -2 -2 0 -1 0 -1 -2 -1 0 -1 0 -1]
[ 0 0 1 -1 0 1 0 -1 -3 -1 -2 0 -1 -2 0 -1 -2 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 y*z + x + y + z + x-1*y + z-1 + y-1 + 4*x-1 + 3*x-1*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + 3*x-2*z-1 + 5*x-2*y-1*z-1 + 2*x-2*y-1*z-2 + x-2*y-2*z-1 + 3*x-3*y-1*z-2 + 2*x-3*y-2*z-2 + x-4*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3499
Image of polytope 3499 PALP id: 3499
grdb id: 140594
Integer points: [ 1 0 1 -1 0 0 -1 -2 -4 -2 -3 -1 -2 -3 0 -1 -2 0 -1]
[ 0 1 -1 1 0 -1 -1 1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 0 0 0 1 -1 0 -1 -3 -1 -2 0 -1 -2 0 -1 -2 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*y-1 + x-1*y + 2*y-1 + 3*x-1 + y-1*z-1 + 3*x-1*z-1 + x-2*y*z-1 + x-1*y-1 + 4*x-1*y-1*z-1 + 4*x-2*z-1 + 3*x-2*y-1*z-1 + 2*x-2*y-1*z-2 + 2*x-3*z-2 + 3*x-3*y-1*z-2 + x-4*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3500
Image of polytope 3500 PALP id: 3500
grdb id: 140258
Integer points: [ 1 0 0 0 0 -1 -1 -3 -3 -2 -1 -3 -2 -1 0 -2 -1 -1 0]
[ 0 1 -1 0 -2 2 0 1 3 2 1 2 1 0 -1 0 -1 1 0]
[ 0 0 0 1 1 -1 -1 -2 -2 -1 0 -2 -1 0 1 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y2*z-1 + 3*x-1*y + 2*y-1*z + 3*x-1*y*z-1 + 3*x-2*y2*z-1 + y-1 + 6*x-1 + y-2*z + x-3*y3*z-2 + x-1*z-1 + 6*x-2*y*z-1 + 3*x-1*y-1 + 2*x-3*y2*z-2 + 3*x-2*z-1 + x-3*y*z-2
13 rank 2, number 12 x + y + z + x-1*y2*z-1 + 3*x-1*y + 2*y-1*z + 2*x-1*y*z-1 + 3*x-2*y2*z-1 + y-1 + 6*x-1 + y-2*z + x-3*y3*z-2 + x-1*z-1 + 6*x-2*y*z-1 + 3*x-1*y-1 + 2*x-3*y2*z-2 + 3*x-2*z-1 + x-3*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 3501
Image of polytope 3501 PALP id: 3501
grdb id: 136423
Integer points: [ 1 0 0 0 0 -1 -1 -3 -5 -2 -3 -4 -1 -2 -3 -1 -2 0 -1]
[ 0 1 -1 0 1 1 1 0 1 1 1 1 1 1 1 0 0 0 0]
[ 0 0 0 1 1 -1 1 -2 -3 0 -1 -2 0 -1 -2 0 -1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? y*z + x + y + z + x-1*y*z + 4*x-1*y + x-1*y*z-1 + y-1 + 4*x-1 + 4*x-2*y + 2*x-1*z-1 + 5*x-2*y*z-1 + 4*x-2*z-1 + 6*x-3*y*z-1 + 2*x-3*y*z-2 + x-3*z-2 + 4*x-4*y*z-2 + x-5*y*z-3
46 ? y*z + x + y + z + x-1*y*z + 4*x-1*y + x-1*y*z-1 + y-1 + 3*x-1 + 4*x-2*y + 2*x-1*z-1 + 5*x-2*y*z-1 + 3*x-2*z-1 + 6*x-3*y*z-1 + 2*x-3*y*z-2 + x-3*z-2 + 4*x-4*y*z-2 + x-5*y*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 93 1 Lattice Minkowski decompositions of facet 93
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3502
Image of polytope 3502 PALP id: 3502
grdb id: 152299
Integer points: [ 1 0 0 0 0 -1 0 -1 -3 -2 -1 0 -1 0 -2 -1 -2 -1 0]
[ 0 1 0 1 -1 -1 -1 1 -1 -1 -1 -1 0 0 -1 -1 0 0 0]
[ 0 0 1 -1 1 1 -1 -1 -1 0 0 0 0 0 -1 -1 -1 -1 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + y*z-1 + y-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + 4*x-1*z-1 + 4*x-1*y-1 + 3*x-1*y-1*z-1 + 2*x-2*z-1 + 2*x-2*y-1 + 3*x-2*y-1*z-1 + x-3*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3503
Image of polytope 3503 PALP id: 3503
grdb id: 610802
Integer points: [ 1 0 0 -2 2 0 -2 0 1 -3 0 -1 1 -1 -2 1 0 -1 -1]
[ 0 1 0 2 -2 0 1 -1 -2 2 -1 0 -1 0 1 -1 0 1 1]
[ 0 0 1 1 -1 -1 0 1 0 1 0 0 -1 1 1 0 0 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
26 rank 2, number 8 x + y + z + 2*x-1*y*z + x-2*y2*z + x*y-1 + x-1*y + y-1*z + 3*x-1*z + 3*x-2*y*z + x-3*y2*z + x2*y-2*z-1 + 2*x*y-1*z-1 + z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 10 2 Lattice Minkowski decompositions of facet 10
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 3504
Image of polytope 3504 PALP id: 3504
grdb id: 610803
Integer points: [ 1 1 -1 -1 0 0 -1 -1 2 2 1 1 1 0 0 0 -1 -1 -1]
[ 0 2 -2 0 0 1 -3 0 2 3 1 1 2 -1 0 1 -2 -1 -1]
[ 0 0 0 0 1 1 -1 -1 1 1 0 1 1 0 0 0 -1 -1 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x2*y3*z + x2*y2*z + 2*x*y2*z + x*y2 + 2*x*y*z + 2*x*y + y*z + x + 2*y + z + 3*y-1 + x-1 + x-1*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2 + 3*x-1*y-2*z-1 + x-1*y-3*z-1
22 ? x2*y3*z + x2*y2*z + 2*x*y2*z + x*y2 + 2*x*y*z + 2*x*y + y*z + x + 3*y + z + 3*y-1 + x-1 + x-1*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2 + 3*x-1*y-2*z-1 + x-1*y-3*z-1
7 rank 1, V12 x2*y3*z + x2*y2*z + 2*x*y2*z + x*y2 + 2*x*y*z + 2*x*y + y*z + x + 3*y + z + 2*y-1 + x-1 + x-1*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2 + 3*x-1*y-2*z-1 + x-1*y-3*z-1
11 rank 2, number 6 x2*y3*z + x2*y2*z + 2*x*y2*z + x*y2 + 2*x*y*z + 2*x*y + y*z + x + 2*y + z + 2*y-1 + x-1 + x-1*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2 + 3*x-1*y-2*z-1 + x-1*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 23 2 Lattice Minkowski decompositions of facet 23
Polytope 3505
Image of polytope 3505 PALP id: 3505
grdb id: 610621
Integer points: [ 1 0 0 -1 1 1 0 -2 1 0 0 0 1 1 -1 -1 0 0 -1]
[ 0 1 0 0 0 -1 -1 1 -1 -1 -1 -1 -1 -1 0 0 0 0 1]
[ 0 0 1 1 -1 1 1 0 -2 -2 0 -1 0 -1 0 -1 0 -1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + x*y-1*z + z + x*z-1 + 3*x*y-1 + 2*x-1*y + y-1*z + x-1*z + 3*x*y-1*z-1 + 3*z-1 + 3*y-1 + 3*x-1 + x-2*y + x*y-1*z-2 + 3*y-1*z-1 + 2*x-1*z-1 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3506
Image of polytope 3506 PALP id: 3506
grdb id: 610781
Integer points: [ 1 0 0 1 0 0 -1 0 -2 -2 -1 -1 0 -2 -1 0 -1 0 -1]
[ 0 1 0 -1 1 -1 1 -1 1 -1 -1 -1 -1 0 0 0 0 0 1]
[ 0 0 1 0 -1 1 1 -1 1 1 0 1 0 1 0 -1 1 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + x-1*y*z + y*z-1 + x*y-1 + 2*x-1*y + y-1*z + 3*x-1*z + x-2*y*z + 2*z-1 + 2*y-1 + 4*x-1 + 2*x-1*y-1*z + 2*x-2*z + y-1*z-1 + 2*x-1*y-1 + x-2*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3507
Image of polytope 3507 PALP id: 3507
grdb id: 610446
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 -1 0 0 -2 2 -2 2 -1 1 0 1 0 -1 -1 1 0 -1]
[ 0 0 0 1 -1 2 -1 1 -2 2 0 1 -1 0 1 0 -1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + 2*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + x-1*y2*z-2 + 3*x-1*y*z-1 + y-1 + 4*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
151 ? x + y + z + 2*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + x-1*y2*z-2 + 4*x-1*y*z-1 + y-1 + 7*x-1 + 5*x-1*y-1*z + x-1*y-2*z2 + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 166 1 Lattice Minkowski decompositions of facet 166
Polytope 3508
Image of polytope 3508 PALP id: 3508
grdb id: 610744
Integer points: [ 1 0 1 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 -1 0 0 2 -2 2 -1 -2 1 0 -1 1 0 -1 1 0 -1]
[ 0 0 0 1 -1 -1 1 -2 2 2 -1 0 1 0 1 0 -1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
51 rank 2, number 7 x + y + z + 2*y*z-1 + x-1*y2*z-1 + x*y-1 + 3*x-1*y + 3*y-1*z + 3*x-1*z + x-1*y-1*z2 + x-1*y2*z-2 + z-1 + 4*x-1*y*z-1 + 2*y-1 + 6*x-1 + y-2*z + 4*x-1*y-1*z + x-1*y-2*z2
18 rank 1, V14 x + y + z + 2*y*z-1 + x-1*y2*z-1 + x*y-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + x-1*y2*z-2 + z-1 + 4*x-1*y*z-1 + 2*y-1 + 6*x-1 + y-2*z + 4*x-1*y-1*z + x-1*y-2*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 3509
Image of polytope 3509 PALP id: 3509
grdb id: 610612
Integer points: [ 1 0 0 0 1 0 -1 0 -1 -3 -2 -1 0 -1 0 -2 -1 -2 -1]
[ 0 1 0 0 -1 -1 1 -1 -1 -1 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 -1 0 1 -1 -1 1 -1 0 0 0 0 0 -1 -1 -1 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*y-1 + y-1*z + z-1 + x-1*y*z-1 + 3*y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + 3*x-1*z-1 + 4*x-1*y-1 + 3*x-1*y-1*z-1 + 2*x-2*z-1 + 2*x-2*y-1 + 3*x-2*y-1*z-1 + x-3*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3510
Image of polytope 3510 PALP id: 3510
grdb id: 610784
Integer points: [ 1 0 0 -2 2 0 -1 -2 2 1 -1 -1 0 -1 0 1 0 1 1]
[ 0 1 0 2 -2 0 0 1 -3 -2 1 0 -1 1 0 -1 -1 -2 -1]
[ 0 0 1 1 -1 -1 1 1 -2 -2 0 0 -1 1 0 -1 0 -1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
51 rank 2, number 7 x + y + z + 2*x-1*y*z + x-2*y2*z + 2*x*y-1 + 2*x-1*y + x-1*z + x-2*y*z + x2*y-2*z-1 + 3*x*y-1*z-1 + z-1 + 3*y-1 + 3*x-1 + 3*x*y-2*z-1 + 3*y-1*z-1 + x2*y-3*z-2 + x*y-2*z-2
18 rank 1, V14 x + y + z + 2*x-1*y*z + x-2*y2*z + 2*x*y-1 + 2*x-1*y + x-1*z + x-2*y*z + x2*y-2*z-1 + 2*x*y-1*z-1 + z-1 + 3*y-1 + 3*x-1 + 3*x*y-2*z-1 + 3*y-1*z-1 + x2*y-3*z-2 + x*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 3511
Image of polytope 3511 PALP id: 3511
grdb id: 610605
Integer points: [ 1 0 0 0 1 0 -1 0 -2 -3 -1 -2 0 -1 -2 -1 1 0 -1]
[ 0 1 0 0 -2 -1 0 -1 2 2 0 1 -1 0 1 1 -1 0 1]
[ 0 0 1 -1 0 1 1 -1 -1 -1 -1 -1 0 0 0 -1 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + x*y-2 + 3*y-1 + 4*x-1 + 2*x-2*y + y-1*z-1 + 3*x-1*z-1 + 3*x-2*y*z-1 + x-3*y2*z-1
40 rank 2, number 10 x + y + z + 2*x*y-1 + 3*x-1*y + y-1*z + x-1*z + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + x*y-2 + 3*y-1 + 4*x-1 + 2*x-2*y + y-1*z-1 + 3*x-1*z-1 + 3*x-2*y*z-1 + x-3*y2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 3512
Image of polytope 3512 PALP id: 3512
grdb id: 610156
Integer points: [ 1 0 0 1 -1 1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 -1 1 -1 -1 1 -1 -1 -1 0 0 0 1 -1 -1 0 0]
[ 0 0 1 0 1 -1 1 -1 1 -1 0 -1 0 1 0 -1 0 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y*z + x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 3*y-1 + 4*x-1 + x-1*y-1*z + 2*y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3513
Image of polytope 3513 PALP id: 3513
grdb id: 608684
Integer points: [ 1 0 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 1 -1 1 -1 0 -1 1 0 0 0 -1 -1 0 0 -1]
[ 0 0 1 1 1 -1 -1 1 -2 -2 0 1 0 -1 0 -1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + 2*x-1*y + y-1*z + 2*x-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 5*x-1 + x-1*y-1*z + y-1*z-1 + 4*x-1*z-1 + 3*x-1*y-1 + x-1*z-2 + 3*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3514
Image of polytope 3514 PALP id: 3514
grdb id: 608808
Integer points: [ 1 0 0 0 -1 1 -1 0 -1 -1 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 1 0 1 1 -1 0 -2 1 -2 -1 0 1 -1 0 -1 0 -1 0]
[ 0 0 1 -1 0 0 1 1 -2 1 1 0 -1 1 0 0 -1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + y*z-1 + x*y-1 + x-1*y + 2*y-1*z + x-1*z + 2*z-1 + 2*x-1*y*z-1 + 3*y-1 + 4*x-1 + y-2*z + 2*x-1*y-1*z + x-1*y*z-2 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3515
Image of polytope 3515 PALP id: 3515
grdb id: 608813
Integer points: [ 1 0 0 1 -1 -1 -1 1 1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 -1 1 0 1 -1 -2 -2 -1 0 -1 0 -2 -1 0 -1 0]
[ 0 0 1 0 0 1 -1 -1 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*y-1 + x-1*y + x-1*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 3*y-1 + 3*x-1 + x*y-2*z-1 + 4*y-1*z-1 + 3*x-1*z-1 + 2*x-1*y-1 + 2*y-2*z-1 + 3*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3516
Image of polytope 3516 PALP id: 3516
grdb id: 608627
Integer points: [ 1 0 0 1 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 -1 0 0]
[ 0 1 0 0 0 1 -1 0 -2 -2 -1 -2 -1 0 -1 0 -1 -1 0]
[ 0 0 1 -1 1 0 1 -1 1 -1 1 0 0 0 0 0 -1 -1 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*z-1 + x-1*y + y-1*z + x-1*z + 2*z-1 + 3*y-1 + 3*x-1 + 2*x-1*y-1*z + 2*y-1*z-1 + x-1*z-1 + 4*x-1*y-1 + x-1*y-2*z + 2*x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-2*z-1
31 rank 3, number 3 x + y + z + x*z-1 + x-1*y + y-1*z + x-1*z + 2*z-1 + 3*y-1 + 4*x-1 + 2*x-1*y-1*z + 2*y-1*z-1 + x-1*z-1 + 5*x-1*y-1 + x-1*y-2*z + 2*x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3517
Image of polytope 3517 PALP id: 3517
grdb id: 608909
Integer points: [ 1 0 0 1 -1 0 -1 -1 0 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 0 1 -1 1 -1 -1 -1 0 0 0 -1 -1 0 0 -1 -1]
[ 0 0 1 -1 1 1 0 1 -2 -2 1 0 -1 0 -1 0 -1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y*z + x*z-1 + x-1*y + y-1*z + 2*x-1*z + 3*z-1 + 3*y-1 + 4*x-1 + x-1*y-1*z + 3*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + y-1*z-2 + 3*x-1*y-1*z-1 + x-1*y-1*z-2
62 rank 2, number 9 x + y + z + x-1*y*z + x*z-1 + x-1*y + y-1*z + 2*x-1*z + 2*z-1 + 3*y-1 + 4*x-1 + x-1*y-1*z + 3*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + y-1*z-2 + 3*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 3518
Image of polytope 3518 PALP id: 3518
grdb id: 608870
Integer points: [ 1 0 0 1 -1 1 1 -2 0 -2 -1 0 1 -1 0 0 -1 0 -1]
[ 0 1 0 -1 1 0 -2 1 -2 0 -1 -1 -1 0 0 -1 0 0 1]
[ 0 0 1 0 1 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y*z + x*z-1 + x*y-1 + 2*x-1*y + 2*x*y-1*z-1 + 3*z-1 + 2*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + 4*y-1*z-1 + 3*x-1*z-1 + y-2*z-1 + 2*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3519
Image of polytope 3519 PALP id: 3519
grdb id: 610102
Integer points: [ 1 0 0 1 1 -1 -1 -1 1 -1 -1 0 0 -1 -1 0 0 1 0]
[ 0 1 0 0 -1 1 0 0 -2 -2 -1 -2 -1 -1 0 -1 0 -1 0]
[ 0 0 1 -1 0 0 1 -1 -1 -1 0 -1 0 -1 0 -1 0 -1 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*z-1 + x*y-1 + x-1*y + x-1*z + 2*x*y-1*z-1 + 2*z-1 + 3*y-1 + 2*x-1 + x*y-2*z-1 + 4*y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + 2*y-2*z-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3520
Image of polytope 3520 PALP id: 3520
grdb id: 607864
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 1 1 -1 -2 -1 -2 0 -1 -2 0 -1 0 -1 0 -1]
[ 0 0 1 -1 0 -1 -1 0 2 2 -1 0 1 0 1 1 0 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
39 ? x + y + z + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + z-1 + x-1*y*z-1 + 2*y-1 + 5*x-1 + 5*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 5*x-1*y-1 + 2*x-1*y-2*z + x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 164 1 Lattice Minkowski decompositions of facet 164
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 3521
Image of polytope 3521 PALP id: 3521
grdb id: 606825
Integer points: [ 1 0 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 1 1 -1 0 -1 -1 -1 -1 -1 0 0 0 -1 0 0]
[ 0 0 1 1 0 -1 -1 -2 2 -2 -1 0 1 -1 0 1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y + y-1*z + 2*x-1*z + x-1*y-1*z2 + 2*z-1 + x-1*y*z-1 + 2*y-1 + 5*x-1 + 4*x-1*y-1*z + y-1*z-1 + 4*x-1*z-1 + 6*x-1*y-1 + x-1*z-2 + 4*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Polytope 3522
Image of polytope 3522 PALP id: 3522
grdb id: 606817
Integer points: [ 1 0 0 0 -1 -1 -1 -1 0 -1 -1 -1 -1 0 0 -1 -1 -1 0]
[ 0 1 0 0 1 0 1 -1 -2 -3 -2 -1 0 -1 0 -2 -1 0 -1]
[ 0 0 1 -1 0 1 -1 1 -1 -1 0 0 0 0 0 -1 -1 -1 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + x-1*y-1*z + 2*y-1*z-1 + 4*x-1*z-1 + 5*x-1*y-1 + y-2*z-1 + 6*x-1*y-1*z-1 + 2*x-1*y-2 + 4*x-1*y-2*z-1 + x-1*y-3*z-1
39 ? x + y + z + x-1*y + x-1*z + z-1 + x-1*y*z-1 + 3*y-1 + 4*x-1 + x-1*y-1*z + 2*y-1*z-1 + 4*x-1*z-1 + 5*x-1*y-1 + y-2*z-1 + 6*x-1*y-1*z-1 + 2*x-1*y-2 + 4*x-1*y-2*z-1 + x-1*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Polytope 3523
Image of polytope 3523 PALP id: 3523
grdb id: 608687
Integer points: [ 1 0 0 0 -1 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 1 1 0 -2 -1 -3 0 -2 -1 0 -2 -1 -1 0 -1]
[ 0 0 1 -1 0 -1 1 1 -1 1 -1 0 0 0 1 1 0 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + x-1*y + 2*y-1*z + x-1*z + z-1 + x-1*y*z-1 + 3*y-1 + 4*x-1 + y-2*z + 3*x-1*y-1*z + 2*x-1*z-1 + 5*x-1*y-1 + 3*x-1*y-2*z + x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-3*z
52 rank 2, number 52 x + y + z + x-1*y + 2*y-1*z + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + y-2*z + 3*x-1*y-1*z + 2*x-1*z-1 + 5*x-1*y-1 + 3*x-1*y-2*z + x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3524
Image of polytope 3524 PALP id: 3524
grdb id: 608931
Integer points: [ 1 0 0 0 -1 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 1 1 0 -2 -1 -3 -1 -2 0 -1 -2 0 -1 0 -1]
[ 0 0 1 -1 1 0 1 -1 -2 -2 0 -1 0 -1 -2 -1 0 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y*z + x-1*y + x-1*z + z-1 + 2*y-1 + 4*x-1 + 3*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + y-2*z-1 + 5*x-1*y-1*z-1 + x-1*y-1*z-2 + 3*x-1*y-2*z-1 + 2*x-1*y-2*z-2 + x-1*y-3*z-2
13 rank 2, number 12 x + y + z + x-1*y*z + x-1*y + x-1*z + z-1 + 2*y-1 + 4*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + y-2*z-1 + 5*x-1*y-1*z-1 + x-1*y-1*z-2 + 3*x-1*y-2*z-1 + 2*x-1*y-2*z-2 + x-1*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3525
Image of polytope 3525 PALP id: 3525
grdb id: 610103
Integer points: [ 1 0 0 1 0 0 -1 -1 -1 -3 -2 -1 -2 -1 0 -2 -1 0 0]
[ 0 1 0 -1 1 -1 1 -1 1 1 1 0 0 1 0 1 0 -1 0]
[ 0 0 1 0 -1 1 0 0 -2 -2 -1 0 -1 -1 0 -2 -1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + y*z-1 + x*y-1 + x-1*y + y-1*z + 2*z-1 + 3*x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*y*z-2 + 4*x-1*z-1 + 2*x-2*y*z-1 + x-1*y-1 + 2*x-2*y*z-2 + 2*x-2*z-1 + x-3*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Polytope 3526
Image of polytope 3526 PALP id: 3526
grdb id: 619055
Integer points: [ 1 0 0 0 0 -1 0 -1 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 0 -1 -1 -1 -1 -1 -1 0 0 -1 -1 -1 0 -1]
[ 0 0 1 -1 1 1 -1 -2 1 -2 0 -1 0 -1 1 0 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + y-1*z + x-1*z + z-1 + 2*y-1 + 3*x-1 + 2*x-1*y-1*z + y-1*z-1 + 2*x-1*z-1 + 5*x-1*y-1 + x-2*y-1*z + 4*x-1*y-1*z-1 + 3*x-2*y-1 + x-1*y-1*z-2 + 3*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3527
Image of polytope 3527 PALP id: 3527
grdb id: 619540
Integer points: [ 1 0 0 0 0 0 -1 -2 -1 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 0 -1 1 0 -2 -3 -1 -2 0 -1 0 -1 -2 0 -1]
[ 0 0 1 -1 -1 1 0 1 0 1 1 1 0 0 1 1 1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + y*z-1 + x-1*y + y-1*z + 2*x-1*z + z-1 + 2*y-1 + 4*x-1 + 4*x-1*y-1*z + x-2*z + 4*x-1*y-1 + 2*x-1*y-2*z + 3*x-2*y-1*z + x-1*y-2 + 3*x-2*y-2*z + x-2*y-3*z
52 rank 2, number 52 x + y + z + y*z-1 + x-1*y + y-1*z + 2*x-1*z + z-1 + 2*y-1 + 3*x-1 + 4*x-1*y-1*z + x-2*z + 3*x-1*y-1 + 2*x-1*y-2*z + 3*x-2*y-1*z + x-1*y-2 + 3*x-2*y-2*z + x-2*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3528
Image of polytope 3528 PALP id: 3528
grdb id: 41156
Integer points: [ 1 0 0 0 -1 -1 1 0 0 -2 -2 -1 -2 -1 0 -1 -1 0 1]
[ 0 1 0 0 1 1 -2 -1 -1 1 1 0 1 0 -1 0 1 0 -1]
[ 0 0 1 -1 1 -1 0 -1 1 1 -1 -1 0 0 0 1 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + z-1 + x-1*y*z-1 + x*y-2 + 3*y-1 + 4*x-1 + 2*x-2*y + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1
40 rank 2, number 10 x + y + z + x-1*y*z + 2*x*y-1 + 3*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + z-1 + x-1*y*z-1 + x*y-2 + 3*y-1 + 4*x-1 + 2*x-2*y + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1
40 rank 2, number 10 x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + z-1 + x-1*y*z-1 + x*y-2 + 4*y-1 + 5*x-1 + 2*x-2*y + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1
161 ? x + y + z + x-1*y*z + 2*x*y-1 + 3*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + z-1 + x-1*y*z-1 + x*y-2 + 4*y-1 + 5*x-1 + 2*x-2*y + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 3529
Image of polytope 3529 PALP id: 3529
grdb id: 41168
Integer points: [ 1 0 0 -1 1 0 -1 -1 -1 0 -1 -1 0 -1 -1 0 0 1 0]
[ 0 1 0 2 -2 0 2 1 1 -2 -1 0 -1 0 1 -1 0 -1 1]
[ 0 0 1 2 -2 -1 1 0 2 -1 0 0 -1 1 1 0 0 -1 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x-1*y2*z2 + 2*y*z + x-1*y2*z + x-1*y*z2 + x + y + z + 3*x-1*y*z + x-1*y + 2*x-1*z + 2*x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + 2*y-1*z-1 + x-1*y-1 + x*y-2*z-2 + y-2*z-1
51 rank 2, number 7 x-1*y2*z2 + 2*y*z + x-1*y2*z + x-1*y*z2 + x + y + z + 3*x-1*y*z + x-1*y + 2*x-1*z + 2*x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + 3*y-1*z-1 + x-1*y-1 + x*y-2*z-2 + y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 3530
Image of polytope 3530 PALP id: 3530
grdb id: 40830
Integer points: [ 1 0 0 1 0 0 -1 -1 -1 0 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 1 -1 1 -1 1 -1 -1 -1 -1 0 0 0 -1 0 0]
[ 0 0 1 -1 -1 1 0 2 -1 -1 -1 0 1 -1 0 1 0 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + x*z-1 + y*z-1 + x-1*y + y-1*z + 2*x-1*z + x-1*y-1*z2 + 2*z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + 3*x-1*y-1*z + y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1
20 rank 1, V16 x + y + z + x*z-1 + y*z-1 + x-1*y + y-1*z + 2*x-1*z + x-1*y-1*z2 + 3*z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + 3*x-1*y-1*z + y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3531
Image of polytope 3531 PALP id: 3531
grdb id: 40767
Integer points: [ 1 0 0 0 -1 -1 1 -2 1 1 -2 0 -1 1 0 -1 0 -1 0]
[ 0 1 0 -1 0 1 -1 1 -2 -2 1 -1 0 -1 0 1 -1 0 0]
[ 0 0 1 1 1 -1 -1 0 0 -1 -1 0 0 0 0 0 -1 -1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + 3*y-1*z-1 + 3*x-1*z-1 + x-2*y*z-1
40 rank 2, number 10 x + y + z + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + x*y-2 + 4*y-1 + 4*x-1 + x-2*y + x*y-2*z-1 + 3*y-1*z-1 + 3*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 11 5 Lattice Minkowski decompositions of facet 11
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Polytope 3532
Image of polytope 3532 PALP id: 3532
grdb id: 41052
Integer points: [ 1 0 0 1 -1 -1 -2 1 -2 1 0 -1 -1 0 0 -1 0 0 1]
[ 0 1 0 -1 1 0 1 -2 1 -2 -1 0 0 -1 -1 1 0 0 -1]
[ 0 0 1 0 1 1 1 -1 0 -2 -2 -1 0 -1 0 0 -1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y*z + x*y-1 + 2*x-1*y + x-1*z + x-2*y*z + 2*x*y-1*z-1 + 2*z-1 + 2*y-1 + 4*x-1 + x-2*y + x*y-2*z-1 + 4*y-1*z-1 + 2*x-1*z-1 + x*y-2*z-2 + y-1*z-2
62 rank 2, number 9 x + y + z + x-1*y*z + x*y-1 + 2*x-1*y + x-1*z + x-2*y*z + 2*x*y-1*z-1 + 2*z-1 + 2*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + 3*y-1*z-1 + 2*x-1*z-1 + x*y-2*z-2 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 96 1 Lattice Minkowski decompositions of facet 96
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3533
Image of polytope 3533 PALP id: 3533
grdb id: 40829
Integer points: [ 1 0 0 1 -1 0 -1 1 -1 0 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 -1 1 -1 0 -1 -1 -1 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 0 0 1 1 -1 1 -2 -2 0 -1 0 -1 0 -1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + z + x*y-1 + x-1*y + y-1*z + x-1*z + x*y-1*z-1 + 2*z-1 + 4*y-1 + 3*x-1 + x-1*y-1*z + 4*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + y-1*z-2 + 3*x-1*y-1*z-1 + x-1*y-1*z-2
10 rank 1, V18 x + y + z + x*y-1 + x-1*y + y-1*z + x-1*z + x*y-1*z-1 + 2*z-1 + 3*y-1 + 3*x-1 + x-1*y-1*z + 3*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + y-1*z-2 + 3*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3534
Image of polytope 3534 PALP id: 3534
grdb id: 41131
Integer points: [ 1 0 0 1 -1 0 1 -1 1 0 -1 0 0 -1 1 0 -1 0 -1]
[ 0 1 0 0 1 1 -1 1 -2 -2 -1 0 -1 0 -1 0 1 -1 0]
[ 0 0 1 -1 1 -1 -1 -1 0 1 1 -1 0 0 0 0 0 1 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x-1*y*z + x*z-1 + y*z-1 + 2*x*y-1 + 2*x-1*y + 2*y-1*z + 2*x-1*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + x*y-2 + 3*y-1 + 2*x-1 + y-2*z + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3535
Image of polytope 3535 PALP id: 3535
grdb id: 41126
Integer points: [ 1 0 0 1 -1 -1 1 -1 -1 1 0 1 0 0 0 0 0 -1 -1]
[ 0 1 0 -1 1 -1 0 1 -1 -1 1 0 -1 0 -1 0 1 0 0]
[ 0 0 1 0 0 2 -2 -1 1 -1 -2 -1 0 -1 1 0 -1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*x*z-1 + 2*y*z-1 + x*y-1 + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + x*z-2 + y*z-2 + x*y-1*z-1 + 3*z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 3 Lattice Minkowski decompositions of facet 15
Polytope 3536
Image of polytope 3536 PALP id: 3536
grdb id: 41127
Integer points: [ 1 0 0 1 -1 1 0 -1 -1 0 -1 0 0 -1 -1 0 0 0 -1]
[ 0 1 0 0 1 -1 1 1 -1 -2 -2 0 -1 0 -1 1 0 -1 0]
[ 0 0 1 -1 0 0 -2 -1 2 1 2 -1 0 0 1 -1 0 1 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x*z-1 + 2*y*z-1 + x*y-1 + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + y*z-2 + 3*z-1 + x-1*y*z-1 + 3*y-1 + 3*x-1 + y-2*z + 3*x-1*y-1*z + x-1*y-2*z2
51 rank 2, number 7 x + y + z + x*z-1 + 2*y*z-1 + x*y-1 + x-1*y + 3*y-1*z + 2*x-1*z + x-1*y-1*z2 + y*z-2 + 3*z-1 + x-1*y*z-1 + 3*y-1 + 3*x-1 + y-2*z + 3*x-1*y-1*z + x-1*y-2*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3537
Image of polytope 3537 PALP id: 3537
grdb id: 41139
Integer points: [ 1 0 1 0 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 -1 0 1 0 2 0 -2 0 -2 1 -1 0 1 -1 -1 0 -1]
[ 0 0 0 1 -1 -1 -1 1 1 -1 1 -1 0 0 0 1 0 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + y*z-1 + x-1*y2*z-1 + x*y-1 + 2*x-1*y + 2*y-1*z + x-1*z + z-1 + 2*x-1*y*z-1 + 3*y-1 + 4*x-1 + y-2*z + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
62 rank 2, number 9 x + y + z + y*z-1 + x-1*y2*z-1 + x*y-1 + 2*x-1*y + 2*y-1*z + x-1*z + z-1 + 2*x-1*y*z-1 + 2*y-1 + 4*x-1 + y-2*z + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3538
Image of polytope 3538 PALP id: 3538
grdb id: 45767
Integer points: [ 1 0 0 0 -1 0 -1 -1 0 -1 -1 -1 -1 -1 -1 0 0 -1 -1]
[ 0 1 0 0 1 -1 1 0 -1 -2 -2 -1 -2 -1 0 -1 0 -1 0]
[ 0 0 1 -1 0 1 -1 1 -1 1 -1 1 0 0 0 0 0 -1 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y + y-1*z + x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + 2*x-1*y-1*z + y-1*z-1 + 3*x-1*z-1 + 5*x-1*y-1 + x-1*y-2*z + 3*x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-2*z-1
39 ? x + y + z + x-1*y + y-1*z + x-1*z + z-1 + x-1*y*z-1 + 3*y-1 + 4*x-1 + 2*x-1*y-1*z + y-1*z-1 + 3*x-1*z-1 + 5*x-1*y-1 + x-1*y-2*z + 3*x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3539
Image of polytope 3539 PALP id: 3539
grdb id: 45839
Integer points: [ 1 0 0 0 0 0 0 -1 -1 -2 -2 -2 -2 -1 -1 -1 -1 -1 0]
[ 0 1 0 1 -1 -1 0 1 -2 -2 1 -1 0 -1 0 1 -1 0 0]
[ 0 0 1 -1 1 0 -1 -2 1 1 -2 0 -1 1 0 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + y*z-1 + y-1*z + z-1 + 2*x-1*y*z-1 + y-1 + 4*x-1 + 2*x-1*y-1*z + x-1*y*z-2 + 4*x-1*z-1 + 4*x-1*y-1 + x-1*y-2*z + x-2*y*z-2 + 3*x-2*z-1 + 3*x-2*y-1 + x-2*y-2*z
13 rank 2, number 12 x + y + z + y*z-1 + y-1*z + z-1 + 2*x-1*y*z-1 + y-1 + 4*x-1 + 2*x-1*y-1*z + x-1*y*z-2 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z + x-2*y*z-2 + 3*x-2*z-1 + 3*x-2*y-1 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Polytope 3540
Image of polytope 3540 PALP id: 3540
grdb id: 45832
Integer points: [ 1 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -1 -1 1 -1 1 0 -1 -1 -1 0 0 0 1 0 0]
[ 0 0 1 -1 1 0 0 2 -2 -2 -1 0 1 -1 0 1 -1 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + y*z-1 + x-1*y + y-1*z + 2*x-1*z + x-1*y-1*z2 + 2*z-1 + 2*x-1*y*z-1 + y-1 + 5*x-1 + 3*x-1*y-1*z + x-1*y*z-2 + 4*x-1*z-1 + 3*x-1*y-1 + x-1*z-2 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3541
Image of polytope 3541 PALP id: 3541
grdb id: 9091
Integer points: [ 1 0 0 -1 1 0 1 -1 0 1 -2 -2 -1 -1 0 -1 0 1 0]
[ 0 1 0 1 -1 0 -2 0 -1 -2 1 1 0 0 -1 1 0 -1 -1]
[ 0 0 1 1 -1 -1 -1 -1 1 0 1 0 1 0 0 0 0 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + x*y-1*z-1 + z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
40 rank 2, number 10 x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + x*y-1*z-1 + z-1 + x*y-2 + 4*y-1 + 4*x-1 + x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 96 1 Lattice Minkowski decompositions of facet 96
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 6 Lattice Minkowski decompositions of facet 11
Polytope 3542
Image of polytope 3542 PALP id: 3542
grdb id: 9094
Integer points: [ 1 0 0 1 0 0 1 -1 1 -1 -2 -2 0 0 -1 1 0 -1 -1]
[ 0 1 0 0 1 -1 -1 1 -2 1 1 1 0 -1 0 -1 0 1 0]
[ 0 0 1 -1 -1 1 -1 1 0 -1 1 0 -1 0 0 0 0 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x-1*y*z + x*z-1 + y*z-1 + 2*x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
51 rank 2, number 7 x + y + z + x-1*y*z + x*z-1 + y*z-1 + 2*x*y-1 + 3*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Polytope 3543
Image of polytope 3543 PALP id: 3543
grdb id: 9098
Integer points: [ 1 0 0 -2 2 1 -1 -2 2 0 1 0 0 -1 1 1 0 -1 -1]
[ 0 1 0 2 -1 0 0 1 -2 0 -2 -1 -1 0 -1 -1 0 1 1]
[ 0 0 1 1 -1 -1 1 1 -1 -1 -1 -1 0 0 -1 0 0 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
51 rank 2, number 7 x + y + z + 2*x-1*y*z + x-2*y2*z + x2*y-1*z-1 + x*z-1 + 2*x*y-1 + 2*x-1*y + x-1*z + x-2*y*z + x2*y-2*z-1 + 3*x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + x*y-2*z-1 + y-1*z-1
18 rank 1, V14 x + y + z + 2*x-1*y*z + x-2*y2*z + x2*y-1*z-1 + x*z-1 + 2*x*y-1 + 2*x-1*y + x-1*z + x-2*y*z + x2*y-2*z-1 + 2*x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + x*y-2*z-1 + y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 24 1 Lattice Minkowski decompositions of facet 24
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 15 3 Lattice Minkowski decompositions of facet 15
Polytope 3544
Image of polytope 3544 PALP id: 3544
grdb id: 10527
Integer points: [ 1 0 0 -1 1 -1 0 1 -1 -1 1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 -1 1 0 -1 0 0 -2 -2 -1 0 -1 -1 0 -2 -1]
[ 0 0 1 1 0 0 -1 -1 1 -1 -1 -1 0 0 -1 0 0 -1 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + x*y-1 + x-1*y + x-1*z + x*y-1*z-1 + z-1 + 3*y-1 + 3*x-1 + x*y-2*z-1 + 3*y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + 2*y-2*z-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 30 3 Lattice Minkowski decompositions of facet 30
Polytope 3545
Image of polytope 3545 PALP id: 3545
grdb id: 10501
Integer points: [ 1 0 0 1 0 -1 1 -1 -1 0 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 0 1 1 -1 0 1 -2 0 -2 -1 0 -1 0 -1 0 -1]
[ 0 0 1 -1 -1 0 0 1 -1 1 -1 1 0 0 1 -1 0 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x*z-1 + y*z-1 + x*y-1 + x-1*y + 2*y-1*z + x-1*z + 2*z-1 + x-1*y*z-1 + 3*y-1 + 3*x-1 + y-2*z + 2*x-1*y-1*z + x-1*z-1 + 2*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3546
Image of polytope 3546 PALP id: 3546
grdb id: 545053
Integer points: [ 1 0 0 -1 -6 -2 -3 -4 -5 -1 -2 -3 -4 0 -1 -2 0 -1 -2 0]
[ 0 1 1 0 -5 -1 -2 -3 -4 0 -1 -2 -3 1 0 -1 0 -1 -2 0]
[ 0 0 2 2 -3 1 0 -1 -2 1 0 -1 -2 1 0 -1 1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 227 1 Lattice Minkowski decompositions of facet 227
Image of facet 9 1 irreducible and admissible
Image of facet 73 1 none
Polytope 3547
Image of polytope 3547 PALP id: 3547
grdb id: 545051
Integer points: [ 1 1 0 1 -5 1 0 -1 0 -1 -2 -1 -2 -3 -3 -4 1 1 0 -1]
[ 0 2 0 4 -5 3 1 -1 2 0 -2 1 -1 -3 -2 -4 1 2 0 -1]
[ 0 0 1 -2 1 -1 0 1 -1 0 1 -1 0 1 0 1 0 -1 0 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 43 1 irreducible and admissible
Image of facet 14 1 none
Image of facet 227 1 Lattice Minkowski decompositions of facet 227
Polytope 3548
Image of polytope 3548 PALP id: 3548
grdb id: 545067
Integer points: [ 1 0 0 -5 -9 -8 -7 -6 -6 -5 -4 -3 -3 -2 -1 -4 -3 -2 -1 0]
[ 0 1 0 -2 -6 -5 -4 -3 -4 -3 -2 -1 -2 -1 0 -3 -2 -1 -1 0]
[ 0 0 1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 228 1 Lattice Minkowski decompositions of facet 228
Image of facet 14 1 none
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 3549
Image of polytope 3549 PALP id: 3549
grdb id: 545056
Integer points: [ 1 0 0 -7 -15 -12 -9 -6 -3 -11 -8 -5 -2 -4 -1 -7 -4 -1 -3 0]
[ 0 1 0 -4 -10 -8 -6 -4 -2 -7 -5 -3 -1 -2 0 -5 -3 -1 -2 0]
[ 0 0 1 -2 -4 -3 -2 -1 0 -3 -2 -1 0 -1 0 -2 -1 0 -1 0]
Degree: 44
Hilbert function: 1 + 25 t + 115 t2 + 315 t3 + 669 t4 + 1221 t5 + 2015 t6 + 3095 t7 + 4505 t8 + 6289 t9 + 8491 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 229 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 73 1 none
Polytope 3550
Image of polytope 3550 PALP id: 3550
grdb id: 525540
Integer points: [ 1 0 0 -2 2 -4 -1 -3 -2 -1 0 1 -3 -2 -1 0 1 -1 0 1]
[ 0 1 0 2 -4 2 1 2 1 0 -1 -2 1 0 -1 -2 -3 1 0 -1]
[ 0 0 1 -1 3 -3 0 -2 -1 0 1 2 -2 -1 0 1 2 -1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 2 none
Image of facet 1 1 irreducible and admissible
Image of facet 212 1 Lattice Minkowski decompositions of facet 212
Image of facet 53 1 irreducible and admissible
Polytope 3551
Image of polytope 3551 PALP id: 3551
grdb id: 525020
Integer points: [ 1 0 0 -3 1 -3 -2 -1 0 -3 -2 -1 0 -2 -1 -1 0 1 -1 0]
[ 0 1 0 0 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
[ 0 0 1 -2 2 -2 -1 0 1 -2 -1 0 1 -1 0 -1 0 1 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*y-1*z + 4*y-1 + 3*x-1 + 4*y-2*z + 2*x-1*z-1 + 6*x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*z-1 + 6*x-1*y-2 + 6*x-2*y-1*z-1 + x-3*z-2 + 4*x-2*y-2*z-1 + 2*x-3*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 1 irreducible and admissible
Image of facet 230 1 Lattice Minkowski decompositions of facet 230
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 3552
Image of polytope 3552 PALP id: 3552
grdb id: 525001
Integer points: [ 1 0 0 -1 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 0 -1 -1 0 0]
[ 0 1 1 0 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 1 -1 -1 0 0]
[ 0 0 2 2 -3 0 -1 -2 1 0 -1 -2 1 0 -1 1 0 -1 1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 14 1 none
Image of facet 231 1 Lattice Minkowski decompositions of facet 231
Polytope 3553
Image of polytope 3553 PALP id: 3553
grdb id: 525383
Integer points: [ 1 0 0 1 -3 1 0 -1 -2 1 0 -1 -2 0 -1 1 0 -1 1 0]
[ 0 1 0 -2 0 -4 -3 -2 -1 -3 -2 -1 0 -1 0 -2 -1 0 -1 0]
[ 0 0 1 0 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Image of facet 80 1 none
Image of facet 9 1 irreducible and admissible
Polytope 3554
Image of polytope 3554 PALP id: 3554
grdb id: 525208
Integer points: [ 1 0 0 -3 -1 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 0]
[ 0 1 0 -2 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 1 -2 2 3 2 1 0 -1 2 1 0 -1 1 0 1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 191 1 none
Polytope 3555
Image of polytope 3555 PALP id: 3555
grdb id: 525455
Integer points: [ 1 0 0 -3 -1 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -2 -4 -3 -2 -1 -3 -2 -1 0 -1 0 -2 -1 0 -1 0]
[ 0 0 1 -2 2 2 1 0 -1 2 1 0 -1 1 0 1 0 -1 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 232 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 3556
Image of polytope 3556 PALP id: 3556
grdb id: 525382
Integer points: [ 1 0 0 -3 1 1 0 -1 -2 1 0 -1 -2 0 -1 1 0 -1 1 0]
[ 0 1 0 0 -2 -4 -3 -2 -1 -3 -2 -1 0 -1 0 -2 -1 0 -1 0]
[ 0 0 1 -2 2 2 1 0 -1 2 1 0 -1 1 0 1 0 -1 1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*x*y-2*z + 4*y-1*z + 2*x*y-3*z2 + 4*y-1 + 3*x-1 + 7*y-2*z + x*y-4*z2 + 2*x-1*z-1 + 8*x-1*y-1 + 4*y-3*z + 3*x-2*z-1 + 6*x-1*y-2 + 4*x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3557
Image of polytope 3557 PALP id: 3557
grdb id: 525431
Integer points: [ 1 0 0 0 -1 -4 -3 -2 -1 -3 -2 -1 -2 -1 -2 -1 0 -1 0 0]
[ 0 1 0 2 -2 -2 -1 0 1 -2 -1 0 -2 -1 -1 0 1 -1 0 -1]
[ 0 0 1 1 -2 1 1 1 1 0 0 0 -1 -1 1 1 1 0 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 148 1 none
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 3558
Image of polytope 3558 PALP id: 3558
grdb id: 524993
Integer points: [ 1 0 0 0 -1 -3 -2 -1 -2 -1 0 -1 0 -2 -1 0 -1 0 0 0]
[ 0 1 1 -2 0 -2 -1 0 -2 -1 0 -2 -1 -1 0 1 -1 0 -1 0]
[ 0 0 2 -1 -2 -4 -2 0 -3 -1 1 -2 0 -3 -1 1 -2 0 -1 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 y*z2 + 2*y*z + x + y + 3*z + 2*z-1 + 3*y-1 + 3*x-1 + 2*y-1*z-1 + 4*x-1*z-1 + x-1*z-2 + y-2*z-1 + 6*x-1*y-1*z-1 + 4*x-1*y-1*z-2 + 3*x-1*y-2*z-2 + 3*x-2*y-1*z-2 + 2*x-2*y-1*z-3 + 3*x-2*y-2*z-3 + x-3*y-2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Image of facet 9 1 irreducible and admissible
Polytope 3559
Image of polytope 3559 PALP id: 3559
grdb id: 524997
Integer points: [ 1 0 0 -2 -2 -5 -4 -3 -4 -3 -2 -1 -3 -2 -1 -1 -2 -1 -1 0]
[ 0 1 0 1 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 1 -1 -1 0 0]
[ 0 0 1 -2 1 -2 -1 0 -2 -1 0 1 -2 -1 0 -1 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 14 2 none
Image of facet 231 1 Lattice Minkowski decompositions of facet 231
Polytope 3560
Image of polytope 3560 PALP id: 3560
grdb id: 525022
Integer points: [ 1 0 0 -1 -3 -5 -2 -1 -4 -3 -2 -1 -4 -3 -2 -1 0 -2 -1 0]
[ 0 1 0 -2 0 -2 0 0 -1 -1 -1 -1 -2 -2 -2 0 0 -1 -1 -1]
[ 0 0 1 0 -2 -4 -1 0 -3 -2 -1 0 -3 -2 -1 -1 0 -2 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
25 ? x + y + z + 2*y-1 + 3*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + 4*x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2 + 6*x-2*y-1*z-1 + 2*x-2*y-1*z-2 + x-3*z-2 + 4*x-2*y-2*z-1 + 6*x-3*y-1*z-2 + 6*x-3*y-2*z-2 + 2*x-4*y-1*z-3 + 4*x-4*y-2*z-3 + x-5*y-2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 230 1 Lattice Minkowski decompositions of facet 230
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 9 1 irreducible and admissible
Polytope 3561
Image of polytope 3561 PALP id: 3561
grdb id: 525456
Integer points: [ 1 0 0 -3 -1 -5 -4 -3 -2 -4 -3 -2 -1 -2 -1 -2 -1 0 -1 0]
[ 0 1 0 0 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
[ 0 0 1 -2 2 -2 -1 0 1 -2 -1 0 1 -1 0 -1 0 1 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + 2*y-1*z + 5*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 4*x-1*y-1 + 3*x-2*z-1 + 7*x-2*y-1 + 4*x-2*y-2*z + 2*x-2*y-1*z-1 + x-3*z-2 + 6*x-3*y-1*z-1 + 6*x-3*y-2 + 2*x-4*y-1*z-2 + 4*x-4*y-2*z-1 + x-5*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 233 1 Lattice Minkowski decompositions of facet 233
Polytope 3562
Image of polytope 3562 PALP id: 3562
grdb id: 525354
Integer points: [ 1 0 0 0 -4 -6 -1 -2 -3 -4 -5 -1 -2 -3 0 -1 -2 -3 0 -1]
[ 0 1 0 1 -4 -5 0 -1 -2 -3 -4 -1 -2 -3 1 0 -1 -2 0 -1]
[ 0 0 1 2 -3 -4 1 0 -1 -2 -3 0 -1 -2 1 0 -1 -2 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Image of facet 8 1 none
Image of facet 173 1 Lattice Minkowski decompositions of facet 173
Image of facet 13 1 irreducible and admissible
Polytope 3563
Image of polytope 3563 PALP id: 3563
grdb id: 525369
Integer points: [ 1 0 0 -3 -3 -7 -4 -5 -6 -2 -3 -4 -5 -1 -2 -1 -2 -3 0 -1]
[ 0 1 0 -2 -2 -6 -3 -4 -5 -1 -2 -3 -4 0 -1 -1 -2 -3 0 -1]
[ 0 0 1 0 -2 -4 -1 -2 -3 0 -1 -2 -3 0 -1 0 -1 -2 0 -1]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
112 rank 3, number 15 x + y + z + 3*x-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*y-1 + 4*x-2*y-1*z-1 + 4*x-2*y-2*z-1 + x-3*y-2 + 8*x-3*y-2*z-1 + x-3*y-2*z-2 + 2*x-3*y-3*z-2 + 4*x-4*y-3*z-1 + 7*x-4*y-3*z-2 + 6*x-5*y-4*z-2 + 2*x-5*y-4*z-3 + 4*x-6*y-5*z-3 + x-7*y-6*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Image of facet 9 1 irreducible and admissible
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Polytope 3564
Image of polytope 3564 PALP id: 3564
grdb id: 525458
Integer points: [ 1 0 0 -3 -3 -7 -6 -5 -4 -5 -4 -3 -2 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 0 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
[ 0 0 1 -2 0 -4 -3 -2 -1 -3 -2 -1 0 -1 0 -2 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
103 ? x + y + z + 3*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + 5*x-2*z-1 + 2*x-2*y-1 + 4*x-2*y-1*z-1 + x-3*z-2 + 7*x-3*y-1*z-1 + x-3*y-2 + 2*x-3*y-1*z-2 + 7*x-4*y-1*z-2 + 4*x-4*y-2*z-1 + 2*x-5*y-1*z-3 + 6*x-5*y-2*z-2 + 4*x-6*y-2*z-3 + x-7*y-2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 234 1 Lattice Minkowski decompositions of facet 234
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 3565
Image of polytope 3565 PALP id: 3565
grdb id: 525433
Integer points: [ 1 0 0 0 -2 -6 -5 -4 -3 -4 -3 -2 -1 -2 -1 -3 -2 -1 -1 0]
[ 0 1 -1 0 -1 3 2 1 0 2 1 0 -1 1 0 2 1 0 1 0]
[ 0 0 0 1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 80 1 none
Image of facet 14 1 none
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Polytope 3566
Image of polytope 3566 PALP id: 3566
grdb id: 525336
Integer points: [ 1 1 0 -1 -5 -7 -6 -5 -4 -3 -2 -3 -2 -1 0 -3 -2 -1 0 1]
[ 0 2 0 -1 -2 -4 -3 -3 -2 -1 0 -2 -1 0 1 -2 -1 -1 0 1]
[ 0 0 1 1 -2 -2 -2 -1 -1 -1 -1 0 0 0 0 -1 -1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 235 1 none
Image of facet 14 1 none
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 3567
Image of polytope 3567 PALP id: 3567
grdb id: 525432
Integer points: [ 1 0 1 0 -2 -8 -6 -4 -2 -5 -3 -1 -2 0 -5 -3 -1 -2 0 1]
[ 0 1 -2 0 2 4 3 2 1 2 1 0 0 -1 3 2 1 1 0 -1]
[ 0 0 0 1 -1 -3 -2 -1 0 -2 -1 0 -1 0 -2 -1 0 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 80 1 none
Image of facet 121 1 none
Polytope 3568
Image of polytope 3568 PALP id: 3568
grdb id: 525498
Integer points: [ 1 0 0 0 -4 -10 -8 -6 -4 -2 -5 -3 -1 -7 -5 -3 -1 -2 0 -2]
[ 0 1 -1 0 3 5 4 3 2 1 2 1 0 4 3 2 1 1 0 2]
[ 0 0 0 1 -2 -4 -3 -2 -1 0 -2 -1 0 -3 -2 -1 0 -1 0 -1]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 236 1 none
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 73 1 none
Polytope 3569
Image of polytope 3569 PALP id: 3569
grdb id: 525460
Integer points: [ 1 0 0 -3 -5 -11 -5 -7 -9 -2 -4 -6 -8 -1 -3 -1 -3 -5 0 -2]
[ 0 1 0 -2 -2 -6 -3 -4 -5 -1 -2 -3 -4 0 -1 -1 -2 -3 0 -1]
[ 0 0 1 0 -2 -4 -1 -2 -3 0 -1 -2 -3 0 -1 0 -1 -2 0 -1]
Degree: 38
Hilbert function: 1 + 22 t + 100 t2 + 273 t3 + 579 t4 + 1056 t5 + 1742 t6 + 2675 t7 + 3893 t8 + 5434 t9 + 7336 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 237 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 3570
Image of polytope 3570 PALP id: 3570
grdb id: 524845
Integer points: [ 1 0 0 -1 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -2 0 -4 -1 -2 -3 0 -1 -2 -3 0 -1 0 -1 -2 0 -1]
[ 0 0 1 0 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + 2*y-1 + 3*x-1 + 2*x-1*z-1 + 4*x-1*y-1 + 4*x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 8*x-2*y-1*z-1 + x-3*z-2 + 7*x-2*y-2*z-1 + 4*x-3*y-1*z-2 + 2*x-2*y-3*z-1 + 6*x-3*y-2*z-2 + 4*x-3*y-3*z-2 + x-3*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 9 1 irreducible and admissible
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Polytope 3571
Image of polytope 3571 PALP id: 3571
grdb id: 524883
Integer points: [ 1 0 0 0 -2 -6 -5 -4 -3 -4 -3 -2 -1 -2 -1 -3 -2 -1 -1 0]
[ 0 1 -1 0 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 0 0 1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 14 1 none
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Polytope 3572
Image of polytope 3572 PALP id: 3572
grdb id: 452175
Integer points: [ 1 0 0 -1 -1 1 1 1 0 0 0 0 -1 -1 -1 1 1 0 0 0]
[ 0 1 0 2 -2 -2 0 -1 1 0 -1 -2 1 0 -1 0 -1 1 0 -1]
[ 0 0 1 -2 2 0 -2 -1 -2 -1 0 1 -1 0 1 -1 0 -1 0 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
11 rank 2, number 6 x + y + z + 2*x*z-1 + 2*y*z-1 + 2*x*y-1 + 2*y-1*z + x*z-2 + 2*y*z-2 + x-1*y2*z-2 + 2*x*y-1*z-1 + 6*z-1 + 4*x-1*y*z-1 + x*y-2 + 6*y-1 + 6*x-1 + 2*y-2*z + 4*x-1*y-1*z + x-1*y-2*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3573
Image of polytope 3573 PALP id: 3573
grdb id: 452201
Integer points: [ 1 0 1 -1 -1 -1 -1 -1 0 0 -1 -1 -1 0 0 1 -1 -1 0 0]
[ 0 1 0 0 1 -2 -2 -1 -1 0 -2 -1 0 -1 0 0 -1 0 -1 0]
[ 0 0 2 -2 -1 0 2 -1 0 -1 1 0 -1 1 0 1 1 0 2 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x*z2 + 2*x*z + x + y + 3*z + 2*y-1*z2 + 4*y-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-2*z + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Polytope 3574
Image of polytope 3574 PALP id: 3574
grdb id: 452184
Integer points: [ 1 0 0 0 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 2 -2 -2 2 -1 0 1 -1 0 1 2 -1 0 1 -1 0 1]
[ 0 0 1 1 -2 -1 3 0 1 2 -1 0 1 2 0 1 2 -1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 y2*z + 2*x-1*y2*z2 + x-2*y2*z3 + 2*y*z + 2*x-1*y*z2 + x + y + z + 5*x-1*y*z + 4*x-2*y*z2 + 4*x-1*z + 6*x-1 + 6*x-2*z + 2*y-1*z-1 + 2*x-1*y-1 + 4*x-1*y-1*z-1 + 4*x-2*y-1 + x-1*y-2*z-2 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 162 1 Lattice Minkowski decompositions of facet 162
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3575
Image of polytope 3575 PALP id: 3575
grdb id: 452188
Integer points: [ 1 0 0 0 0 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 -1 -1 -1 0 0]
[ 0 1 0 0 -2 2 -2 -1 0 1 -2 -1 0 1 -1 -1 0 1 -1 0]
[ 0 0 1 -1 1 -1 3 2 1 0 2 1 0 -1 0 2 1 0 1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 80 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3576
Image of polytope 3576 PALP id: 3576
grdb id: 452149
Integer points: [ 1 0 0 -1 0 -1 -4 -3 -2 -3 -2 -1 -2 -1 0 -2 -1 -1 0 0]
[ 0 1 0 1 -2 -2 1 1 1 0 0 0 -1 -1 -1 1 1 0 0 -1]
[ 0 0 1 1 -1 -2 -2 -1 0 -2 -1 0 -2 -1 0 -1 0 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 14 1 none
Image of facet 174 1 Lattice Minkowski decompositions of facet 174
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Polytope 3577
Image of polytope 3577 PALP id: 3577
grdb id: 452204
Integer points: [ 1 1 -1 0 -1 1 -1 -1 -1 0 0 0 1 -1 -1 0 0 1 1 0]
[ 0 2 -2 0 -1 4 2 1 0 3 2 1 3 0 -1 1 0 2 1 -1]
[ 0 0 0 1 1 -2 -2 -1 0 -2 -1 0 -1 -1 0 -1 0 -1 0 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 14 1 none
Polytope 3578
Image of polytope 3578 PALP id: 3578
grdb id: 452326
Integer points: [ 1 0 0 -1 1 -3 -3 -2 -1 -3 -2 -1 0 -3 -2 -1 -1 0 1 -1]
[ 0 1 0 2 -2 3 0 2 1 2 1 0 -1 1 0 -1 1 0 -1 0]
[ 0 0 1 -1 2 -2 -2 -1 0 -2 -1 0 1 -2 -1 0 -1 0 1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 193 1 none
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3579
Image of polytope 3579 PALP id: 3579
grdb id: 452163
Integer points: [ 1 1 0 -1 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0 0 1]
[ 0 2 0 1 -3 -4 0 -3 -2 -1 -2 -1 0 -2 -1 0 -1 0 1 1]
[ 0 0 1 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0 0 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 2 none
Image of facet 1 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 134 1 Lattice Minkowski decompositions of facet 134
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 3580
Image of polytope 3580 PALP id: 3580
grdb id: 452136
Integer points: [ 1 0 1 0 -3 1 0 -1 -2 0 -1 -2 1 0 -1 0 -1 1 0 1]
[ 0 1 -2 0 3 -4 -3 -1 1 -2 0 2 -3 -1 1 -1 1 -2 0 -1]
[ 0 0 0 1 1 -2 -2 -1 0 -1 0 1 -1 0 1 -1 0 -1 0 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 14 1 none
Image of facet 174 1 Lattice Minkowski decompositions of facet 174
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3581
Image of polytope 3581 PALP id: 3581
grdb id: 452429
Integer points: [ 1 0 -1 1 0 -3 -5 -1 -2 -3 -4 0 -1 -2 -3 -1 -2 1 0 -1]
[ 0 1 -1 0 1 1 1 1 1 1 1 0 0 0 0 1 1 0 0 0]
[ 0 0 0 2 1 -3 -4 0 -1 -2 -3 1 0 -1 -2 -1 -2 1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 146 1 Lattice Minkowski decompositions of facet 146
Image of facet 150 1 Lattice Minkowski decompositions of facet 150
Image of facet 8 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3582
Image of polytope 3582 PALP id: 3582
grdb id: 452335
Integer points: [ 1 0 0 -1 1 -3 -5 -4 -3 -2 -3 -2 -1 -1 0 -2 -1 -1 0 1]
[ 0 1 0 1 -2 1 1 1 1 1 0 0 0 -1 -1 1 1 0 0 -1]
[ 0 0 1 0 2 -3 -4 -3 -2 -1 -2 -1 0 0 1 -2 -1 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 148 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3583
Image of polytope 3583 PALP id: 3583
grdb id: 452344
Integer points: [ 1 0 0 -1 0 -2 -6 -5 -4 -3 -4 -3 -2 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 1 -1 1 -3 -2 -1 0 -2 -1 0 -1 0 -2 -1 0 -1 0]
[ 0 0 1 1 -1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 148 1 none
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Polytope 3584
Image of polytope 3584 PALP id: 3584
grdb id: 451458
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 2 -2 -1 -2 -2 -1 0 -2 -1 0 1 -1 0 1 -1 -1 0]
[ 0 0 1 -1 -1 2 2 1 1 1 0 0 0 0 -1 -1 -1 1 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 13 1 irreducible and admissible
Image of facet 14 1 none
Polytope 3585
Image of polytope 3585 PALP id: 3585
grdb id: 450161
Integer points: [ 1 0 0 0 -2 0 -2 -2 -2 -2 -1 -1 -1 -1 0 -1 -1 -1 0 0]
[ 0 1 0 0 2 -2 -2 1 0 -1 1 0 -1 -2 -1 1 0 -1 0 -1]
[ 0 0 1 -1 -1 1 -1 -1 -1 -1 0 0 0 0 1 -1 -1 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + 2*x-1*y + 2*y-1*z + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 6*x-1 + y-2*z + 4*x-1*z-1 + 4*x-2*y*z-1 + 6*x-1*y-1 + 2*x-1*y-1*z-1 + 6*x-2*z-1 + 2*x-1*y-2 + 4*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3586
Image of polytope 3586 PALP id: 3586
grdb id: 449943
Integer points: [ 1 0 0 0 0 -1 -3 -2 -1 0 -1 0 0 -2 -1 -2 -1 0 -1 0]
[ 0 1 0 1 -2 1 1 1 1 1 0 0 -1 1 1 0 0 0 -1 -1]
[ 0 0 1 -2 1 1 1 1 0 -1 1 0 1 0 -1 1 0 -1 1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x-1*y*z + 2*y*z-1 + 4*x-1*y + 2*y-1*z + 4*x-1*z + 2*x-2*y*z + y*z-2 + 3*z-1 + 3*x-1*y*z-1 + 3*y-1 + 6*x-1 + 3*x-2*y + y-2*z + 3*x-1*y-1*z + 3*x-2*z + x-3*y*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Image of facet 9 1 irreducible and admissible
Polytope 3587
Image of polytope 3587 PALP id: 3587
grdb id: 449907
Integer points: [ 1 0 0 0 1 -2 -2 -2 -2 -1 -1 -1 0 0 -1 -1 -1 0 0 1]
[ 0 1 0 0 -2 1 -2 -1 0 -2 -1 0 -2 -1 -1 0 1 -1 0 -1]
[ 0 0 1 -1 0 0 -3 -2 -1 -2 -1 0 -1 0 -2 -1 0 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + 2*x*y-1 + 2*x-1*y + z-1 + x*y-2 + 2*y-1 + 2*x-1 + x-2*y + 4*y-1*z-1 + 4*x-1*z-1 + 3*y-2*z-1 + 5*x-1*y-1*z-1 + 3*x-2*z-1 + 2*x-1*y-1*z-2 + 3*x-1*y-2*z-2 + 3*x-2*y-1*z-2 + x-2*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Image of facet 132 1 Lattice Minkowski decompositions of facet 132
Polytope 3588
Image of polytope 3588 PALP id: 3588
grdb id: 451905
Integer points: [ 1 0 0 0 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 -2 3 -2 2 1 0 -1 2 1 0 -1 1 0 -1 0 -1]
[ 0 0 0 1 2 -2 3 -1 0 1 2 -1 0 1 2 -1 0 1 0 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + 2*x-1*y2*z-1 + 6*x-1*y + 2*y-1*z + 6*x-1*z + 2*x-1*y-1*z2 + x-2*y3*z-2 + 2*x-1*y*z-1 + 5*x-2*y2*z-1 + y-1 + 5*x-1 + 10*x-2*y + 4*x-1*y-1*z + 10*x-2*z + x-1*y-2*z2 + 5*x-2*y-1*z2 + x-2*y-2*z3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Polytope 3589
Image of polytope 3589 PALP id: 3589
grdb id: 451154
Integer points: [ 1 0 0 -2 -2 -3 -3 -3 -3 -3 -2 -2 -2 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 -2 2 -2 2 -1 0 1 -1 0 1 -1 0 1 -1 0 1 0]
[ 0 0 1 -1 -1 -2 -2 -2 -2 -2 -1 -1 -1 0 0 0 -1 -1 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
67 ? x + y + z + 2*x-1*y + 2*x-1*y*z-1 + x-2*y2*z-1 + 5*x-1 + 4*x-1*z-1 + 6*x-2*y*z-1 + 2*x-1*y-1 + x-3*y2*z-2 + 2*x-1*y-1*z-1 + 10*x-2*z-1 + 4*x-3*y*z-2 + 6*x-2*y-1*z-1 + 6*x-3*z-2 + x-2*y-2*z-1 + 4*x-3*y-1*z-2 + x-3*y-2*z-2
46 ? x + y + z + 2*x-1*y + 2*x-1*y*z-1 + x-2*y2*z-1 + 4*x-1 + 4*x-1*z-1 + 5*x-2*y*z-1 + 2*x-1*y-1 + x-3*y2*z-2 + 2*x-1*y-1*z-1 + 8*x-2*z-1 + 4*x-3*y*z-2 + 5*x-2*y-1*z-1 + 6*x-3*z-2 + x-2*y-2*z-1 + 4*x-3*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 223 1 Lattice Minkowski decompositions of facet 223
Polytope 3590
Image of polytope 3590 PALP id: 3590
grdb id: 450075
Integer points: [ 1 0 0 -1 -1 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -2 2 -2 0 -1 -2 -1 0 1 -1 0 1 -1 0 -1 0 1]
[ 0 0 1 2 -2 0 -2 -1 1 0 -1 -2 1 0 -1 0 -1 1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 3*x-1*y*z-1 + 3*x-1 + 2*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-2*y*z-2 + 5*x-2*z-1 + 5*x-2*y-1 + 2*x-2*y-2*z + x-3*z-2 + 2*x-3*y-1*z-1 + x-3*y-2
13 rank 2, number 12 x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 2*x-1*y*z-1 + 3*x-1 + 2*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-2*y*z-2 + 4*x-2*z-1 + 4*x-2*y-1 + 2*x-2*y-2*z + x-3*z-2 + 2*x-3*y-1*z-1 + x-3*y-2
52 rank 2, number 52 x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 2*x-1*y*z-1 + 3*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-2*y*z-2 + 5*x-2*z-1 + 5*x-2*y-1 + 2*x-2*y-2*z + x-3*z-2 + 2*x-3*y-1*z-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 238 1 Lattice Minkowski decompositions of facet 238
Image of facet 16 3 Lattice Minkowski decompositions of facet 16
Polytope 3591
Image of polytope 3591 PALP id: 3591
grdb id: 449870
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 1 1 0 -2 0 -3 -1 -2 0 -1 -2 0 -1 0 -1 1 0 -1 0]
[ 0 0 2 1 -1 -2 -2 0 -1 0 -1 -2 -1 -2 1 0 1 0 -1 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
51 rank 2, number 7 y*z2 + 2*y*z + x + y + 3*z + x-1*z + 2*z-1 + 3*y-1 + 3*x-1 + 3*y-1*z-1 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*z-2 + y-2*z-1 + 6*x-1*y-1*z-1 + 3*x-1*y-1*z-2 + 3*x-1*y-2*z-1 + 3*x-1*y-2*z-2 + x-1*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 3592
Image of polytope 3592 PALP id: 3592
grdb id: 450157
Integer points: [ 1 0 0 0 -2 0 -2 0 -1 -1 -1 -1 -2 -2 -2 0 0 -1 -1 -1]
[ 0 1 0 0 0 -2 -4 -1 -3 -2 -1 0 -3 -2 -1 -1 0 -2 -1 0]
[ 0 0 1 -1 1 -1 -3 0 -2 -1 0 1 -2 -1 0 -1 0 -2 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 80 1 none
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3593
Image of polytope 3593 PALP id: 3593
grdb id: 451429
Integer points: [ 1 0 1 0 -2 -1 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 1 -1 0 0 -2 -4 -3 -2 -1 -3 -2 -1 0 -2 -1 -1 0 -1 0]
[ 0 0 0 1 1 -2 -3 -2 -1 0 -2 -1 0 1 -1 0 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 64 1 none
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Polytope 3594
Image of polytope 3594 PALP id: 3594
grdb id: 449995
Integer points: [ 1 0 0 -1 -1 -3 -3 -2 -1 -3 -2 -1 -3 -2 -1 -2 -1 0 -1 0]
[ 0 1 0 -2 2 0 3 2 1 2 1 0 1 0 -1 -1 1 0 0 -1]
[ 0 0 1 0 -1 -2 -2 -1 0 -2 -1 0 -2 -1 0 -1 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
128 ? x + y + z + x-1*y2*z-1 + 3*x-1*y + 3*x-1*y*z-1 + 3*x-2*y2*z-1 + 2*y-1 + 3*x-1 + x-3*y3*z-2 + 2*x-1*z-1 + 6*x-2*y*z-1 + 3*x-1*y-1 + 3*x-3*y2*z-2 + 6*x-2*z-1 + x-1*y-2 + 3*x-3*y*z-2 + 2*x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 194 1 Lattice Minkowski decompositions of facet 194
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3595
Image of polytope 3595 PALP id: 3595
grdb id: 450327
Integer points: [ 1 0 0 -1 0 -2 -2 0 0 -1 -1 -1 -1 -2 -2 0 0 0 -1 -1]
[ 0 1 0 2 -3 -1 2 -2 -1 -2 -1 0 1 0 1 -1 0 1 0 1]
[ 0 0 1 2 -2 0 3 -1 0 -1 0 1 2 1 2 -1 0 1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x-1*y2*z2 + x-2*y2*z3 + 2*y*z + 2*x-1*y*z2 + x + y + z + 3*x-1*y*z + 3*x-2*y*z2 + 6*x-1*z + 3*y-1 + 2*x-1 + 3*x-2*z + 2*y-1*z-1 + 6*x-1*y-1 + 3*y-2*z-1 + x-2*y-1 + 2*x-1*y-2*z-1 + y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3596
Image of polytope 3596 PALP id: 3596
grdb id: 451416
Integer points: [ 1 0 0 0 -1 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 0]
[ 0 1 0 -1 2 -1 3 2 1 0 2 1 0 -1 1 0 -1 1 0 0]
[ 0 0 1 1 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Image of facet 64 1 none
Polytope 3597
Image of polytope 3597 PALP id: 3597
grdb id: 449935
Integer points: [ 1 0 0 2 -2 3 0 0 0 1 1 1 2 2 -1 -1 0 0 1 -1]
[ 0 1 0 -1 1 -3 -3 -1 -2 -1 -2 -3 -2 -3 0 -1 0 -1 -1 1]
[ 0 0 1 -1 0 -2 -2 0 -1 0 -1 -2 -1 -2 0 -1 0 -1 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 14 1 none
Polytope 3598
Image of polytope 3598 PALP id: 3598
grdb id: 449927
Integer points: [ 1 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 1 0 -1 -1 -4 -3 -2 -3 -2 -1 -2 -1 0 0 -2 -1 -1 0]
[ 0 0 0 1 -1 2 2 1 0 2 1 0 2 1 0 1 1 0 1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 194 1 Lattice Minkowski decompositions of facet 194
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Polytope 3599
Image of polytope 3599 PALP id: 3599
grdb id: 451769
Integer points: [ 1 0 0 -1 -1 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -2 2 -2 -4 -3 0 -1 -2 -3 1 0 -1 -1 -2 1 0 -1]
[ 0 0 1 2 -2 0 2 1 -1 0 1 2 -1 0 1 0 1 -1 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 3*x-1*y*z-1 + 3*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*y-1 + 2*x-1*y-2*z + 2*x-2*z-1 + 5*x-2*y-1 + 4*x-2*y-2*z + 2*x-2*y-3*z2 + x-3*y-2 + 2*x-3*y-3*z + x-3*y-4*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 16 3 Lattice Minkowski decompositions of facet 16
Image of facet 239 1 Lattice Minkowski decompositions of facet 239
Polytope 3600
Image of polytope 3600 PALP id: 3600
grdb id: 450189
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 0 0]
[ 0 1 0 2 -2 -2 -4 1 0 -1 0 -1 -2 -3 1 0 -1 -3 -1 -2]
[ 0 0 1 -2 2 0 2 -1 0 1 -1 0 1 2 -1 0 1 1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 4*x-1*y*z-1 + 2*y-1 + 6*x-1 + 2*y-2*z + 4*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 6*x-1*y-1 + 6*x-1*y-2*z + 2*x-1*y-3*z2 + x-1*y-2 + 2*x-1*y-3*z + x-1*y-4*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3601
Image of polytope 3601 PALP id: 3601
grdb id: 449940
Integer points: [ 1 0 0 -1 1 -1 -4 -2 -3 -1 -2 -3 -1 -2 0 -1 -2 1 0 -1]
[ 0 1 0 2 -2 -1 2 0 1 0 1 2 1 2 -1 0 1 -1 0 1]
[ 0 0 1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y2*z-1 + 2*x*y-1 + 3*x-1*y + 3*x-1*y*z-1 + 3*x-2*y2*z-1 + x*y-2 + 3*y-1 + 3*x-1 + 2*x-2*y + 3*x-1*z-1 + 6*x-2*y*z-1 + 3*x-3*y2*z-1 + x-1*y-1*z-1 + 3*x-2*z-1 + 3*x-3*y*z-1 + x-4*y2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 56 1 Lattice Minkowski decompositions of facet 56
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3602
Image of polytope 3602 PALP id: 3602
grdb id: 451427
Integer points: [ 1 0 0 0 -1 -2 -4 -1 -2 -3 0 -1 -2 -3 -1 -2 -1 0 -1 0]
[ 0 1 0 2 -2 -1 -2 1 0 -1 1 0 -1 -2 -1 -2 0 0 -1 -1]
[ 0 0 1 1 0 -2 -3 0 -1 -2 1 0 -1 -2 0 -1 -1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 y2*z + 2*y*z + x + y + z + 4*x-1*y + 2*y-1 + 7*x-1 + 2*x-1*z-1 + 4*x-1*y-1 + 3*x-1*y-1*z-1 + 6*x-2*z-1 + x-1*y-2 + 8*x-2*y-1*z-1 + x-2*y-1*z-2 + 3*x-2*y-2*z-1 + 4*x-3*y-1*z-2 + 3*x-3*y-2*z-2 + x-4*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Polytope 3603
Image of polytope 3603 PALP id: 3603
grdb id: 450158
Integer points: [ 1 0 0 0 0 -2 -4 -3 -2 -1 -2 -1 0 -3 -2 -1 0 -1 0 -1]
[ 0 1 0 0 -2 2 2 1 0 -1 1 0 -1 2 1 0 -1 1 0 1]
[ 0 0 1 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + 2*x-1*y + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 4*x-1 + 2*x-2*y + 2*y-1*z-1 + 6*x-1*z-1 + 6*x-2*y*z-1 + 2*x-3*y2*z-1 + y-2*z-1 + 4*x-1*y-1*z-1 + 6*x-2*z-1 + 4*x-3*y*z-1 + x-4*y2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3604
Image of polytope 3604 PALP id: 3604
grdb id: 450160
Integer points: [ 1 0 0 0 0 -2 -4 -1 -3 -2 -1 0 -3 -2 -1 -1 0 -2 -1 0]
[ 0 1 0 0 -2 2 2 1 2 1 0 -1 1 0 -1 1 0 1 0 -1]
[ 0 0 1 -1 1 -1 -3 0 -2 -1 0 1 -2 -1 0 -1 0 -2 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + 2*x-1*y + 2*y-1*z + z-1 + 3*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 6*x-1 + y-2*z + 4*x-1*z-1 + 6*x-2*y*z-1 + 4*x-1*y-1 + 2*x-2*y*z-2 + 2*x-3*y2*z-2 + 6*x-2*z-1 + 4*x-3*y*z-2 + x-4*y2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3605
Image of polytope 3605 PALP id: 3605
grdb id: 451359
Integer points: [ 1 0 -1 0 0 0 -4 -3 -2 -1 -3 -2 -1 -2 -1 -2 -1 0 -1 0]
[ 0 1 1 0 -1 -1 -5 -4 -3 -2 -3 -2 -1 -1 0 -3 -2 -1 -1 0]
[ 0 0 0 1 -1 1 -3 -2 -1 0 -2 -1 0 -1 0 -2 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 148 1 none
Image of facet 80 1 none
Polytope 3606
Image of polytope 3606 PALP id: 3606
grdb id: 449922
Integer points: [ 1 0 0 -1 -2 -2 -5 -4 -3 -4 -3 -2 -1 -3 -2 -1 -2 -1 -1 0]
[ 0 1 0 1 1 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 0 0]
[ 0 0 1 0 -1 -1 -4 -3 -2 -3 -2 -1 0 -2 -1 0 -2 -1 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 220 1 Lattice Minkowski decompositions of facet 220
Image of facet 14 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3607
Image of polytope 3607 PALP id: 3607
grdb id: 449908
Integer points: [ 1 0 0 1 -2 1 1 1 0 1 0 -1 0 -1 1 1 0 1 0 -1]
[ 0 1 0 -1 1 -2 -5 -3 -1 -4 -2 0 -3 -1 -1 -2 0 -3 -1 1]
[ 0 0 1 -1 0 0 -3 -1 0 -2 -1 0 -2 -1 0 -1 0 -2 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Image of facet 124 1 none
Polytope 3608
Image of polytope 3608 PALP id: 3608
grdb id: 449926
Integer points: [ 1 0 0 -1 -2 -2 -5 -4 -3 -4 -3 -2 -3 -2 -1 -1 -2 -1 -1 0]
[ 0 1 0 0 -1 -1 -4 -3 -2 -3 -2 -1 -2 -1 0 0 -2 -1 -1 0]
[ 0 0 1 -1 -1 2 2 1 0 2 1 0 2 1 0 1 1 0 1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 220 1 Lattice Minkowski decompositions of facet 220
Image of facet 14 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3609
Image of polytope 3609 PALP id: 3609
grdb id: 451932
Integer points: [ 1 0 0 -1 -1 -2 -6 -5 -4 -3 -2 -3 -2 -1 -4 -3 -2 -1 -1 0]
[ 0 1 0 -1 1 -2 -4 -3 -2 -1 0 -2 -1 0 -3 -2 -1 0 -1 0]
[ 0 0 1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + x-1*y*z-1 + 4*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1 + 5*x-2*z-1 + 5*x-2*y-1 + 6*x-2*y-1*z-1 + x-2*y-2*z-1 + 10*x-3*y-1*z-1 + 2*x-3*y-2 + 6*x-3*y-2*z-1 + 10*x-4*y-2*z-1 + 2*x-4*y-3*z-1 + 5*x-5*y-3*z-1 + x-6*y-4*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Polytope 3610
Image of polytope 3610 PALP id: 3610
grdb id: 450159
Integer points: [ 1 0 0 0 -2 -2 -6 -3 -4 -5 -1 -2 -3 -4 -1 -1 -2 -3 0 -1]
[ 0 1 -1 0 -1 -3 -5 -2 -3 -4 -1 -2 -3 -4 -2 0 -1 -2 0 -1]
[ 0 0 0 1 0 -2 -4 -1 -2 -3 0 -1 -2 -3 -1 0 -1 -2 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
50 ? x + y + z + y-1 + 2*x-1 + 4*x-1*y-1 + 2*x-1*y-1*z-1 + x-2*y-1 + 2*x-1*y-2*z-1 + 4*x-2*y-1*z-1 + 7*x-2*y-2*z-1 + 4*x-3*y-2*z-1 + x-2*y-3*z-2 + 2*x-3*y-2*z-2 + 6*x-3*y-3*z-2 + 6*x-4*y-3*z-2 + 2*x-4*y-4*z-3 + 4*x-5*y-4*z-3 + x-6*y-5*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 180 1 Lattice Minkowski decompositions of facet 180
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 3611
Image of polytope 3611 PALP id: 3611
grdb id: 450146
Integer points: [ 1 0 0 0 -2 -2 -6 -3 -4 -5 -1 -2 -3 -1 -2 -3 -4 0 -1 -1]
[ 0 1 -1 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1]
[ 0 0 0 1 0 -2 -4 -1 -2 -3 0 -1 -2 0 -1 -2 -3 0 -1 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + 2*x-1*y + 2*x-1*y*z-1 + y-1 + 3*x-1 + x-2*y + 2*x-1*z-1 + 6*x-2*y*z-1 + x-2*y*z-2 + 4*x-2*z-1 + 4*x-3*y*z-1 + 6*x-3*y*z-2 + 2*x-3*z-2 + 6*x-4*y*z-2 + 2*x-4*y*z-3 + 4*x-5*y*z-3 + x-6*y*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3612
Image of polytope 3612 PALP id: 3612
grdb id: 451361
Integer points: [ 1 0 0 0 -1 -2 -6 -3 -4 -5 -2 -3 -4 -1 -2 -1 -2 -3 0 -1]
[ 0 1 0 -1 0 -1 -5 -2 -3 -4 -1 -2 -3 0 -1 -1 -2 -3 0 -1]
[ 0 0 1 -1 1 1 -3 0 -1 -2 0 -1 -2 0 -1 0 -1 -2 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 148 1 none
Image of facet 14 1 none
Polytope 3613
Image of polytope 3613 PALP id: 3613
grdb id: 449941
Integer points: [ 1 0 0 1 -1 -2 -5 -3 -4 -1 -2 -3 0 -1 -1 -2 -3 0 -1 1]
[ 0 1 0 -2 2 1 4 2 3 0 1 2 -1 0 1 2 3 0 1 -1]
[ 0 0 1 0 -1 0 -3 -1 -2 0 -1 -2 0 -1 0 -1 -2 0 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y2*z-1 + 2*x*y-1 + 3*x-1*y + 4*x-1*y*z-1 + 4*x-2*y2*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + 2*x-3*y3*z-2 + 3*x-1*z-1 + 6*x-2*y*z-1 + 3*x-3*y2*z-1 + 3*x-3*y2*z-2 + 3*x-4*y3*z-2 + x-5*y4*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 9 1 irreducible and admissible
Polytope 3614
Image of polytope 3614 PALP id: 3614
grdb id: 447951
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 -2 2 -2 0 -1 1 0 -1 -2 1 0 -1 0 -1 1 0 -1]
[ 0 0 1 2 -2 0 -2 -1 -2 -1 0 1 -1 0 1 -1 0 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 2*z-1 + 4*x-1*y*z-1 + 2*y-1 + 6*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*y*z-2 + 6*x-1*z-1 + 6*x-1*y-1 + 2*x-1*y-2*z + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 16 3 Lattice Minkowski decompositions of facet 16
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3615
Image of polytope 3615 PALP id: 3615
grdb id: 448025
Integer points: [ 1 0 0 0 0 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0 -1]
[ 0 0 1 0 -2 2 -2 -1 0 1 -1 0 1 -2 -1 0 1 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + 2*x-1*z + 2*z-1 + y-1 + 4*x-1 + 2*x-1*y-1*z + x-2*y-1*z2 + 2*y-1*z-1 + 2*x-1*z-1 + 6*x-1*y-1 + 4*x-2*y-1*z + y-1*z-2 + 6*x-1*y-1*z-1 + 6*x-2*y-1 + 2*x-1*y-1*z-2 + 4*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3616
Image of polytope 3616 PALP id: 3616
grdb id: 447729
Integer points: [ 1 0 0 -1 0 0 -3 -2 -1 0 -1 0 0 -2 -1 -2 -1 0 -1 0]
[ 0 1 0 1 -2 1 1 1 0 -1 1 0 1 0 -1 1 0 -1 1 0]
[ 0 0 1 0 1 -2 -2 -1 0 1 -1 0 -1 -1 0 -2 -1 0 -2 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 x + y + z + 2*y*z-1 + x-1*y + 2*y-1*z + y*z-2 + 3*z-1 + 4*x-1*y*z-1 + 3*y-1 + 4*x-1 + y-2*z + 3*x-1*y*z-2 + 6*x-1*z-1 + 2*x-2*y*z-1 + 3*x-1*y-1 + 3*x-2*y*z-2 + 3*x-2*z-1 + x-3*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 9 1 irreducible and admissible
Polytope 3617
Image of polytope 3617 PALP id: 3617
grdb id: 448027
Integer points: [ 1 0 0 0 0 -2 -4 -3 -2 -1 -2 -1 0 -3 -2 -1 0 -1 0 -1]
[ 0 1 0 0 -2 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + 2*y-1*z + 2*x-1*z + z-1 + 2*y-1 + 2*x-1 + y-2*z + 6*x-1*y-1*z + x-2*z + 4*x-1*y-1 + 4*x-1*y-2*z + 6*x-2*y-1*z + 2*x-2*y-1 + 6*x-2*y-2*z + 2*x-3*y-1*z + 4*x-3*y-2*z + x-4*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3618
Image of polytope 3618 PALP id: 3618
grdb id: 306957
Integer points: [ 1 0 0 -2 2 -1 0 -3 -2 -1 -1 -2 -1 0 1 -1 0 1 0 1]
[ 0 1 0 2 -3 0 -1 2 1 0 1 1 0 -1 -2 1 0 -1 -1 -2]
[ 0 0 1 1 -1 -1 1 1 1 1 1 0 0 0 0 0 0 0 -1 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 2 none
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Polytope 3619
Image of polytope 3619 PALP id: 3619
grdb id: 306960
Integer points: [ 1 0 0 -3 1 -2 3 2 -1 0 -2 -1 0 1 2 -1 0 1 1 2]
[ 0 1 0 3 -2 1 -4 -3 0 -1 2 1 -1 -2 -3 1 0 -1 -1 -2]
[ 0 0 1 1 0 0 -2 -2 0 0 1 1 -1 -1 -1 0 0 0 -1 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
11 rank 2, number 6 x + y + z + 3*x-1*y*z + 3*x-2*y2*z + x-3*y3*z + 2*x*y-1 + 2*x-1*y + 2*x2*y-2*z-1 + 2*x*y-1*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + 2*x2*y-3*z-1 + 4*x*y-2*z-1 + 2*y-1*z-1 + x3*y-4*z-2 + x2*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3620
Image of polytope 3620 PALP id: 3620
grdb id: 306074
Integer points: [ 1 0 0 0 -1 -2 0 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 1 1 -2 -2 0 -1 0 -1 1 0 -1 -2 0 -1 0 -1]
[ 0 0 1 -1 1 1 -1 1 1 1 1 1 0 0 0 0 0 0 -1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + x-1*y*z + y*z-1 + 2*x-1*y + 3*x-1*z + x-2*y*z + 3*z-1 + 2*y-1 + 6*x-1 + 2*x-1*y-1*z + 3*x-2*z + 3*y-1*z-1 + 6*x-1*y-1 + 3*x-2*y-1*z + y-2*z-1 + 2*x-1*y-2 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Polytope 3621
Image of polytope 3621 PALP id: 3621
grdb id: 306351
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 0 -2 -1 -2 -2 -2 -2 -1 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 1 0 -1 -2 2 2 1 0 -1 1 0 -1 1 0 1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 202 1 none
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Polytope 3622
Image of polytope 3622 PALP id: 3622
grdb id: 306881
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 2 -2 2 -2 -1 1 0 1 0 -1 0 -1 -2 1 0 -1 -1]
[ 0 0 1 -1 2 -2 0 2 0 1 -1 0 1 -1 0 1 -1 0 1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + 2*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + x-1*y2*z-2 + 3*x-1*y*z-1 + 2*y-1 + 5*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 3*x-1*y-1 + 2*x-1*y-2*z + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 197 1 Lattice Minkowski decompositions of facet 197
Polytope 3623
Image of polytope 3623 PALP id: 3623
grdb id: 306022
Integer points: [ 1 0 0 0 0 1 -2 -2 -1 -2 -1 0 -1 -1 0 -1 0 -1 0 0]
[ 0 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 1]
[ 0 0 2 0 -2 -1 0 -2 -2 -1 -1 -1 0 -1 -1 0 0 1 1 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 y*z2 + 2*y*z + x + y + 2*z + 2*x-1*z + x*y-1*z-1 + 2*z-1 + y-1 + 4*x-1 + 3*y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + y-1*z-2 + 4*x-1*y-1*z-1 + x-2*y-1 + 2*x-1*y-1*z-2 + 2*x-2*y-1*z-1 + x-2*y-1*z-2
51 rank 2, number 7 y*z2 + 2*y*z + x + y + 2*z + 2*x-1*z + x*y-1*z-1 + 2*z-1 + y-1 + 4*x-1 + 4*y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + y-1*z-2 + 5*x-1*y-1*z-1 + x-2*y-1 + 2*x-1*y-1*z-2 + 2*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Polytope 3624
Image of polytope 3624 PALP id: 3624
grdb id: 305807
Integer points: [ 1 0 0 2 -2 2 -1 -2 1 0 -1 1 0 0 -1 -2 1 0 -1 -1]
[ 0 1 0 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 1]
[ 0 0 1 -1 0 -2 2 2 -1 0 1 0 1 -1 0 1 -1 0 1 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + x2*y-1*z-1 + 2*x*z-1 + 3*x*y-1 + 2*x-1*y + 3*y-1*z + 3*x-1*z + x-1*y-1*z2 + x2*y-1*z-2 + 4*x*y-1*z-1 + 2*z-1 + 6*y-1 + 4*x-1 + x-2*y + 4*x-1*y-1*z + 2*x-2*z + x-2*y-1*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3625
Image of polytope 3625 PALP id: 3625
grdb id: 306072
Integer points: [ 1 0 1 -1 -1 0 -1 -1 -1 -1 0 0 -1 -1 -1 0 0 0 1 0]
[ 0 1 0 0 1 1 1 -2 -1 0 -1 0 -1 0 1 -1 0 1 0 0]
[ 0 0 2 -2 -1 2 1 -2 -1 0 0 1 -2 -1 0 -1 0 1 1 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x*z2 + y*z2 + 2*x*z + 2*y*z + x + y + 3*z + x-1*y*z + 2*x-1*y + 2*z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + 2*y-1*z-1 + 4*x-1*z-1 + x-1*z-2 + 3*x-1*y-1*z-1 + 2*x-1*y-1*z-2 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3626
Image of polytope 3626 PALP id: 3626
grdb id: 305770
Integer points: [ 1 0 0 0 -1 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 -1 0 2 -2 -1 3 0 1 2 -1 0 1 0 1 2 -1 0 1]
[ 0 0 0 1 2 -2 -2 2 -1 0 1 -1 0 1 -1 0 1 -1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? x-1*y2*z2 + x-2*y3*z2 + 2*y*z + 2*x-1*y2*z + x + y + z + 5*x-1*y*z + 4*x-2*y2*z + 4*x-1*y + y-1 + 7*x-1 + 6*x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + 4*x-1*y-1*z-1 + 4*x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
10 rank 1, V18 x-1*y2*z2 + x-2*y3*z2 + 2*y*z + 2*x-1*y2*z + x + y + z + 3*x-1*y*z + 4*x-2*y2*z + 4*x-1*y + y-1 + 4*x-1 + 6*x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1*z-1 + 4*x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Image of facet 165 1 Lattice Minkowski decompositions of facet 165
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 3627
Image of polytope 3627 PALP id: 3627
grdb id: 305859
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 2 2 1 -1 -3 1 0 1 0 -1 -2 0 -1 -2 1 0 -1]
[ 0 0 1 -1 -2 -2 2 2 0 1 -1 0 1 2 -1 0 1 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 198 1 Lattice Minkowski decompositions of facet 198
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 13 1 irreducible and admissible
Polytope 3628
Image of polytope 3628 PALP id: 3628
grdb id: 305762
Integer points: [ 1 0 0 -1 2 1 -2 -3 0 -1 -2 1 0 -1 0 -1 -2 1 0 -1]
[ 0 1 0 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 0 1 0 -2 -2 2 2 -1 0 1 -1 0 1 -1 0 1 -1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*x*z-1 + x-1*y + 2*x-1*z + x2*y-1*z-2 + 4*x*y-1*z-1 + 2*z-1 + 6*y-1 + 4*x-1 + 4*x-1*y-1*z + 2*x-2*z + x-2*y-1*z2 + x*y-1*z-2 + 4*y-1*z-1 + 6*x-1*y-1 + 4*x-2*y-1*z + x-3*y-1*z2
51 rank 2, number 7 x + y + z + 2*x*z-1 + x-1*y + 3*x-1*z + x2*y-1*z-2 + 4*x*y-1*z-1 + 2*z-1 + 6*y-1 + 4*x-1 + 4*x-1*y-1*z + 2*x-2*z + x-2*y-1*z2 + x*y-1*z-2 + 4*y-1*z-1 + 6*x-1*y-1 + 4*x-2*y-1*z + x-3*y-1*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 134 1 Lattice Minkowski decompositions of facet 134
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3629
Image of polytope 3629 PALP id: 3629
grdb id: 305845
Integer points: [ 1 0 0 -1 0 -2 -1 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 -2 0 -2 -4 -1 -2 -3 0 -1 0 -1 -2 -3 0 -1 -1]
[ 0 0 1 1 -1 1 -2 -3 0 -1 -2 0 -1 1 0 -1 -2 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + x-1*y*z + 2*x-1*z + 2*y-1 + 3*x-1 + x-2*z + 2*y-1*z-1 + 6*x-1*y-1 + y-2*z-1 + 3*x-1*y-1*z-1 + 4*x-2*y-1 + 6*x-1*y-2*z-1 + x-1*y-2*z-2 + 6*x-2*y-2*z-1 + 2*x-1*y-3*z-2 + 4*x-2*y-3*z-2 + x-2*y-4*z-3
17 rank 1, V22 x + y + z + x-1*y*z + 2*x-1*z + 2*y-1 + 4*x-1 + x-2*z + 2*y-1*z-1 + 6*x-1*y-1 + y-2*z-1 + 4*x-1*y-1*z-1 + 4*x-2*y-1 + 6*x-1*y-2*z-1 + x-1*y-2*z-2 + 6*x-2*y-2*z-1 + 2*x-1*y-3*z-2 + 4*x-2*y-3*z-2 + x-2*y-4*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 1 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 93 1 Lattice Minkowski decompositions of facet 93
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3630
Image of polytope 3630 PALP id: 3630
grdb id: 306091
Integer points: [ 1 0 1 0 -1 0 -3 -3 -2 -1 -3 -2 -1 0 -2 -1 -1 0 -1 0]
[ 0 1 -1 0 2 -2 3 1 2 1 2 1 0 -1 0 -1 1 0 0 -1]
[ 0 0 0 1 -1 1 -2 -2 -1 0 -2 -1 0 1 -1 0 -1 0 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Image of facet 14 1 none
Polytope 3631
Image of polytope 3631 PALP id: 3631
grdb id: 306039
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 2 -3 -2 1 -4 1 0 -1 0 -1 -2 -3 1 0 -1 -1 -2]
[ 0 0 1 2 -2 -2 2 -3 1 0 -1 1 0 -1 -2 1 0 -1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x-1*y2*z2 + 2*y*z + x-1*y*z2 + x + y + z + 4*x-1*y*z + 5*x-1*z + 3*y-1 + 6*x-1 + y-1*z-1 + 10*x-1*y-1 + 3*y-2*z-1 + 4*x-1*y-1*z-1 + 10*x-1*y-2*z-1 + y-3*z-2 + x-1*y-2*z-2 + 5*x-1*y-3*z-2 + x-1*y-4*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 146 1 Lattice Minkowski decompositions of facet 146
Image of facet 9 1 irreducible and admissible
Image of facet 10 1 Lattice Minkowski decompositions of facet 10
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 13 1 irreducible and admissible
Image of facet 157 1 Lattice Minkowski decompositions of facet 157
Polytope 3632
Image of polytope 3632 PALP id: 3632
grdb id: 306089
Integer points: [ 1 0 0 0 -2 1 1 1 1 1 0 -1 1 0 1 0 -1 1 0 -1]
[ 0 1 0 0 2 -2 -2 -4 -1 -3 -1 1 -2 0 -1 -2 0 -3 -1 1]
[ 0 0 1 -1 -1 0 2 2 0 1 0 -1 1 0 1 1 0 2 1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*x*y-1 + 2*x-1*y + 4*x*y-2*z + 4*y-1*z + 2*x*y-3*z2 + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + x*y-2 + 4*y-1 + 3*x-1 + 2*x*y-3*z + 3*y-2*z + x*y-4*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Polytope 3633
Image of polytope 3633 PALP id: 3633
grdb id: 306075
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 0 1 -1 -2 -4 -2 -3 0 -1 -2 -3 0 -1 -1 -2 0 -1]
[ 0 0 1 -1 -1 -1 2 2 0 1 -1 0 1 2 0 1 0 1 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + 2*y-1*z + z-1 + x-1*y*z-1 + 3*y-1 + 3*x-1 + 2*y-2*z + 3*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 6*x-1*y-1 + 6*x-1*y-2*z + 2*x-1*y-3*z2 + x-1*y-1*z-1 + 3*x-1*y-2 + 3*x-1*y-3*z + x-1*y-4*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Polytope 3634
Image of polytope 3634 PALP id: 3634
grdb id: 305846
Integer points: [ 1 0 0 1 -2 -2 0 -4 -1 -2 -3 0 -1 -2 -3 -1 -1 1 0 -1]
[ 0 1 0 2 -1 -2 2 -2 1 0 -1 1 0 -1 -2 -1 0 1 0 -1]
[ 0 0 1 2 -2 -1 1 -3 0 -1 -2 1 0 -1 -2 0 -1 1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 1 none
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 180 1 Lattice Minkowski decompositions of facet 180
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Polytope 3635
Image of polytope 3635 PALP id: 3635
grdb id: 306132
Integer points: [ 1 0 0 2 0 -2 -2 -4 0 -3 -1 1 -2 -1 1 -2 0 -3 -1 -1]
[ 0 1 0 -1 -1 1 1 1 0 1 0 -1 0 1 0 1 0 1 0 1]
[ 0 0 1 -2 0 2 0 2 -1 1 0 -1 1 0 -1 1 0 2 1 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*x-1*y*z + x-2*y*z2 + 2*x*z-1 + 2*x-1*y + 2*x-1*z + 4*x-2*y*z + 2*x-3*y*z2 + x2*y-1*z-2 + 2*x*y-1*z-1 + 2*z-1 + y-1 + 4*x-1 + x-2*y + 2*x-2*z + 2*x-3*y*z + x-4*y*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 36 2 Lattice Minkowski decompositions of facet 36
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 3636
Image of polytope 3636 PALP id: 3636
grdb id: 306131
Integer points: [ 1 0 1 0 -1 -1 -1 -3 0 0 -1 -2 -2 1 0 0 -1 -1 -2 0]
[ 0 1 0 1 0 0 -2 -2 -1 0 -1 -2 -1 0 -1 0 -1 0 -1 0]
[ 0 0 2 1 -2 0 -2 -4 0 1 -1 -3 -2 1 -1 0 -2 -1 -3 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x*z2 + 2*x*z + y*z + x + y + 2*z + 2*z-1 + 2*y-1 + x-1 + 2*y-1*z-1 + 3*x-1*z-1 + x-1*z-2 + 4*x-1*y-1*z-1 + 4*x-1*y-1*z-2 + x-1*y-2*z-2 + 2*x-2*y-1*z-2 + 2*x-2*y-1*z-3 + 2*x-2*y-2*z-3 + x-3*y-2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 36 2 Lattice Minkowski decompositions of facet 36
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3637
Image of polytope 3637 PALP id: 3637
grdb id: 306344
Integer points: [ 1 0 1 0 0 -1 -3 -5 -2 -3 -4 -1 -2 -3 0 -1 -1 -2 0 -1]
[ 0 1 -1 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 0 1 1 1 -2 -3 0 -1 -2 0 -1 -2 0 -1 0 -1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 148 1 none
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 93 1 Lattice Minkowski decompositions of facet 93
Polytope 3638
Image of polytope 3638 PALP id: 3638
grdb id: 306682
Integer points: [ 1 0 0 -3 1 -3 0 -5 -1 -2 -3 -4 0 -1 -2 -1 -2 1 0 -1]
[ 0 1 0 -2 2 -3 1 -4 0 -1 -2 -3 1 0 -1 -1 -2 1 0 -1]
[ 0 0 1 -2 2 -2 2 -3 1 0 -1 -2 1 0 -1 0 -1 1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
109 ? x*y2*z2 + 2*x*y*z + y*z2 + 4*y*z + x + y + z + 5*x-1*z + 7*x-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + 10*x-2*y-1 + 5*x-2*y-1*z-1 + 3*x-2*y-2*z-1 + 10*x-3*y-2*z-1 + x-3*y-2*z-2 + x-3*y-3*z-2 + 5*x-4*y-3*z-2 + x-5*y-4*z-3
39 ? x*y2*z2 + 2*x*y*z + y*z2 + 3*y*z + x + y + z + 5*x-1*z + 4*x-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + 10*x-2*y-1 + 3*x-2*y-1*z-1 + 3*x-2*y-2*z-1 + 10*x-3*y-2*z-1 + x-3*y-2*z-2 + x-3*y-3*z-2 + 5*x-4*y-3*z-2 + x-5*y-4*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 160 1 Lattice Minkowski decompositions of facet 160
Image of facet 1 2 irreducible and admissible
Image of facet 146 1 Lattice Minkowski decompositions of facet 146
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 9 1 irreducible and admissible
Polytope 3639
Image of polytope 3639 PALP id: 3639
grdb id: 299475
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 -2 1 1 -2 1 1 1 0 0 0 -1 -1 1 0 0 -1 -1]
[ 0 0 1 1 -2 1 1 -2 0 -1 1 0 -1 1 0 -1 0 -1 1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x-1*y*z + 2*y*z-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + y*z-2 + 3*z-1 + 3*x-1*y*z-1 + 3*y-1 + 6*x-1 + y-2*z + 3*x-1*y-1*z + x-1*y*z-2 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 9 1 irreducible and admissible
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 3640
Image of polytope 3640 PALP id: 3640
grdb id: 301937
Integer points: [ 1 0 0 -2 2 0 -2 0 -1 0 -1 -2 -1 1 0 -1 1 0 -1 1]
[ 0 1 0 2 -2 0 0 -2 -1 -1 0 1 1 -2 -1 0 -1 0 1 -1]
[ 0 0 1 1 -1 -1 1 -1 0 -1 0 1 0 -1 0 1 -1 0 1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
51 rank 2, number 7 x + y + z + 2*x-1*y*z + x-2*y2*z + 2*x*y-1 + 2*x-1*y + 2*x-1*z + 2*x-2*y*z + x2*y-2*z-1 + 2*x*y-1*z-1 + z-1 + 4*y-1 + 4*x-1 + x-2*z + 2*x*y-2*z-1 + 2*y-1*z-1 + 2*x-1*y-1 + y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 36 2 Lattice Minkowski decompositions of facet 36
Polytope 3641
Image of polytope 3641 PALP id: 3641
grdb id: 299999
Integer points: [ 1 0 0 1 0 1 -2 -2 -2 -2 -1 -1 -1 0 0 -1 -1 -1 0 0]
[ 0 1 0 -1 -1 -1 2 -1 1 0 1 0 -1 0 -1 1 0 -1 0 -1]
[ 0 0 1 0 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x*y-1 + 2*x-1*y + y-1*z + x*y-1*z-1 + 3*z-1 + 3*x-1*y*z-1 + x-2*y2*z-1 + 3*y-1 + 4*x-1 + 3*y-1*z-1 + 6*x-1*z-1 + 3*x-2*y*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + 3*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Polytope 3642
Image of polytope 3642 PALP id: 3642
grdb id: 299752
Integer points: [ 1 0 -1 0 -2 0 -3 -3 -2 -1 -3 -2 -1 0 -2 -1 -1 0 -1 0]
[ 0 1 1 0 1 -2 0 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 0 1 -1 1 -2 -2 -1 0 -2 -1 0 1 -1 0 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 225 1 Lattice Minkowski decompositions of facet 225
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Polytope 3643
Image of polytope 3643 PALP id: 3643
grdb id: 299902
Integer points: [ 1 0 0 -1 -1 -1 -3 -3 -2 -3 -2 -1 -3 -2 -1 -2 -1 0 -1 0]
[ 0 1 0 1 1 -2 1 -2 -2 -1 -1 -1 0 0 0 1 -1 -1 0 0]
[ 0 0 1 0 -1 0 -2 -2 -1 -2 -1 0 -2 -1 0 -1 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
100 ? x + y + z + x-1*y + x-1*y*z-1 + 2*y-1 + 5*x-1 + 3*x-1*z-1 + 2*x-2*y*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + 7*x-2*z-1 + x-1*y-2 + x-3*y*z-2 + 6*x-2*y-1*z-1 + 3*x-3*z-2 + 2*x-2*y-2*z-1 + 3*x-3*y-1*z-2 + x-3*y-2*z-2
38 ? x + y + z + x-1*y + x-1*y*z-1 + 2*y-1 + 3*x-1 + 3*x-1*z-1 + 2*x-2*y*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 5*x-2*z-1 + x-1*y-2 + x-3*y*z-2 + 5*x-2*y-1*z-1 + 3*x-3*z-2 + 2*x-2*y-2*z-1 + 3*x-3*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 199 1 Lattice Minkowski decompositions of facet 199
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3644
Image of polytope 3644 PALP id: 3644
grdb id: 299287
Integer points: [ 1 0 0 1 -2 1 -2 1 0 -1 1 0 -1 1 0 0 -1 1 0 -1]
[ 0 1 0 0 1 -2 0 -3 -2 -1 -2 -1 0 -1 0 -1 0 -1 0 1]
[ 0 0 1 -1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 x + y + z + x*z-1 + 2*x*y-1 + 2*x-1*y + 3*x*y-1*z-1 + 3*z-1 + x*y-2 + 4*y-1 + 3*x-1 + x-2*y + 3*x*y-2*z-1 + 6*y-1*z-1 + 3*x-1*z-1 + x*y-3*z-1 + 3*y-2*z-1 + 3*x-1*y-1*z-1 + x-2*z-1
62 rank 2, number 9 x + y + z + x*z-1 + 2*x*y-1 + 2*x-1*y + 3*x*y-1*z-1 + 3*z-1 + x*y-2 + 2*y-1 + 2*x-1 + x-2*y + 3*x*y-2*z-1 + 6*y-1*z-1 + 3*x-1*z-1 + x*y-3*z-1 + 3*y-2*z-1 + 3*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Polytope 3645
Image of polytope 3645 PALP id: 3645
grdb id: 300021
Integer points: [ 1 0 0 1 -1 0 -2 -2 -2 -2 -1 -1 -1 0 0 -1 -1 -1 0 0]
[ 0 1 0 0 1 -1 0 -3 -2 -1 -2 -1 0 -1 0 -2 -1 0 -1 0]
[ 0 0 1 -1 0 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*z-1 + x-1*y + y-1*z + 3*z-1 + 3*y-1 + 3*x-1 + 3*y-1*z-1 + 3*x-1*z-1 + 4*x-1*y-1 + 6*x-1*y-1*z-1 + x-2*z-1 + 2*x-1*y-2 + 3*x-1*y-2*z-1 + 3*x-2*y-1*z-1 + 3*x-2*y-2*z-1 + x-2*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Polytope 3646
Image of polytope 3646 PALP id: 3646
grdb id: 300000
Integer points: [ 1 0 1 -1 0 1 0 -3 -2 -1 -2 -1 0 -1 0 -2 -1 -1 0 0]
[ 0 1 -1 1 0 -2 -3 -3 -2 -1 -3 -2 -1 -3 -2 -1 0 -1 0 -1]
[ 0 0 0 0 1 -1 -2 -2 -1 0 -2 -1 0 -2 -1 -1 0 -1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 14 1 none
Image of facet 153 1 Lattice Minkowski decompositions of facet 153
Polytope 3647
Image of polytope 3647 PALP id: 3647
grdb id: 301745
Integer points: [ 1 0 0 0 0 -1 -2 -2 -1 -1 -1 0 0 0 -2 -2 -1 -1 -1 0]
[ 0 1 0 0 -2 2 0 3 0 1 2 -1 0 1 1 2 -1 0 1 -1]
[ 0 0 1 -1 1 -2 1 -2 1 0 -1 1 0 -1 0 -1 1 0 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + 2*y*z-1 + 2*x-1*y2*z-1 + 4*x-1*y + 2*y-1*z + 2*x-1*z + x-1*y2*z-2 + x-2*y3*z-2 + z-1 + 4*x-1*y*z-1 + 3*x-2*y2*z-1 + 2*y-1 + 5*x-1 + 3*x-2*y + y-2*z + 2*x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3648
Image of polytope 3648 PALP id: 3648
grdb id: 304635
Integer points: [ 1 0 0 -1 -1 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -2 2 -2 2 -3 1 0 -1 -2 1 0 -1 1 0 -1 0 -1]
[ 0 0 1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y2*z-1 + 2*x-1*y + 4*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 5*x-1 + 6*x-1*z-1 + 5*x-2*y*z-1 + 4*x-1*y-1 + 4*x-1*y-1*z-1 + 10*x-2*z-1 + x-1*y-2 + x-1*y-2*z-1 + 10*x-2*y-1*z-1 + 5*x-2*y-2*z-1 + x-2*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 13 1 irreducible and admissible
Image of facet 157 1 Lattice Minkowski decompositions of facet 157
Polytope 3649
Image of polytope 3649 PALP id: 3649
grdb id: 301133
Integer points: [ 1 0 0 0 -2 -1 -3 -3 -1 -2 -1 0 -3 -2 -1 -2 -1 0 -1 0]
[ 0 1 0 -2 2 -2 2 0 1 1 0 -1 1 0 -1 -1 1 0 0 -1]
[ 0 0 1 1 -1 0 -2 -2 0 -1 0 1 -2 -1 0 -1 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + 2*x-1*y + 2*y-1*z + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 5*x-1 + y-2*z + 2*x-1*z-1 + 4*x-2*y*z-1 + 4*x-1*y-1 + x-3*y2*z-2 + 5*x-2*z-1 + x-1*y-2 + 2*x-3*y*z-2 + 2*x-2*y-1*z-1 + x-3*z-2
39 ? x + y + z + 2*x-1*y + 2*y-1*z + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 6*x-1 + y-2*z + 2*x-1*z-1 + 5*x-2*y*z-1 + 5*x-1*y-1 + x-3*y2*z-2 + 6*x-2*z-1 + x-1*y-2 + 2*x-3*y*z-2 + 2*x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 224 1 Lattice Minkowski decompositions of facet 224
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 3650
Image of polytope 3650 PALP id: 3650
grdb id: 304633
Integer points: [ 1 0 0 0 -1 -2 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 1 2 -2 -3 1 0 -1 -2 1 0 -1 -2 0 -1 0 -1]
[ 0 0 1 1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 146 1 Lattice Minkowski decompositions of facet 146
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Image of facet 8 1 none
Image of facet 9 1 irreducible and admissible
Polytope 3651
Image of polytope 3651 PALP id: 3651
grdb id: 304637
Integer points: [ 1 0 -1 0 -1 -2 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 1 0 1 1 -3 -4 -3 -2 -1 0 -2 -1 0 -2 -1 0 -1 0]
[ 0 0 0 1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 8 1 none
Image of facet 13 1 irreducible and admissible
Image of facet 157 1 Lattice Minkowski decompositions of facet 157
Polytope 3652
Image of polytope 3652 PALP id: 3652
grdb id: 299833
Integer points: [ 1 0 0 -1 -1 -1 -3 -3 -2 -3 -2 -1 -3 -2 -1 -2 -1 0 -1 0]
[ 0 1 0 1 0 -2 -1 -4 -3 -3 -2 -1 -2 -1 0 0 -2 -1 -1 0]
[ 0 0 1 0 -1 0 -2 -2 -1 -2 -1 0 -2 -1 0 -1 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
143 ? x + y + z + x-1*y + 2*y-1 + 3*x-1 + x-1*z-1 + 5*x-1*y-1 + 3*x-1*y-1*z-1 + 2*x-2*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 6*x-2*y-1*z-1 + 7*x-2*y-2*z-1 + x-3*y-1*z-2 + 2*x-2*y-3*z-1 + 3*x-3*y-2*z-2 + 3*x-3*y-3*z-2 + x-3*y-4*z-2
46 ? x + y + z + x-1*y + 2*y-1 + 2*x-1 + x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + 2*x-2*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 5*x-2*y-1*z-1 + 5*x-2*y-2*z-1 + x-3*y-1*z-2 + 2*x-2*y-3*z-1 + 3*x-3*y-2*z-2 + 3*x-3*y-3*z-2 + x-3*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 199 1 Lattice Minkowski decompositions of facet 199
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3653
Image of polytope 3653 PALP id: 3653
grdb id: 299581
Integer points: [ 1 0 0 -1 0 -1 -2 -4 -2 -1 0 -3 -2 -1 -3 -2 -1 0 -1 0]
[ 0 1 0 1 -2 -2 1 1 1 0 -1 1 0 -1 0 -1 1 0 0 -1]
[ 0 0 1 0 1 0 -2 -3 -1 0 1 -2 -1 0 -2 -1 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y + 2*y-1*z + 2*x-1*y*z-1 + 2*y-1 + 5*x-1 + y-2*z + 3*x-1*z-1 + 3*x-2*y*z-1 + 5*x-1*y-1 + x-2*y*z-2 + 7*x-2*z-1 + x-1*y-2 + 3*x-3*y*z-2 + 3*x-2*y-1*z-1 + 3*x-3*z-2 + x-4*y*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 174 1 Lattice Minkowski decompositions of facet 174
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3654
Image of polytope 3654 PALP id: 3654
grdb id: 300022
Integer points: [ 1 0 0 0 -1 0 -1 -4 -3 -2 -3 -2 -1 -2 -1 0 -2 -1 -1 0]
[ 0 1 0 -1 0 -2 -3 -3 -2 -1 -3 -2 -1 -3 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 1 -1 -2 -2 -1 0 -2 -1 0 -2 -1 0 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 14 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 174 1 Lattice Minkowski decompositions of facet 174
Polytope 3655
Image of polytope 3655 PALP id: 3655
grdb id: 300039
Integer points: [ 1 0 0 0 0 -1 -1 -4 -3 -2 -3 -2 -1 -2 -1 -2 -1 -1 0 0]
[ 0 1 0 0 -1 1 -2 -2 -1 0 -2 -1 0 -2 -1 -1 0 -1 0 -1]
[ 0 0 1 -1 1 0 0 -3 -2 -1 -2 -1 0 -1 0 -2 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y + y-1*z + z-1 + 2*y-1 + 3*x-1 + 3*x-1*z-1 + 4*x-1*y-1 + 4*x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2 + 6*x-2*y-1*z-1 + 2*x-2*y-1*z-2 + 3*x-2*y-2*z-1 + 3*x-3*y-1*z-2 + 3*x-3*y-2*z-2 + x-4*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 153 1 Lattice Minkowski decompositions of facet 153
Polytope 3656
Image of polytope 3656 PALP id: 3656
grdb id: 301802
Integer points: [ 1 0 0 0 1 -2 -1 -4 -1 0 -3 -2 -1 0 -1 0 -3 -2 -2 -1]
[ 0 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 -1 0 0 -2 -2 0 0 -1 -1 -1 -1 0 0 -2 -2 -1 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*y-1 + z-1 + 3*y-1 + 2*x-1 + 2*y-1*z-1 + 3*x-1*z-1 + 3*x-1*y-1 + 6*x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1 + x-1*y-1*z-2 + 6*x-2*y-1*z-1 + 3*x-2*y-1*z-2 + 2*x-3*y-1*z-1 + 3*x-3*y-1*z-2 + x-4*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Polytope 3657
Image of polytope 3657 PALP id: 3657
grdb id: 299865
Integer points: [ 1 0 1 0 -2 0 -1 -4 -2 -1 0 -3 -2 -1 -3 0 -1 0 -2 -1]
[ 0 1 -1 0 1 -2 -2 1 -1 -1 -1 0 0 0 1 -1 0 0 1 1]
[ 0 0 0 1 0 -1 -2 -2 -2 -1 0 -2 -1 0 -1 -1 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*y-1 + 2*x-1*y + 2*y-1 + 3*x-1 + x-2*y + 2*y-1*z-1 + 4*x-1*z-1 + 2*x-2*y*z-1 + y-2*z-1 + 4*x-1*y-1*z-1 + 5*x-2*z-1 + 2*x-3*y*z-1 + x-1*y-2*z-2 + 3*x-2*y-1*z-2 + 3*x-3*z-2 + x-4*y*z-2
39 ? x + y + z + x*y-1 + 2*x-1*y + 2*y-1 + 4*x-1 + x-2*y + 2*y-1*z-1 + 4*x-1*z-1 + 2*x-2*y*z-1 + y-2*z-1 + 5*x-1*y-1*z-1 + 6*x-2*z-1 + 2*x-3*y*z-1 + x-1*y-2*z-2 + 3*x-2*y-1*z-2 + 3*x-3*z-2 + x-4*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 155 1 Lattice Minkowski decompositions of facet 155
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3658
Image of polytope 3658 PALP id: 3658
grdb id: 303278
Integer points: [ 1 0 0 -1 -1 -1 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 1 -1 -1 2 -1 3 0 1 2 -1 0 1 2 0 1 0 1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + 3*x-1*z + x-1*y-1*z2 + 4*x-1 + 3*x-1*y-1*z + 3*x-2*y-1*z2 + x-1*z-1 + 3*x-1*y-1 + 8*x-2*y-1*z + x-3*y-2*z3 + x-1*y-1*z-1 + 7*x-2*y-1 + 4*x-3*y-2*z2 + 2*x-2*y-1*z-1 + 6*x-3*y-2*z + 4*x-3*y-2 + x-3*y-2*z-1
144 rank 3, number 12 x + y + z + 3*x-1*z + x-1*y-1*z2 + 4*x-1 + 4*x-1*y-1*z + 3*x-2*y-1*z2 + x-1*z-1 + 4*x-1*y-1 + 8*x-2*y-1*z + x-3*y-2*z3 + x-1*y-1*z-1 + 7*x-2*y-1 + 4*x-3*y-2*z2 + 2*x-2*y-1*z-1 + 6*x-3*y-2*z + 4*x-3*y-2 + x-3*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 93 1 Lattice Minkowski decompositions of facet 93
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Polytope 3659
Image of polytope 3659 PALP id: 3659
grdb id: 300524
Integer points: [ 1 0 0 -1 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 2 0 0 -3 -4 -3 -2 -1 -2 -1 0 1 1 -2 -1 -1 0]
[ 0 0 1 -1 -1 1 1 1 1 1 1 0 0 0 0 -1 1 1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 8 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3660
Image of polytope 3660 PALP id: 3660
grdb id: 299797
Integer points: [ 1 0 0 0 -1 -3 -2 -5 -1 -3 -2 -1 -4 -3 -2 -4 -1 0 -2 -1]
[ 0 1 0 1 0 -2 -1 -4 0 -2 -1 0 -3 -2 -1 -3 -1 0 -2 -1]
[ 0 0 1 1 -1 -2 1 -2 1 0 0 0 -1 -1 -1 -2 0 0 -1 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? y*z + x + y + z + 2*x-1*z + 4*x-1 + x-1*z-1 + 3*x-1*y-1 + x-2*y-1*z + 2*x-1*y-1*z-1 + 6*x-2*y-1 + 4*x-2*y-1*z-1 + 2*x-2*y-2*z-1 + 3*x-3*y-2 + 6*x-3*y-2*z-1 + x-3*y-2*z-2 + 3*x-4*y-3*z-1 + 2*x-4*y-3*z-2 + x-5*y-4*z-2
67 ? y*z + x + y + z + 2*x-1*z + 5*x-1 + x-1*z-1 + 3*x-1*y-1 + x-2*y-1*z + 2*x-1*y-1*z-1 + 7*x-2*y-1 + 5*x-2*y-1*z-1 + 2*x-2*y-2*z-1 + 3*x-3*y-2 + 7*x-3*y-2*z-1 + x-3*y-2*z-2 + 3*x-4*y-3*z-1 + 2*x-4*y-3*z-2 + x-5*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 225 1 Lattice Minkowski decompositions of facet 225
Polytope 3661
Image of polytope 3661 PALP id: 3661
grdb id: 300046
Integer points: [ 1 0 0 0 0 -1 -1 -4 -3 -2 -3 -2 -1 -2 -1 -2 -1 -1 0 0]
[ 0 1 0 0 1 1 -2 -2 -1 0 -2 -1 0 -2 -1 -1 0 -1 0 -1]
[ 0 0 1 -1 -1 0 0 3 2 1 2 1 0 1 0 2 1 1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + y*z-1 + x-1*y + 3*x-1*z + z-1 + 2*y-1 + 4*x-1 + 4*x-1*y-1*z + 3*x-2*z + 2*x-2*y-1*z2 + 3*x-1*y-1 + 6*x-2*y-1*z + 3*x-3*y-1*z2 + x-1*y-2 + 3*x-2*y-2*z + 3*x-3*y-2*z2 + x-4*y-2*z3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 153 1 Lattice Minkowski decompositions of facet 153
Polytope 3662
Image of polytope 3662 PALP id: 3662
grdb id: 296153
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 -1 0 0 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 1 1 -2 1 -2 0 -1 1 0 -1 -2 0 -1 0 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + y-1*z + x-1*z + 2*z-1 + 3*y-1 + 3*x-1 + 2*x-1*y-1*z + 2*y-1*z-1 + 3*x-1*z-1 + 6*x-1*y-1 + x-1*y-2*z + x-1*z-2 + 6*x-1*y-1*z-1 + 3*x-1*y-2 + 2*x-1*y-1*z-2 + 3*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Polytope 3663
Image of polytope 3663 PALP id: 3663
grdb id: 129141
Integer points: [ 1 0 0 0 -1 -1 1 0 -3 -2 -1 -2 -1 0 -2 -1 0 -1 0 1]
[ 0 1 0 0 1 1 -2 -2 1 0 -1 1 0 -1 1 0 -1 1 0 -1]
[ 0 0 1 -1 -1 1 0 1 1 1 1 0 0 0 1 1 1 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + 2*y-1*z + 4*x-1*z + 2*x-2*y*z + z-1 + x-1*y*z-1 + x*y-2 + 3*y-1 + 4*x-1 + 2*x-2*y + y-2*z + 3*x-1*y-1*z + 3*x-2*z + x-3*y*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3664
Image of polytope 3664 PALP id: 3664
grdb id: 128990
Integer points: [ 1 0 0 1 -1 1 1 -2 -3 -2 -1 0 -2 -1 0 -1 0 -1 0 1]
[ 0 1 0 -2 1 -2 -3 1 1 0 -1 -2 1 0 -1 0 -1 1 0 -1]
[ 0 0 1 -1 1 0 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 8 1 none
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3665
Image of polytope 3665 PALP id: 3665
grdb id: 129152
Integer points: [ 1 0 0 -1 1 0 0 -2 -2 -1 0 -1 0 1 -1 0 -2 -1 -1 0]
[ 0 1 0 2 -2 0 -2 2 0 -1 -1 0 -1 -1 0 0 1 1 1 1]
[ 0 0 1 2 -2 -1 -1 3 1 0 -1 0 0 -1 1 0 2 1 2 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x-1*y2*z2 + x-2*y2*z3 + 2*y*z + 2*x-1*y*z2 + x + y + z + 3*x-1*y*z + 2*x-2*y*z2 + 4*x-1*z + 2*x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + x-2*z + 2*y-1*z-1 + 2*x-1*y-1 + x*y-2*z-2 + y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3666
Image of polytope 3666 PALP id: 3666
grdb id: 129112
Integer points: [ 1 0 1 -1 1 0 -2 1 0 0 0 -1 -1 1 1 0 0 0 -1 1]
[ 0 1 0 0 -1 -1 1 -1 -1 -1 -1 0 0 -1 -1 0 0 0 1 0]
[ 0 0 2 -2 0 -1 -2 3 2 0 1 -1 0 1 2 -1 0 1 -1 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x*z2 + x*y-1*z3 + 2*x*z + 3*x*y-1*z2 + x + y + 3*x*y-1*z + 3*z + y-1*z2 + x*y-1 + 3*y-1*z + 2*z-1 + 2*x-1*y*z-1 + 3*y-1 + 2*x-1 + y-1*z-1 + 3*x-1*z-1 + x-1*z-2 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3667
Image of polytope 3667 PALP id: 3667
grdb id: 129150
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 1 -1 -1 -2 2 -2 2 1 0 -1 1 0 -1 0 1 0 -1 0]
[ 0 0 2 -2 0 -2 2 -3 1 1 0 -1 0 -1 -2 1 1 0 -1 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
26 rank 2, number 8 y*z2 + x-1*y2*z2 + y*z + x-1*y2*z + x + y + 2*z + 4*x-1*y*z + 4*x-1*y + 2*z-1 + y-1 + 6*x-1 + y-1*z-1 + 6*x-1*z-1 + y-1*z-2 + 4*x-1*y-1*z-1 + 4*x-1*y-1*z-2 + x-1*y-2*z-2 + x-1*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 10 2 Lattice Minkowski decompositions of facet 10
Image of facet 59 2 Lattice Minkowski decompositions of facet 59
Image of facet 134 1 Lattice Minkowski decompositions of facet 134
Polytope 3668
Image of polytope 3668 PALP id: 3668
grdb id: 125301
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 -1 1 -1 0 -2 -2 -2 -1 0 -2 -1 0 -1 -1 0 -1 0]
[ 0 0 1 1 -1 1 -2 1 -2 0 0 0 -1 -1 -1 -2 0 0 -1 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + y-1*z + 2*z-1 + x-1*y*z-1 + 3*y-1 + 2*x-1 + x-1*y-1*z + 2*y-1*z-1 + 4*x-1*z-1 + 5*x-1*y-1 + x-1*y-2*z + x-1*z-2 + 6*x-1*y-1*z-1 + 3*x-1*y-2 + 2*x-1*y-1*z-2 + 3*x-1*y-2*z-1 + x-1*y-2*z-2
13 rank 2, number 12 x + y + z + y-1*z + 2*z-1 + x-1*y*z-1 + 3*y-1 + 2*x-1 + x-1*y-1*z + 2*y-1*z-1 + 3*x-1*z-1 + 4*x-1*y-1 + x-1*y-2*z + x-1*z-2 + 5*x-1*y-1*z-1 + 3*x-1*y-2 + 2*x-1*y-1*z-2 + 3*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 155 1 Lattice Minkowski decompositions of facet 155
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 3669
Image of polytope 3669 PALP id: 3669
grdb id: 125267
Integer points: [ 1 0 1 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 -1 0 1 1 -2 1 -2 1 1 0 0 0 -1 -1 0 0 -1 -1]
[ 0 0 0 1 -1 1 1 -2 1 0 -1 1 0 -1 1 0 0 -1 1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x-1*y*z + y*z-1 + x*y-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + 2*z-1 + 3*x-1*y*z-1 + 3*y-1 + 6*x-1 + y-2*z + 3*x-1*y-1*z + x-1*y*z-2 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Polytope 3670
Image of polytope 3670 PALP id: 3670
grdb id: 125848
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 1 0 -2 -1 -2 -1 -2 -1 0 -1 0 0 -1 0 -1 0]
[ 0 0 1 0 -1 -2 0 2 2 -1 1 0 -1 1 0 1 0 -1 1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + 2*z-1 + x-1*y*z-1 + 2*y-1 + 5*x-1 + 5*x-1*y-1*z + x-1*y-2*z2 + 3*x-1*z-1 + 5*x-1*y-1 + 2*x-1*y-2*z + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
56 rank 2, number 11 x + y + z + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + 2*z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-2*z + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 203 1 Lattice Minkowski decompositions of facet 203
Polytope 3671
Image of polytope 3671 PALP id: 3671
grdb id: 127551
Integer points: [ 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 0 -1 -1 -1 0 0 -1 0 0]
[ 0 1 0 1 2 -2 2 0 -2 0 -1 -1 1 0 -1 0 -1 1 1 0]
[ 0 0 1 0 -1 1 -2 -2 0 0 0 1 -1 -1 -1 0 0 -2 -1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + 2*y*z-1 + x-1*y2*z-1 + x-1*y + 2*y-1*z + x-1*y2*z-2 + 2*z-1 + 4*x-1*y*z-1 + 2*y-1 + 3*x-1 + y-2*z + 2*x-1*y*z-2 + 5*x-1*z-1 + 3*x-1*y-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 3672
Image of polytope 3672 PALP id: 3672
grdb id: 126033
Integer points: [ 1 0 0 0 0 -1 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 -2 2 2 -2 1 0 -1 1 0 -1 1 0 -1 0 -1]
[ 0 0 1 -1 -1 0 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + y*z-1 + x-1*y2*z-1 + 2*x-1*y + z-1 + 4*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 4*x-1 + 5*x-1*z-1 + 4*x-2*y*z-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + 6*x-2*z-1 + x-1*y-2 + 4*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3673
Image of polytope 3673 PALP id: 3673
grdb id: 126173
Integer points: [ 1 0 0 1 -1 1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 -1 1 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 0 1 0 0 -1 -2 2 -2 -1 0 1 -1 0 1 -1 0 1 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x*y-1 + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + x*y-1*z-1 + 2*z-1 + 5*y-1 + 4*x-1 + 4*x-1*y-1*z + 4*y-1*z-1 + 2*x-1*z-1 + 6*x-1*y-1 + y-1*z-2 + 4*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3674
Image of polytope 3674 PALP id: 3674
grdb id: 127678
Integer points: [ 1 0 0 1 1 -1 0 -2 -2 -1 -2 -1 0 -1 0 0 -1 0 -1 0]
[ 0 1 0 -1 0 2 -2 2 0 1 1 1 1 0 0 -1 0 0 -1 -1]
[ 0 0 1 0 -1 -1 1 -1 -1 0 -1 -1 -1 0 0 1 -1 -1 0 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x*z-1 + 2*y*z-1 + x-1*y2*z-1 + x*y-1 + 2*x-1*y + 2*y-1*z + 3*z-1 + 4*x-1*y*z-1 + x-2*y2*z-1 + 3*y-1 + 4*x-1 + y-2*z + 3*x-1*z-1 + 2*x-2*y*z-1 + 2*x-1*y-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Polytope 3675
Image of polytope 3675 PALP id: 3675
grdb id: 127722
Integer points: [ 1 0 1 0 1 -2 -2 1 0 0 -1 0 -1 -2 -1 1 0 -1 0 -1]
[ 0 1 -1 0 -2 1 1 -2 -1 -1 0 -1 0 1 0 -1 0 1 0 1]
[ 0 0 0 1 -1 0 2 -2 -2 0 1 -1 0 1 -1 -1 0 1 -1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*x-1*y*z + x-2*y*z2 + x*y-1 + 2*x-1*y + 3*x-1*z + 2*x-2*y*z + 2*x*y-1*z-1 + 2*z-1 + 3*y-1 + 5*x-1 + x-2*y + x*y-2*z-1 + 4*y-1*z-1 + 2*x-1*z-1 + x*y-2*z-2 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3676
Image of polytope 3676 PALP id: 3676
grdb id: 125177
Integer points: [ 1 0 0 -1 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 0 -1 -1 -2 -2 -2 -1 -2 -1 0 -1 0 -1 -1 0 0]
[ 0 0 1 0 1 1 -2 0 -3 -1 0 -2 -1 0 -2 -1 0 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y + x-1*z + 2*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + 3*y-1*z-1 + 3*x-1*z-1 + 4*x-1*y-1 + y-1*z-2 + 6*x-1*y-1*z-1 + x-1*y-2 + 3*x-1*y-1*z-2 + 3*x-1*y-2*z-1 + 3*x-1*y-2*z-2 + x-1*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 153 1 Lattice Minkowski decompositions of facet 153
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3677
Image of polytope 3677 PALP id: 3677
grdb id: 125176
Integer points: [ 1 0 0 -1 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 0 1 -2 0 -3 -1 0 -2 -1 0 -2 -1 -1 0 -1 0]
[ 0 0 1 0 1 -1 1 -2 1 1 0 1 0 -1 0 -1 1 0 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y + 2*y-1*z + x-1*z + 2*z-1 + x-1*y*z-1 + 3*y-1 + 4*x-1 + y-2*z + 3*x-1*y-1*z + 3*x-1*z-1 + 6*x-1*y-1 + 3*x-1*y-2*z + x-1*z-2 + 3*x-1*y-1*z-1 + 3*x-1*y-2 + x-1*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 153 1 Lattice Minkowski decompositions of facet 153
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3678
Image of polytope 3678 PALP id: 3678
grdb id: 126080
Integer points: [ 1 0 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 1 1 -2 -1 -3 0 -2 -1 0 1 -2 -1 0 -1 0 -1]
[ 0 0 1 -1 -1 1 1 -1 1 -1 0 0 0 0 1 1 1 0 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + z + x-1*y*z + 2*x-1*y + 2*y-1*z + 4*x-1*z + z-1 + x-1*y*z-1 + 3*y-1 + 6*x-1 + y-2*z + 6*x-1*y-1*z + 2*x-1*z-1 + 6*x-1*y-1 + 4*x-1*y-2*z + x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-3*z
10 rank 1, V18 x + y + z + x-1*y*z + 2*x-1*y + 2*y-1*z + 4*x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 6*x-1 + y-2*z + 6*x-1*y-1*z + 2*x-1*z-1 + 6*x-1*y-1 + 4*x-1*y-2*z + x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 1 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3679
Image of polytope 3679 PALP id: 3679
grdb id: 127689
Integer points: [ 1 0 0 1 -1 1 -2 1 1 1 0 -1 0 -1 1 0 1 0 -1 0]
[ 0 1 0 0 1 -1 0 -1 -3 -2 -1 0 -2 -1 -1 0 -2 -1 0 0]
[ 0 0 1 -1 0 0 1 -2 -2 -1 0 1 -1 0 -1 0 -2 -1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + x*z-1 + x*y-1 + x-1*y + 2*x-1*z + 3*x*y-1*z-1 + 2*z-1 + 4*y-1 + 2*x-1 + x-2*z + x*y-1*z-2 + 2*x*y-2*z-1 + 4*y-1*z-1 + 3*x-1*y-1 + 2*x*y-2*z-2 + 3*y-2*z-1 + x*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Polytope 3680
Image of polytope 3680 PALP id: 3680
grdb id: 126185
Integer points: [ 1 0 0 1 0 -1 1 -1 -3 -2 -1 0 -1 0 -2 -1 0 -2 -1 0]
[ 0 1 0 -1 -1 1 -1 -1 -1 -1 -1 -1 0 0 -1 -1 -1 0 0 0]
[ 0 0 1 0 1 -1 -1 1 -1 0 0 0 0 0 -1 -1 -1 -1 -1 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*y-1 + y-1*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 4*y-1 + 3*x-1 + x-1*y-1*z + 4*y-1*z-1 + 4*x-1*z-1 + 5*x-1*y-1 + 6*x-1*y-1*z-1 + 2*x-2*z-1 + 2*x-2*y-1 + 4*x-2*y-1*z-1 + x-3*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3681
Image of polytope 3681 PALP id: 3681
grdb id: 127686
Integer points: [ 1 0 1 0 0 -1 -2 0 -2 -2 -2 -1 -1 -1 0 -1 -1 -1 0 0]
[ 0 1 -1 0 0 1 1 -2 -2 0 -1 0 -1 -2 -1 1 0 -1 0 -1]
[ 0 0 0 1 -1 1 0 -1 -3 -1 -2 0 -1 -2 0 0 -1 -2 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + x*y-1 + 2*x-1*y + z-1 + 2*y-1 + 4*x-1 + x-2*y + 3*y-1*z-1 + 4*x-1*z-1 + y-2*z-1 + 5*x-1*y-1*z-1 + 3*x-2*z-1 + 2*x-1*y-1*z-2 + 2*x-1*y-2*z-2 + 3*x-2*y-1*z-2 + x-2*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3682
Image of polytope 3682 PALP id: 3682
grdb id: 127896
Integer points: [ 1 0 0 -2 2 0 -2 3 2 -1 1 -1 -2 0 2 -1 1 -1 1 0]
[ 0 1 0 2 -2 0 0 -2 -1 1 0 1 1 0 -1 0 -1 0 -1 -1]
[ 0 0 1 1 -1 -1 1 -2 -2 0 -1 1 1 0 -1 0 -1 1 0 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + 2*x-1*y*z + x-2*y2*z + 2*x2*y-1*z-1 + 2*x*z-1 + 2*x*y-1 + 2*x-1*y + 2*x-1*z + 2*x-2*y*z + x3*y-2*z-2 + x2*y-1*z-2 + x2*y-2*z-1 + 3*x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 3 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 3 Lattice Minkowski decompositions of facet 15
Polytope 3683
Image of polytope 3683 PALP id: 3683
grdb id: 126503
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 1 -1 -1 0 0 1 1 1 1 1 0 0 0 -1 1 0 0 0]
[ 0 0 2 -2 0 -2 2 3 -1 2 1 0 1 0 -1 -1 1 1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 y*z2 + x-1*y*z3 + 2*y*z + 4*x-1*y*z2 + x + y + 2*z + 6*x-1*y*z + x-1*z2 + 4*x-1*y + 4*x-1*z + 2*z-1 + x-1*y*z-1 + 6*x-1 + 4*x-1*z-1 + x-1*y-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-1*z-2
151 ? y*z2 + x-1*y*z3 + 2*y*z + 4*x-1*y*z2 + x + y + 2*z + 6*x-1*y*z + x-1*z2 + 4*x-1*y + 5*x-1*z + 2*z-1 + x-1*y*z-1 + 8*x-1 + 5*x-1*z-1 + x-1*y-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 4 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 187 1 Lattice Minkowski decompositions of facet 187
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Polytope 3684
Image of polytope 3684 PALP id: 3684
grdb id: 126035
Integer points: [ 1 0 0 -1 1 -2 1 -3 1 0 -1 -2 0 -1 -2 0 -1 1 0 -1]
[ 0 1 0 1 -2 1 -2 1 -3 -2 -1 0 -1 0 1 -1 0 -1 0 1]
[ 0 0 1 0 1 -2 2 -2 2 1 0 -1 1 0 -1 0 -1 1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + 2*x*y-1*z + z + x*y-2*z2 + x-1*y + x*y-2*z + 4*y-1*z + x*y-3*z2 + 2*x-1*y*z-1 + 3*y-1 + 5*x-1 + 4*y-2*z + 3*x-1*z-1 + 2*x-2*y*z-1 + 6*x-1*y-1 + x-2*y*z-2 + 4*x-2*z-1 + x-3*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 9 1 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3685
Image of polytope 3685 PALP id: 3685
grdb id: 125153
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 -2 2 0 2 -2 -3 1 -1 0 1 -2 -1 0 -1 0 1 -1]
[ 0 0 1 1 -1 1 -2 0 1 0 1 0 -1 1 0 -1 1 0 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + 2*y*z-1 + x-1*y2*z-1 + 2*x-1*y + 2*y-1*z + x-1*z + x-1*y2*z-2 + 4*x-1*y*z-1 + 2*y-1 + 6*x-1 + y-2*z + 3*x-1*y-1*z + 2*x-1*z-1 + 5*x-1*y-1 + 3*x-1*y-2*z + x-1*y-2 + x-1*y-3*z
62 rank 2, number 9 x + y + z + 2*y*z-1 + x-1*y2*z-1 + 2*x-1*y + 2*y-1*z + x-1*z + x-1*y2*z-2 + 3*x-1*y*z-1 + 2*y-1 + 5*x-1 + y-2*z + 3*x-1*y-1*z + 2*x-1*z-1 + 4*x-1*y-1 + 3*x-1*y-2*z + x-1*y-2 + x-1*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 155 1 Lattice Minkowski decompositions of facet 155
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3686
Image of polytope 3686 PALP id: 3686
grdb id: 125313
Integer points: [ 1 0 0 0 1 -1 -1 -2 -2 -2 -2 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 1 0 1 0 1 -2 0 -3 -1 -2 0 -1 -2 0 -1 0 -1 0 -1]
[ 0 0 1 -1 -1 -1 2 -1 2 0 1 -1 0 1 -1 0 0 1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + x*z-1 + y*z-1 + 2*y-1*z + 3*z-1 + x-1*y*z-1 + 3*y-1 + 3*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + 3*x-1*z-1 + 6*x-1*y-1 + 3*x-1*y-2*z + x-2*z-1 + 3*x-2*y-1 + 3*x-2*y-2*z + x-2*y-3*z2
20 rank 1, V16 x + y + z + x*z-1 + y*z-1 + 2*y-1*z + 3*z-1 + x-1*y*z-1 + 3*y-1 + 4*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + 3*x-1*z-1 + 6*x-1*y-1 + 3*x-1*y-2*z + x-2*z-1 + 3*x-2*y-1 + 3*x-2*y-2*z + x-2*y-3*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Polytope 3687
Image of polytope 3687 PALP id: 3687
grdb id: 125281
Integer points: [ 1 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 1 0 0 0 -1 -2 -4 -2 -3 -1 -2 -3 0 -1 -1 -2 0 -1]
[ 0 0 0 1 -1 1 1 -2 -2 0 -1 0 -1 -2 0 -1 0 -1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y + x-1*z + 3*y-1 + 3*x-1 + x-1*y-1*z + 2*y-1*z-1 + x-1*z-1 + 4*x-1*y-1 + 2*y-2*z-1 + 4*x-1*y-1*z-1 + 3*x-1*y-2 + 5*x-1*y-2*z-1 + x-1*y-2*z-2 + 3*x-1*y-3*z-1 + 2*x-1*y-3*z-2 + x-1*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 204 1 Lattice Minkowski decompositions of facet 204
Polytope 3688
Image of polytope 3688 PALP id: 3688
grdb id: 126180
Integer points: [ 1 0 -1 0 -1 0 -2 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 1 0 0 -1 0 -2 -4 -3 -2 -1 -2 -1 0 -3 -2 -1 -1 0]
[ 0 0 0 1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + x-1*y + 2*y-1 + 3*x-1 + y-1*z-1 + x-1*z-1 + 4*x-1*y-1 + y-2*z-1 + 4*x-1*y-1*z-1 + x-2*z-1 + 2*x-1*y-2 + 5*x-1*y-2*z-1 + 4*x-2*y-1*z-1 + 2*x-1*y-3*z-1 + 6*x-2*y-2*z-1 + 4*x-2*y-3*z-1 + x-2*y-4*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 3689
Image of polytope 3689 PALP id: 3689
grdb id: 126175
Integer points: [ 1 0 1 -1 0 -1 -1 1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 1 -1 1 0 0 0 -2 -4 -3 -2 -1 -3 -2 -1 -2 -1 0 -1 0]
[ 0 0 0 0 1 -1 1 -1 -3 -2 -1 0 -2 -1 0 -2 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 80 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Polytope 3690
Image of polytope 3690 PALP id: 3690
grdb id: 125261
Integer points: [ 1 0 0 0 0 0 -1 -1 -4 -3 -2 -3 -2 -1 -2 -1 -2 -1 -1 0]
[ 0 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 1 -1 0 1 -1 2 2 1 0 2 1 0 2 1 1 0 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + y-1*z + 3*x-1*z + x-1*y-1*z2 + z-1 + y-1 + 3*x-1 + 4*x-1*y-1*z + 2*x-2*z + 3*x-2*y-1*z2 + 3*x-1*y-1 + 6*x-2*y-1*z + 3*x-3*y-1*z2 + x-1*y-1*z-1 + 3*x-2*y-1 + 3*x-3*y-1*z + x-4*y-1*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 153 1 Lattice Minkowski decompositions of facet 153
Polytope 3691
Image of polytope 3691 PALP id: 3691
grdb id: 120787
Integer points: [ 1 0 0 0 0 0 -1 -2 -2 -2 -2 -1 -1 -1 0 -1 -1 -1 0 0]
[ 0 1 0 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 0 1 -1 1 -1 2 2 -1 0 1 -1 0 1 0 -1 0 1 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + y*z-1 + y-1*z + 2*x-1*z + x-1*y-1*z2 + 2*z-1 + 2*y-1 + 4*x-1 + 4*x-1*y-1*z + x-2*y-1*z2 + y-1*z-1 + 2*x-1*z-1 + 5*x-1*y-1 + 3*x-2*y-1*z + 2*x-1*y-1*z-1 + 3*x-2*y-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Polytope 3692
Image of polytope 3692 PALP id: 3692
grdb id: 120954
Integer points: [ 1 0 0 0 0 -1 0 -2 -2 -2 -2 -1 -1 -1 0 -1 -1 -1 0 0]
[ 0 1 0 1 -1 1 -1 0 -3 -2 -1 -2 -1 0 0 -2 -1 0 -1 0]
[ 0 0 1 -1 1 0 -1 1 1 1 1 0 0 0 -1 1 1 1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + y*z-1 + x-1*y + y-1*z + 2*x-1*z + 2*z-1 + 2*y-1 + 4*x-1 + 4*x-1*y-1*z + x-2*z + y-1*z-1 + 5*x-1*y-1 + 2*x-1*y-2*z + 3*x-2*y-1*z + 2*x-1*y-2 + 3*x-2*y-2*z + x-2*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3693
Image of polytope 3693 PALP id: 3693
grdb id: 120965
Integer points: [ 1 0 0 1 -1 1 -1 0 -3 -1 -2 0 -1 -2 0 -1 -2 0 -1 0]
[ 0 1 0 0 0 -1 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 1 -1 1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*z-1 + x-1*z + x*y-1*z-1 + 2*z-1 + 2*y-1 + 2*x-1 + 4*y-1*z-1 + x-1*z-1 + 4*x-1*y-1 + y-2*z-1 + 5*x-1*y-1*z-1 + 2*x-2*y-1 + 3*x-1*y-2*z-1 + 2*x-2*y-1*z-1 + 3*x-2*y-2*z-1 + x-3*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3694
Image of polytope 3694 PALP id: 3694
grdb id: 116207
Integer points: [ 1 0 0 0 0 -1 -2 -3 -3 -2 -1 -3 -2 -1 -3 -2 -1 -1 0 -1]
[ 0 1 -1 0 -1 2 -1 0 3 2 1 2 1 0 1 0 -1 1 0 0]
[ 0 0 0 1 1 -1 -1 -2 -2 -1 0 -2 -1 0 -2 -1 0 -1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y2*z-1 + 3*x-1*y + y-1*z + 3*x-1*y*z-1 + 3*x-2*y2*z-1 + y-1 + 5*x-1 + x-3*y3*z-2 + 2*x-1*z-1 + 7*x-2*y*z-1 + 2*x-1*y-1 + 3*x-3*y2*z-2 + 5*x-2*z-1 + 3*x-3*y*z-2 + x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 174 1 Lattice Minkowski decompositions of facet 174
Polytope 3695
Image of polytope 3695 PALP id: 3695
grdb id: 118065
Integer points: [ 1 0 0 0 0 -1 -1 -1 -5 -2 -3 -4 -1 -2 -3 -1 -2 -3 0 -1]
[ 0 1 -1 0 -1 0 0 2 4 1 2 3 1 2 3 0 1 2 0 1]
[ 0 0 0 1 1 -1 1 -1 -3 0 -1 -2 0 -1 -2 0 -1 -2 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y2*z-1 + 4*x-1*y + y-1*z + x-1*z + 2*x-1*y*z-1 + 5*x-2*y2*z-1 + y-1 + 4*x-1 + 4*x-2*y + 2*x-3*y3*z-2 + x-1*z-1 + 5*x-2*y*z-1 + 6*x-3*y2*z-1 + 2*x-3*y2*z-2 + 4*x-4*y3*z-2 + x-5*y4*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 6 irreducible and admissible
Image of facet 107 2 Lattice Minkowski decompositions of facet 107
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 3696
Image of polytope 3696 PALP id: 3696
grdb id: 597806
Integer points: [ 1 0 0 -1 2 -1 -2 1 -2 2 -1 0 -1 0 1 -1 0 1 0 1]
[ 0 1 0 1 -1 -1 0 0 -1 -1 0 0 -1 -1 -1 0 0 0 -1 -1]
[ 0 0 1 1 -2 1 1 -2 1 -3 0 -1 0 -1 -2 1 0 -1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
26 rank 2, number 8 x + y + z + x-1*y*z + x*z-1 + x-1*z + x2*y-1*z-2 + x*z-2 + 3*x*y-1*z-1 + 3*z-1 + 3*y-1 + 3*x-1 + x-1*y-1*z + x-2*z + x2*y-1*z-3 + 4*x*y-1*z-2 + 6*y-1*z-1 + 4*x-1*y-1 + x-2*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 10 2 Lattice Minkowski decompositions of facet 10
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 90 2 Lattice Minkowski decompositions of facet 90
Polytope 3697
Image of polytope 3697 PALP id: 3697
grdb id: 597527
Integer points: [ 1 0 0 0 0 -1 1 0 -2 -2 -1 -2 -1 0 -1 -1 0 -1 0 1]
[ 0 1 0 1 -1 1 -2 -1 1 1 0 1 0 -1 0 1 0 1 0 -1]
[ 0 0 1 -1 1 1 0 -1 1 -1 -1 0 0 0 1 -1 -1 0 0 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x-1*y*z + y*z-1 + 2*x*y-1 + 3*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + 2*z-1 + 2*x-1*y*z-1 + x*y-2 + 3*y-1 + 4*x-1 + 2*x-2*y + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1
51 rank 2, number 7 x + y + z + x-1*y*z + y*z-1 + 2*x*y-1 + 3*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + 2*z-1 + 2*x-1*y*z-1 + x*y-2 + 4*y-1 + 5*x-1 + 2*x-2*y + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3698
Image of polytope 3698 PALP id: 3698
grdb id: 597560
Integer points: [ 1 0 0 1 -1 0 1 1 -2 -2 -1 -2 -1 0 -1 0 -1 0 -1 0]
[ 0 1 0 -1 1 0 -1 -2 0 -2 0 -1 -1 -1 0 0 -2 -2 -1 -1]
[ 0 0 1 -1 1 -1 0 -1 1 -1 1 0 0 0 0 0 -1 -1 -1 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + x*y-1 + 2*x-1*z + x*y-1*z-1 + z-1 + 4*y-1 + 3*x-1 + x-2*z + x*y-2*z-1 + 3*y-1*z-1 + 5*x-1*y-1 + 3*y-2*z-1 + 2*x-1*y-1*z-1 + 2*x-2*y-1 + 3*x-1*y-2*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3699
Image of polytope 3699 PALP id: 3699
grdb id: 597548
Integer points: [ 1 0 1 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 -1 0 1 -1 1 -1 0 -1 1 0 0 0 -1 -1 0 0 -1 -1]
[ 0 0 0 1 1 1 -1 1 -2 -2 0 1 0 -1 0 -1 0 -1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y*z + x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + 2*z-1 + x-1*y*z-1 + 3*y-1 + 5*x-1 + x-1*y-1*z + 2*y-1*z-1 + 4*x-1*z-1 + 3*x-1*y-1 + x-1*z-2 + 3*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3700
Image of polytope 3700 PALP id: 3700
grdb id: 597556
Integer points: [ 1 0 0 -1 -1 2 -2 1 -1 -2 -2 -1 0 -1 0 1 -1 0 0 1]
[ 0 1 0 1 1 -1 1 -1 -1 -1 0 0 0 0 0 0 -1 -1 -1 -1]
[ 0 0 1 1 0 -2 1 -2 1 1 1 0 -1 1 0 -1 0 -1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x-1*y*z + 2*x*z-1 + x-1*y + 2*x-1*z + x-2*y*z + x2*y-1*z-2 + 3*x*y-1*z-1 + 2*z-1 + 3*y-1 + 4*x-1 + x-1*y-1*z + 2*x-2*z + x*y-1*z-2 + 3*y-1*z-1 + 3*x-1*y-1 + x-2*y-1*z
51 rank 2, number 7 x + y + z + x-1*y*z + 2*x*z-1 + x-1*y + 3*x-1*z + x-2*y*z + x2*y-1*z-2 + 3*x*y-1*z-1 + 2*z-1 + 3*y-1 + 4*x-1 + x-1*y-1*z + 2*x-2*z + x*y-1*z-2 + 3*y-1*z-1 + 3*x-1*y-1 + x-2*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3701
Image of polytope 3701 PALP id: 3701
grdb id: 597737
Integer points: [ 1 0 0 -1 1 2 -1 -1 -1 -1 -1 0 -1 1 0 -1 0 0 1 0]
[ 0 1 0 2 -2 -2 0 2 1 0 1 -1 0 -1 0 1 1 -1 -1 0]
[ 0 0 1 -1 1 1 1 -2 -2 -1 0 1 0 1 0 -1 -1 0 0 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + x2*y-2*z + 2*x*y-1*z + z + 2*y*z-1 + x-1*y2*z-1 + 3*x*y-1 + 2*x-1*y + x*y-2*z + 2*y-1*z + x-1*z + x-1*y2*z-2 + 3*z-1 + 3*x-1*y*z-1 + 2*y-1 + 2*x-1 + x-1*y*z-2 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3702
Image of polytope 3702 PALP id: 3702
grdb id: 597551
Integer points: [ 1 0 0 -1 1 0 1 -2 0 -3 -2 -1 -1 0 -2 -1 0 -1 0 1]
[ 0 1 0 1 -1 0 -2 1 -2 1 0 -1 0 -1 1 0 -1 1 0 -1]
[ 0 0 1 1 -1 -1 0 0 1 1 1 1 0 0 1 1 1 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + 2*y-1*z + 4*x-1*z + 2*x-2*y*z + x*y-1*z-1 + z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + y-2*z + 3*x-1*y-1*z + 3*x-2*z + x-3*y*z
40 rank 2, number 10 x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + 2*y-1*z + 4*x-1*z + 2*x-2*y*z + x*y-1*z-1 + z-1 + x*y-2 + 4*y-1 + 4*x-1 + x-2*y + y-2*z + 3*x-1*y-1*z + 3*x-2*z + x-3*y*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3703
Image of polytope 3703 PALP id: 3703
grdb id: 597738
Integer points: [ 1 0 0 2 -2 0 -1 1 -3 -1 0 0 -1 -2 -2 1 1 0 -1 -1]
[ 0 1 0 -2 2 0 0 -2 2 0 -1 -1 0 1 1 -1 -1 0 1 1]
[ 0 0 1 -1 1 -1 1 -1 1 -1 -1 0 0 0 1 -1 0 0 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*x-1*y*z + x-2*y2*z + 2*x*y-1 + 2*x-1*y + x-1*z + 2*x-2*y*z + x-3*y2*z + x2*y-2*z-1 + 2*x*y-1*z-1 + z-1 + 2*y-1 + 4*x-1 + 2*x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
51 rank 2, number 7 x + y + z + 2*x-1*y*z + x-2*y2*z + 2*x*y-1 + 3*x-1*y + x-1*z + 2*x-2*y*z + x-3*y2*z + x2*y-2*z-1 + 2*x*y-1*z-1 + z-1 + 2*y-1 + 4*x-1 + 2*x-2*y + x*y-2*z-1 + 2*y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 15 3 Lattice Minkowski decompositions of facet 15
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 3704
Image of polytope 3704 PALP id: 3704
grdb id: 592333
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 0 1 -1 0 -2 -2 -1 0 -2 -1 0 -1 -1 0 -1 0]
[ 0 0 1 0 1 -1 1 -2 0 -2 0 0 -1 -1 -1 -2 0 0 -1 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + x-1*y + x-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + x-1*y-1*z + 2*y-1*z-1 + 5*x-1*z-1 + 4*x-1*y-1 + x-1*z-2 + 6*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-1*z-2 + 2*x-1*y-2*z-1 + x-1*y-2*z-2
52 rank 2, number 52 x + y + z + x-1*y + x-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + 2*y-1*z-1 + 4*x-1*z-1 + 4*x-1*y-1 + x-1*z-2 + 5*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-1*z-2 + 2*x-1*y-2*z-1 + x-1*y-2*z-2
13 rank 2, number 12 x + y + z + x-1*y + x-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + 2*y-1*z-1 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*z-2 + 4*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-1*z-2 + 2*x-1*y-2*z-1 + x-1*y-2*z-2
39 ? x + y + z + x-1*y + x-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + x-1*y-1*z + 2*y-1*z-1 + 4*x-1*z-1 + 5*x-1*y-1 + x-1*z-2 + 6*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-1*z-2 + 2*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 205 1 Lattice Minkowski decompositions of facet 205
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 3705
Image of polytope 3705 PALP id: 3705
grdb id: 591419
Integer points: [ 1 0 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 1 -1 0 -1 -2 -2 -1 -2 -1 0 -2 -1 0 -1 0 -1]
[ 0 0 1 -1 0 1 1 -2 1 -2 1 0 0 0 -1 -1 -1 0 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + x-1*y + y-1*z + x-1*z + z-1 + 3*y-1 + 4*x-1 + 2*x-1*y-1*z + 2*y-1*z-1 + 2*x-1*z-1 + 6*x-1*y-1 + x-1*y-2*z + 5*x-1*y-1*z-1 + 3*x-1*y-2 + x-1*y-1*z-2 + 3*x-1*y-2*z-1 + x-1*y-2*z-2
52 rank 2, number 52 x + y + z + x-1*y + y-1*z + x-1*z + z-1 + 3*y-1 + 3*x-1 + 2*x-1*y-1*z + 2*y-1*z-1 + 2*x-1*z-1 + 5*x-1*y-1 + x-1*y-2*z + 4*x-1*y-1*z-1 + 3*x-1*y-2 + x-1*y-1*z-2 + 3*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 155 1 Lattice Minkowski decompositions of facet 155
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3706
Image of polytope 3706 PALP id: 3706
grdb id: 595148
Integer points: [ 1 0 0 0 -1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 -1 -1 1 -2 -2 0 -1 1 0 -1 -2 0 -1 0 -1]
[ 0 0 1 -1 1 -1 1 -1 1 -1 1 1 0 0 0 0 -1 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + 2*x-1*y + y-1*z + 3*x-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 6*x-1 + 3*x-1*y-1*z + y-1*z-1 + 3*x-1*z-1 + 6*x-1*y-1 + x-1*y-2*z + 3*x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-2*z-1
31 rank 3, number 3 x + y + z + x-1*y*z + 2*x-1*y + y-1*z + 3*x-1*z + z-1 + x-1*y*z-1 + 3*y-1 + 6*x-1 + 3*x-1*y-1*z + y-1*z-1 + 3*x-1*z-1 + 6*x-1*y-1 + x-1*y-2*z + 3*x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Polytope 3707
Image of polytope 3707 PALP id: 3707
grdb id: 595050
Integer points: [ 1 0 0 1 -1 0 -1 -2 0 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 1 0 1 1 -2 -2 -1 0 -1 0 -2 -1 0 -1 0 -1]
[ 0 0 1 0 0 -1 -1 -1 -1 -1 -1 -1 0 0 -1 -1 -1 0 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*y-1 + x-1*y + z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + 2*y-1*z-1 + 4*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + y-2*z-1 + 5*x-1*y-1*z-1 + 3*x-2*z-1 + 2*x-1*y-2*z-1 + 3*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3708
Image of polytope 3708 PALP id: 3708
grdb id: 595052
Integer points: [ 1 0 0 1 -1 1 -1 -1 1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 0 1 -1 1 -1 -1 -1 0 0 0 -1 -1 0 0 -1 -1 -1]
[ 0 0 1 -1 1 -1 0 1 -2 -2 1 0 -1 0 -1 0 -1 0 -1 -2]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y*z + x*z-1 + x-1*y + 2*x-1*z + x*y-1*z-1 + 3*z-1 + 2*y-1 + 4*x-1 + x-1*y-1*z + x*y-1*z-2 + 4*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + 2*y-1*z-2 + 3*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3709
Image of polytope 3709 PALP id: 3709
grdb id: 595268
Integer points: [ 1 0 0 1 0 -1 1 -2 0 -2 -2 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 0 1 1 -1 0 -2 -2 -1 -1 0 -2 -1 0 -1 0 -1 0]
[ 0 0 1 -1 -1 0 -1 1 -1 1 1 1 1 0 0 0 0 0 -1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x*z-1 + y*z-1 + x-1*y + 2*x-1*z + x*y-1*z-1 + 3*z-1 + 3*y-1 + 4*x-1 + 2*x-1*y-1*z + x-2*z + 3*y-1*z-1 + 5*x-1*y-1 + 2*x-2*y-1*z + y-2*z-1 + 2*x-1*y-2 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3710
Image of polytope 3710 PALP id: 3710
grdb id: 595226
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 0]
[ 0 1 0 0 -2 0 2 2 1 -2 1 -1 0 1 -1 0 1 -1 0 -1]
[ 0 0 1 -1 1 1 -1 -2 -2 1 0 1 0 -1 1 0 -1 0 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + 2*y*z-1 + x-1*y2*z-1 + 2*x-1*y + 2*y-1*z + x-1*z + x-1*y2*z-2 + z-1 + 4*x-1*y*z-1 + 2*y-1 + 5*x-1 + y-2*z + 2*x-1*y-1*z + x-1*y*z-2 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3711
Image of polytope 3711 PALP id: 3711
grdb id: 596349
Integer points: [ 1 0 0 1 1 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 0 -1 1 -1 1 -1 1 1 0 0 0 -1 1 0 0 -1 -1]
[ 0 0 1 -1 0 0 2 -2 0 -2 -1 -1 0 1 1 -1 -1 0 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x*z-1 + 2*y*z-1 + x*y-1 + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + y*z-2 + 3*z-1 + 2*x-1*y*z-1 + 2*y-1 + 4*x-1 + 2*x-1*y-1*z + x-1*y*z-2 + 2*x-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3712
Image of polytope 3712 PALP id: 3712
grdb id: 592451
Integer points: [ 1 0 0 0 -1 -1 -1 -1 0 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
[ 0 1 0 1 1 0 -1 1 -2 -3 -2 -1 0 -1 0 -2 -1 0 -1 0]
[ 0 0 1 -1 0 1 1 -1 -1 -1 0 0 0 0 0 -1 -1 -1 -1 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + y*z-1 + x-1*y + x-1*z + 3*z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + x-1*y-1*z + 3*y-1*z-1 + 4*x-1*z-1 + 5*x-1*y-1 + y-2*z-1 + 6*x-1*y-1*z-1 + 2*x-1*y-2 + 4*x-1*y-2*z-1 + x-1*y-3*z-1
31 rank 3, number 3 x + y + z + y*z-1 + x-1*y + x-1*z + 3*z-1 + x-1*y*z-1 + 3*y-1 + 4*x-1 + x-1*y-1*z + 3*y-1*z-1 + 4*x-1*z-1 + 5*x-1*y-1 + y-2*z-1 + 6*x-1*y-1*z-1 + 2*x-1*y-2 + 4*x-1*y-2*z-1 + x-1*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 9 1 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Polytope 3713
Image of polytope 3713 PALP id: 3713
grdb id: 595151
Integer points: [ 1 0 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 1 0 1 1 -1 -2 1 0 -3 0 -2 -1 0 -1 0 -2 -1 -1 0]
[ 0 0 1 -1 -1 1 1 -2 -2 1 0 1 0 -1 1 0 0 -1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + y*z-1 + 2*y-1*z + 2*z-1 + x-1*y*z-1 + 3*y-1 + 2*x-1 + y-2*z + x-1*y-1*z + x-1*y*z-2 + 4*x-1*z-1 + 5*x-1*y-1 + 2*x-1*y-2*z + x-1*z-2 + 3*x-1*y-1*z-1 + 3*x-1*y-2 + x-1*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3714
Image of polytope 3714 PALP id: 3714
grdb id: 592519
Integer points: [ 1 0 0 0 -1 0 -1 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 -1 1 -2 1 -3 -2 -1 0 -1 0 -2 -1 0 -1 0]
[ 0 0 1 -1 0 -1 -1 0 -1 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + x-1*y + z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + y-1*z-1 + 4*x-1*z-1 + x-2*y*z-1 + 4*x-1*y-1 + 5*x-1*y-1*z-1 + 4*x-2*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 6*x-2*y-1*z-1 + 4*x-2*y-2*z-1 + x-2*y-3*z-1
17 rank 1, V22 x + y + z + x-1*y + z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + y-1*z-1 + 4*x-1*z-1 + x-2*y*z-1 + 3*x-1*y-1 + 5*x-1*y-1*z-1 + 4*x-2*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 6*x-2*y-1*z-1 + 4*x-2*y-2*z-1 + x-2*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 93 1 Lattice Minkowski decompositions of facet 93
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3715
Image of polytope 3715 PALP id: 3715
grdb id: 595061
Integer points: [ 1 0 0 1 -1 -1 1 -1 -1 -1 -1 -1 -1 0 0 -1 -1 0 0 0]
[ 0 1 0 0 0 1 -1 -1 0 -3 -2 -1 0 -1 0 -2 -1 -2 -1 0]
[ 0 0 1 -1 1 0 -1 1 -1 -1 0 0 0 0 0 -1 -1 -1 -1 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*z-1 + x-1*y + x-1*z + x*y-1*z-1 + 2*z-1 + 3*y-1 + 3*x-1 + x-1*y-1*z + 4*y-1*z-1 + x-1*z-1 + 4*x-1*y-1 + 2*y-2*z-1 + 3*x-1*y-1*z-1 + 2*x-1*y-2 + 3*x-1*y-2*z-1 + x-1*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3716
Image of polytope 3716 PALP id: 3716
grdb id: 595051
Integer points: [ 1 0 0 1 -1 0 1 0 -1 -3 -1 -2 -1 -2 0 -1 -2 0 -1 0]
[ 0 1 0 -1 1 0 -1 -1 -1 -1 -1 -1 0 0 -1 -1 -1 0 0 -1]
[ 0 0 1 0 0 -1 1 1 -2 -2 0 -1 0 -1 0 -1 -2 0 -1 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + x*y-1*z + z + x*y-1 + x-1*y + y-1*z + z-1 + 4*y-1 + 3*x-1 + 2*y-1*z-1 + 3*x-1*z-1 + 3*x-1*y-1 + 5*x-1*y-1*z-1 + 2*x-2*z-1 + x-1*y-1*z-2 + 3*x-2*y-1*z-1 + 2*x-2*y-1*z-2 + x-3*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3717
Image of polytope 3717 PALP id: 3717
grdb id: 34551
Integer points: [ 1 0 0 1 0 -1 1 -2 1 -2 0 0 0 -1 -1 1 0 -1 0 -1]
[ 0 1 0 0 1 1 -1 1 -2 0 -2 0 -1 0 -1 -1 0 1 -1 0]
[ 0 0 1 -1 -1 -1 -1 0 0 1 1 -1 0 0 1 0 0 0 1 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
51 rank 2, number 7 x + y + z + x*z-1 + y*z-1 + 2*x*y-1 + 2*x-1*y + 2*y-1*z + 2*x-1*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + x*y-2 + 4*y-1 + 4*x-1 + x-2*y + y-2*z + 2*x-1*y-1*z + x-2*z
18 rank 1, V14 x + y + z + x*z-1 + y*z-1 + 2*x*y-1 + 2*x-1*y + 2*y-1*z + 2*x-1*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + y-2*z + 2*x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 96 1 Lattice Minkowski decompositions of facet 96
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3718
Image of polytope 3718 PALP id: 3718
grdb id: 34356
Integer points: [ 1 0 0 1 1 -1 0 -2 1 -2 0 -1 -1 -1 -1 0 0 0 0 1]
[ 0 1 0 0 -1 1 -1 1 -1 1 -1 1 0 0 0 0 0 -1 -1 -1]
[ 0 0 1 -1 0 1 1 1 -2 0 -2 0 1 0 -1 0 -1 0 -1 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x-1*y*z + x*z-1 + x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + 2*x*y-1*z-1 + 3*z-1 + 3*y-1 + 4*x-1 + x-2*y + x*y-1*z-2 + 3*y-1*z-1 + 2*x-1*z-1 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3719
Image of polytope 3719 PALP id: 3719
grdb id: 34364
Integer points: [ 1 0 0 -1 1 -1 0 -2 1 -2 1 -1 0 -1 0 1 -1 0 0 1]
[ 0 1 0 1 -1 1 0 1 -2 0 -3 -1 -2 0 -1 -2 0 -1 0 -1]
[ 0 0 1 1 0 0 -1 1 -2 1 -2 0 -1 1 0 -1 0 -1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y*z + x*y-1 + x-1*y + 2*x-1*z + x-2*y*z + 2*x*y-1*z-1 + z-1 + 4*y-1 + 4*x-1 + x-2*z + 2*x*y-2*z-1 + 4*y-1*z-1 + 3*x-1*y-1 + x*y-2*z-2 + 3*y-2*z-1 + x*y-3*z-2
62 rank 2, number 9 x + y + z + x-1*y*z + x*y-1 + x-1*y + 2*x-1*z + x-2*y*z + 2*x*y-1*z-1 + z-1 + 4*y-1 + 3*x-1 + x-2*z + 2*x*y-2*z-1 + 3*y-1*z-1 + 3*x-1*y-1 + x*y-2*z-2 + 3*y-2*z-1 + x*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3720
Image of polytope 3720 PALP id: 3720
grdb id: 40408
Integer points: [ 1 0 0 -1 1 -1 1 -1 -1 1 -1 -1 -1 -1 0 0 0 0 0 1]
[ 0 1 0 1 0 1 -1 0 0 -2 -2 -1 0 -1 -1 0 -2 -1 0 -1]
[ 0 0 1 1 -1 0 0 1 -1 -1 -1 0 0 -1 0 0 -1 -1 -1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y*z + x*z-1 + x*y-1 + x-1*y + x-1*z + 2*x*y-1*z-1 + 2*z-1 + 3*y-1 + 3*x-1 + x*y-2*z-1 + 4*y-1*z-1 + x-1*z-1 + 2*x-1*y-1 + 2*y-2*z-1 + 2*x-1*y-1*z-1 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Polytope 3721
Image of polytope 3721 PALP id: 3721
grdb id: 37682
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 -1 1 0 -2 1 0 -2 -1 0 1 -1 0 -1 0 -1 0]
[ 0 0 1 -1 1 0 1 1 -2 -2 0 1 0 -1 0 -1 -1 0 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + z + y*z-1 + x-1*y + y-1*z + x-1*z + 2*z-1 + 2*x-1*y*z-1 + 2*y-1 + 5*x-1 + 2*x-1*y-1*z + x-1*y*z-2 + 5*x-1*z-1 + 5*x-1*y-1 + x-1*y-2*z + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
10 rank 1, V18 x + y + z + y*z-1 + x-1*y + y-1*z + x-1*z + 2*z-1 + 2*x-1*y*z-1 + 2*y-1 + 4*x-1 + 2*x-1*y-1*z + x-1*y*z-2 + 4*x-1*z-1 + 4*x-1*y-1 + x-1*y-2*z + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 164 1 Lattice Minkowski decompositions of facet 164
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 3722
Image of polytope 3722 PALP id: 3722
grdb id: 39241
Integer points: [ 1 0 0 0 0 -1 -1 -1 0 -1 -1 -1 -1 -1 -1 0 0 -1 -1 0]
[ 0 1 0 1 -1 1 0 1 -1 -2 -2 -1 -2 -1 0 -1 0 -1 0 0]
[ 0 0 1 -1 1 0 1 -1 -1 1 -1 1 0 0 0 0 0 -1 -1 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + z + y*z-1 + x-1*y + y-1*z + x-1*z + 2*z-1 + x-1*y*z-1 + 3*y-1 + 4*x-1 + 2*x-1*y-1*z + y-1*z-1 + 3*x-1*z-1 + 5*x-1*y-1 + x-1*y-2*z + 3*x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-2*z-1
10 rank 1, V18 x + y + z + y*z-1 + x-1*y + y-1*z + x-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + 2*x-1*y-1*z + y-1*z-1 + 3*x-1*z-1 + 5*x-1*y-1 + x-1*y-2*z + 3*x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3723
Image of polytope 3723 PALP id: 3723
grdb id: 7560
Integer points: [ 1 0 0 -1 2 1 -1 -2 2 -2 1 -1 0 1 -1 0 -1 0 1 0]
[ 0 1 0 1 -1 -1 1 1 -1 0 -1 -1 0 0 0 0 0 -1 -1 -1]
[ 0 0 1 1 -1 0 0 1 -2 1 -2 0 -1 -1 0 0 1 -1 -1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x-1*y*z + x2*y-1*z-1 + 2*x*z-1 + x*y-1 + x-1*y + 2*x-1*z + x-2*y*z + x2*y-1*z-2 + 3*x*y-1*z-1 + 2*z-1 + 2*y-1 + 3*x-1 + x-2*z + x*y-1*z-2 + 2*y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3724
Image of polytope 3724 PALP id: 3724
grdb id: 1223
Integer points: [ 1 0 0 1 1 0 0 -1 -1 -1 1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 0 -1 1 -1 1 0 -1 -1 1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 -1 0 -1 1 0 1 1 -1 -1 -1 0 -1 0 -1 0 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x*z-1 + y*z-1 + x*y-1 + x-1*y + y-1*z + x-1*z + x*y-1*z-1 + 3*z-1 + x-1*y*z-1 + 3*y-1 + 3*x-1 + x-1*y-1*z + 2*y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 3 6 Lattice Minkowski decompositions of facet 3
Image of facet 30 3 Lattice Minkowski decompositions of facet 30
Polytope 3725
Image of polytope 3725 PALP id: 3725
grdb id: 547424
Integer points: [ 1 0 0 -6 -1 -2 -3 -4 -5 0 -1 -2 -3 -4 0 -1 -2 0 -1 -2 0]
[ 0 1 1 -5 0 -1 -2 -3 -4 1 0 -1 -2 -3 1 0 -1 0 -1 -2 0]
[ 0 0 3 -3 2 1 0 -1 -2 2 1 0 -1 -2 1 0 -1 1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 240 1 none
Image of facet 9 2 irreducible and admissible
Image of facet 241 1 Lattice Minkowski decompositions of facet 241
Polytope 3726
Image of polytope 3726 PALP id: 3726
grdb id: 547423
Integer points: [ 1 0 0 -3 -2 -1 -2 -1 0 -2 -1 0 -1 0 -1 0 0 -1 0 0 0]
[ 0 1 1 -2 -1 0 -1 0 1 -1 0 1 0 1 0 1 1 -1 0 0 0]
[ 0 0 6 -6 -2 2 -3 1 5 -4 0 4 -1 3 -2 2 1 -3 1 0 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 241 1 Lattice Minkowski decompositions of facet 241
Image of facet 53 1 irreducible and admissible
Image of facet 14 2 none
Polytope 3727
Image of polytope 3727 PALP id: 3727
grdb id: 547426
Integer points: [ 1 1 0 -8 -6 -4 -2 -5 -3 -1 -2 0 -5 -3 -1 -2 0 1 -2 0 1]
[ 0 3 0 -12 -9 -6 -3 -7 -4 -1 -2 1 -8 -5 -2 -3 0 2 -4 -1 1]
[ 0 0 1 -3 -2 -1 0 -2 -1 0 -1 0 -2 -1 0 -1 0 0 -1 0 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 9 1 irreducible and admissible
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 121 2 none
Polytope 3728
Image of polytope 3728 PALP id: 3728
grdb id: 544966
Integer points: [ 1 0 0 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 0 -1 -1 -1 0 0]
[ 0 1 1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 1 -1 -1 -1 0 0]
[ 0 0 2 -2 2 1 0 -1 2 1 0 -1 2 1 0 1 1 0 -1 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 2 irreducible and admissible
Image of facet 242 1 none
Image of facet 14 1 none
Polytope 3729
Image of polytope 3729 PALP id: 3729
grdb id: 544884
Integer points: [ 1 0 0 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 1 1 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 0 1 1 -1 -1 0 0]
[ 0 0 3 -3 0 -1 -2 1 0 -1 -2 2 1 0 -1 2 1 0 -1 1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 9 2 irreducible and admissible
Image of facet 243 1 Lattice Minkowski decompositions of facet 243
Image of facet 14 2 none
Polytope 3730
Image of polytope 3730 PALP id: 3730
grdb id: 544886
Integer points: [ 1 0 0 0 -3 -2 -1 -2 -1 0 -1 0 -2 -1 0 -1 0 0 -1 0 0]
[ 0 1 1 -2 -2 -2 -2 -1 -1 -1 0 0 -1 -1 -1 0 0 1 0 0 1]
[ 0 0 3 -3 0 -1 -2 1 0 -1 2 1 0 -1 -2 1 0 2 0 -1 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 y*z3 + 3*y*z2 + 3*y*z + x + y + 2*z + 3*x-1*z2 + 6*x-1*z + 3*z-1 + 3*x-1 + 2*y-1*z-1 + 5*x-1*y-1 + 3*x-2*y-1*z + 3*y-1*z-2 + 6*x-1*y-1*z-1 + 3*x-2*y-1 + y-2*z-3 + 3*x-1*y-2*z-2 + 3*x-2*y-2*z-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 9 2 irreducible and admissible
Image of facet 132 1 Lattice Minkowski decompositions of facet 132
Image of facet 52 2 Lattice Minkowski decompositions of facet 52
Polytope 3731
Image of polytope 3731 PALP id: 3731
grdb id: 544947
Integer points: [ 1 0 0 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 -6 -5 -4 -3 -2 -4 -3 -2 -1 -2 -1 0 -3 -2 -1 -1 0]
[ 0 0 1 -1 4 3 2 1 0 3 2 1 0 2 1 0 2 1 0 1 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 73 1 none
Image of facet 244 1 none
Image of facet 14 1 none
Polytope 3732
Image of polytope 3732 PALP id: 3732
grdb id: 544885
Integer points: [ 1 0 0 -2 -2 -2 -2 -1 -1 -1 0 0 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 1 -3 -3 -3 -3 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0 0 1 1]
[ 0 0 3 -3 -6 -4 -5 -2 -3 -4 -1 -2 0 -1 -2 -3 1 0 -1 2 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 9 1 irreducible and admissible
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Image of facet 14 2 none
Polytope 3733
Image of polytope 3733 PALP id: 3733
grdb id: 544948
Integer points: [ 1 0 0 -1 -6 -5 -4 -3 -2 -4 -3 -2 -1 -2 -1 -3 -2 -1 0 -1 0]
[ 0 1 0 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 -1 0 0]
[ 0 0 1 -2 3 2 1 0 -1 2 1 0 -1 1 0 2 1 0 -1 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Image of facet 14 1 none
Image of facet 191 1 none
Polytope 3734
Image of polytope 3734 PALP id: 3734
grdb id: 544887
Integer points: [ 1 0 1 -2 -5 -3 -1 -4 -2 0 -3 -1 -3 -1 1 -2 0 -1 -1 1 0]
[ 0 1 0 0 -3 -2 -1 -2 -1 0 -1 0 -2 -1 0 -1 0 0 -1 0 0]
[ 0 0 3 -3 -6 -3 0 -5 -2 1 -4 -1 -4 -1 2 -3 0 -2 -2 1 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 9 2 irreducible and admissible
Image of facet 52 2 Lattice Minkowski decompositions of facet 52
Image of facet 124 1 none
Polytope 3735
Image of polytope 3735 PALP id: 3735
grdb id: 544855
Integer points: [ 1 0 0 0 -3 -1 0 -2 -1 0 -2 -1 0 -1 0 -2 -1 0 0 -1 0]
[ 0 1 1 -2 1 -1 -1 0 0 0 1 1 -1 0 0 1 1 1 0 1 1]
[ 0 0 3 -3 0 -2 -1 -1 0 1 1 2 -2 -1 0 0 1 2 -1 0 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
34 rank 2, number 5 y*z3 + 3*y*z2 + 3*y*z + 3*x-1*y*z2 + x + y + 3*z + 6*x-1*y*z + 3*x-1*y + 3*x-2*y*z + 3*z-1 + 6*x-1 + 3*x-2*y + 3*y-1*z-1 + 6*x-1*z-1 + x-3*y + 3*y-1*z-2 + 3*x-2*z-1 + 3*x-1*y-1*z-2 + y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 9 3 irreducible and admissible
Image of facet 52 3 Lattice Minkowski decompositions of facet 52
Polytope 3736
Image of polytope 3736 PALP id: 3736
grdb id: 524395
Integer points: [ 1 0 0 -1 0 -4 -3 -2 -1 -3 -2 -1 0 -2 -1 0 -2 -1 0 -1 0]
[ 0 1 0 1 -3 1 0 -1 -2 1 0 -1 -2 1 0 -1 1 0 -1 1 0]
[ 0 0 1 1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 80 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Image of facet 14 1 none
Polytope 3737
Image of polytope 3737 PALP id: 3737
grdb id: 524380
Integer points: [ 1 1 0 0 -3 -3 -2 -1 -3 -2 -1 0 -2 -1 -1 0 -1 0 -1 0 1]
[ 0 2 0 2 -6 -4 -2 0 -5 -3 -1 1 -4 -2 -1 1 -2 0 -3 -1 1]
[ 0 0 1 1 -2 -2 -1 0 -2 -1 0 1 -1 0 -1 0 -1 0 -1 0 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Image of facet 14 2 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3738
Image of polytope 3738 PALP id: 3738
grdb id: 524396
Integer points: [ 1 0 0 -4 3 2 0 1 2 -2 -1 0 1 -3 -2 -1 1 2 -1 0 1]
[ 0 1 0 4 -6 -5 -2 -3 -4 1 0 -1 -2 3 2 1 -2 -3 1 0 -1]
[ 0 0 1 1 -2 -2 -1 -1 -1 0 0 0 0 1 1 1 -1 -1 0 0 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 14 2 none
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3739
Image of polytope 3739 PALP id: 3739
grdb id: 524375
Integer points: [ 1 1 0 -1 -1 -4 -3 -2 -3 -2 -1 -2 -1 -2 -1 0 -1 0 1 0 1]
[ 0 3 0 0 -3 -6 -4 -2 -5 -3 -1 -4 -2 -3 -1 1 -2 0 2 -1 1]
[ 0 0 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
22 ? x*y3 + 3*x*y2 + 3*x*y + x + 3*y + z + 3*y-1 + x-1*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + 3*x-1*y-2 + 3*x-1*y-2*z-1 + x-1*y-3*z-1 + 3*x-2*y-2*z-1 + 2*x-2*y-3 + 6*x-2*y-3*z-1 + 3*x-2*y-4*z-1 + 3*x-3*y-4*z-1 + 3*x-3*y-5*z-1 + x-4*y-6*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 56 2 Lattice Minkowski decompositions of facet 56
Image of facet 9 1 irreducible and admissible
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 3740
Image of polytope 3740 PALP id: 3740
grdb id: 524106
Integer points: [ 1 0 0 -2 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 2 -3 2 1 0 -1 -2 1 0 -1 -2 1 0 -1 1 0 -1 0]
[ 0 0 1 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 227 1 Lattice Minkowski decompositions of facet 227
Image of facet 9 1 irreducible and admissible
Image of facet 73 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3741
Image of polytope 3741 PALP id: 3741
grdb id: 524265
Integer points: [ 1 0 0 0 -1 -4 -3 -2 -1 -3 -2 -1 0 -2 -1 -2 -1 0 -1 0 0]
[ 0 1 -1 1 -2 1 1 1 1 0 0 0 0 -1 -1 1 1 1 0 0 -1]
[ 0 0 0 2 -2 -2 -1 0 1 -2 -1 0 1 -2 -1 -1 0 1 -1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 y*z2 + 2*y*z + x + y + 2*z + 4*x-1*y*z + 4*x-1*y + y-1 + 7*x-1 + 6*x-2*y + 2*y-1*z-1 + 4*x-1*z-1 + 2*x-2*y*z-1 + 4*x-1*y-1*z-1 + 8*x-2*z-1 + 4*x-3*y*z-1 + x-1*y-2*z-2 + 3*x-2*y-1*z-2 + 3*x-3*z-2 + x-4*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 3 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Polytope 3742
Image of polytope 3742 PALP id: 3742
grdb id: 524219
Integer points: [ 1 0 0 -3 -1 -5 -2 -3 -4 -1 -2 -3 -4 0 -1 -2 0 -1 -2 0 -1]
[ 0 1 1 -2 0 -4 -1 -2 -3 0 -1 -2 -3 1 0 -1 0 -1 -2 0 -1]
[ 0 0 2 -2 2 -2 1 0 -1 1 0 -1 -2 1 0 -1 1 0 -1 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 y*z2 + 2*y*z + x + y + 2*z + x-1*z2 + 6*x-1*z + 5*x-1 + 4*x-1*y-1 + 4*x-2*y-1*z + 2*x-1*y-1*z-1 + 10*x-2*y-1 + 3*x-2*y-1*z-1 + 2*x-2*y-2*z-1 + 6*x-3*y-2 + 7*x-3*y-2*z-1 + x-3*y-2*z-2 + 4*x-4*y-3*z-1 + 2*x-4*y-3*z-2 + x-5*y-4*z-2
60 rank 2, number 18 y*z2 + 2*y*z + x + y + 2*z + x-1*z2 + 4*x-1*z + 3*x-1 + 4*x-1*y-1 + 4*x-2*y-1*z + 2*x-1*y-1*z-1 + 7*x-2*y-1 + 2*x-2*y-1*z-1 + 2*x-2*y-2*z-1 + 6*x-3*y-2 + 6*x-3*y-2*z-1 + x-3*y-2*z-2 + 4*x-4*y-3*z-1 + 2*x-4*y-3*z-2 + x-5*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 3 irreducible and admissible
Image of facet 245 1 Lattice Minkowski decompositions of facet 245
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 3743
Image of polytope 3743 PALP id: 3743
grdb id: 524325
Integer points: [ 1 0 1 -2 -3 -5 -4 -4 -3 -2 -1 -3 -2 -1 0 -1 -2 -1 -1 0 1]
[ 0 1 0 1 -2 -2 -2 -1 -1 -1 -1 0 0 0 0 1 -1 -1 0 0 0]
[ 0 0 2 -2 0 -2 -1 -2 -1 0 1 -2 -1 0 1 -1 -1 0 -1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 14 1 none
Image of facet 246 1 Lattice Minkowski decompositions of facet 246
Polytope 3744
Image of polytope 3744 PALP id: 3744
grdb id: 524280
Integer points: [ 1 0 0 -2 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -2 -6 -5 -4 -3 -4 -3 -2 -1 -2 -1 0 -3 -2 -1 -1 0]
[ 0 0 1 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 213 1 Lattice Minkowski decompositions of facet 213
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Polytope 3745
Image of polytope 3745 PALP id: 3745
grdb id: 524277
Integer points: [ 1 0 0 -2 -1 -5 -4 -3 -2 -4 -3 -2 -1 -3 -2 -1 -2 -1 0 -1 0]
[ 0 1 0 0 -2 -6 -5 -4 -3 -4 -3 -2 -1 -2 -1 0 -3 -2 -1 -1 0]
[ 0 0 1 -1 2 2 2 2 2 1 1 1 1 0 0 0 1 1 1 0 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 14 1 none
Image of facet 247 1 Lattice Minkowski decompositions of facet 247
Polytope 3746
Image of polytope 3746 PALP id: 3746
grdb id: 524263
Integer points: [ 1 0 0 -1 -2 -5 -2 -3 -4 -1 -2 -3 -4 -1 -2 -3 0 -1 -2 0 -1]
[ 0 1 0 -2 0 -6 -3 -4 -5 -1 -2 -3 -4 0 -1 -2 -1 -2 -3 0 -1]
[ 0 0 1 0 -1 -4 -1 -2 -3 0 -1 -2 -3 0 -1 -2 0 -1 -2 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
8 ? x + y + z + 2*y-1 + 2*x-1 + 4*x-1*y-1 + 3*x-1*y-1*z-1 + x-2*z-1 + x-1*y-2 + 4*x-1*y-2*z-1 + 4*x-2*y-1*z-1 + 8*x-2*y-2*z-1 + 4*x-2*y-3*z-1 + 2*x-2*y-3*z-2 + 3*x-3*y-2*z-2 + 8*x-3*y-3*z-2 + 6*x-3*y-4*z-2 + 3*x-4*y-4*z-3 + 4*x-4*y-5*z-3 + x-5*y-6*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 213 1 Lattice Minkowski decompositions of facet 213
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 3747
Image of polytope 3747 PALP id: 3747
grdb id: 524279
Integer points: [ 1 0 0 -1 -3 -7 -6 -5 -4 -5 -4 -3 -2 -3 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 0 1 -1 0 -4 -3 -2 -1 -3 -2 -1 0 -2 -1 0 -2 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 248 1 Lattice Minkowski decompositions of facet 248
Image of facet 14 1 none
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 3748
Image of polytope 3748 PALP id: 3748
grdb id: 524266
Integer points: [ 1 0 0 -1 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -2 -6 -3 -4 -5 -1 -2 -3 -4 0 -1 -2 -1 -2 -3 0 -1]
[ 0 0 1 -1 0 4 1 2 3 0 1 2 3 0 1 2 0 1 2 0 1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Image of facet 14 1 none
Polytope 3749
Image of polytope 3749 PALP id: 3749
grdb id: 523886
Integer points: [ 1 0 0 1 -3 -6 -4 -2 -5 -3 -1 -4 -2 0 -1 -3 -1 -2 0 -1 1]
[ 0 1 0 -2 0 3 2 1 2 1 0 1 0 -1 -1 2 1 1 0 0 -1]
[ 0 0 1 0 -2 -2 -1 0 -2 -1 0 -2 -1 0 -1 -1 0 -1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 194 1 Lattice Minkowski decompositions of facet 194
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 14 1 none
Polytope 3750
Image of polytope 3750 PALP id: 3750
grdb id: 524097
Integer points: [ 1 0 0 0 -1 -10 -8 -6 -4 -2 -7 -5 -3 -1 -4 -2 -5 -3 -1 -2 0]
[ 0 1 -1 0 2 5 4 3 2 1 4 3 2 1 3 2 2 1 0 1 0]
[ 0 0 0 1 -1 -4 -3 -2 -1 0 -3 -2 -1 0 -2 -1 -2 -1 0 -1 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 218 1 none
Image of facet 73 1 none
Polytope 3751
Image of polytope 3751 PALP id: 3751
grdb id: 524281
Integer points: [ 1 0 0 -2 -3 -11 -5 -7 -9 -2 -4 -6 -8 -1 -3 -5 -1 -3 -5 0 -2]
[ 0 1 0 0 -2 -6 -3 -4 -5 -1 -2 -3 -4 0 -1 -2 -1 -2 -3 0 -1]
[ 0 0 1 -1 0 -4 -1 -2 -3 0 -1 -2 -3 0 -1 -2 0 -1 -2 0 -1]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 14 1 none
Image of facet 249 1 none
Polytope 3752
Image of polytope 3752 PALP id: 3752
grdb id: 524111
Integer points: [ 1 0 0 -1 -5 -11 -9 -7 -5 -3 -8 -6 -4 -2 -3 -1 -5 -3 -1 -2 0]
[ 0 1 0 -1 -2 -6 -5 -4 -3 -2 -4 -3 -2 -1 -1 0 -3 -2 -1 -1 0]
[ 0 0 1 1 -2 -4 -3 -2 -1 0 -3 -2 -1 0 -1 0 -2 -1 0 -1 0]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 250 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 73 1 none
Polytope 3753
Image of polytope 3753 PALP id: 3753
grdb id: 523807
Integer points: [ 1 0 0 0 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 0 -4 -1 -2 -3 0 -1 -2 -3 0 -1 -2 0 -1 -2 0 -1]
[ 0 0 1 1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 9 1 irreducible and admissible
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Image of facet 14 1 none
Polytope 3754
Image of polytope 3754 PALP id: 3754
grdb id: 447227
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 2 2 -3 0 1 -2 -1 0 1 2 -2 -1 0 1 -1 0 1]
[ 0 0 1 2 -1 -3 2 1 0 2 1 0 -1 -2 1 0 -1 -2 1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 8 2 none
Image of facet 43 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 216 1 Lattice Minkowski decompositions of facet 216
Polytope 3755
Image of polytope 3755 PALP id: 3755
grdb id: 446982
Integer points: [ 1 0 1 -1 -2 1 1 0 1 0 -1 0 -1 1 0 1 0 1 0 -1 1]
[ 0 1 0 0 1 -2 -2 -1 -2 -1 0 -1 0 -1 0 -1 0 -1 0 1 0]
[ 0 0 2 -2 -2 2 4 0 3 1 -1 2 0 1 -1 2 0 3 1 -1 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
11 rank 2, number 6 x*z2 + 2*x*y-1*z3 + x*y-2*z4 + 2*x*z + 4*x*y-1*z2 + 2*x*y-2*z3 + x + y + 2*x*y-1*z + 4*z + x*y-2*z2 + 3*y-1*z2 + 4*y-1*z + 2*z-1 + 2*x-1*y*z-1 + 2*y-1 + 3*x-1 + 2*x-1*z-1 + x-1*z-2 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3756
Image of polytope 3756 PALP id: 3756
grdb id: 446949
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 1 0 -2 -4 -3 -2 -1 -3 -2 -1 0 -1 0 -2 -1 0 -1 0]
[ 0 0 1 -1 -2 2 2 1 0 -1 2 1 0 -1 1 0 1 0 -1 1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
23 ? x + y + z + 2*y-1*z + 2*z-1 + x-1*y*z-1 + 4*y-1 + 3*x-1 + 2*y-2*z + 3*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 6*x-1*y-1 + 6*x-1*y-2*z + 2*x-1*y-3*z2 + x-1*z-2 + 4*x-1*y-1*z-1 + 6*x-1*y-2 + 4*x-1*y-3*z + x-1*y-4*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 230 1 Lattice Minkowski decompositions of facet 230
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3757
Image of polytope 3757 PALP id: 3757
grdb id: 447229
Integer points: [ 1 0 0 0 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 -1 -1 -1 0 0]
[ 0 1 0 -2 -2 1 -4 -3 -2 -1 0 -3 -2 -1 0 -1 -1 0 1 -1 0]
[ 0 0 1 -1 -2 2 -3 -2 -1 0 1 -2 -1 0 1 0 -1 0 1 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 236 1 none
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Polytope 3758
Image of polytope 3758 PALP id: 3758
grdb id: 446950
Integer points: [ 1 0 0 1 -2 0 -4 -3 -2 -1 -3 -2 -1 0 -1 -2 -1 0 -1 0 1]
[ 0 1 -1 0 -1 1 1 1 1 1 0 0 0 0 -1 1 1 1 0 0 0]
[ 0 0 0 2 -2 2 -2 -1 0 1 -2 -1 0 1 -1 -1 0 1 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x*z2 + y*z2 + 2*x*z + 2*y*z + x + y + 4*z + 4*x-1*y*z + 4*x-1*y + y-1 + 7*x-1 + 6*x-2*y + 2*x-1*z-1 + 2*x-2*y*z-1 + 2*x-1*y-1*z-1 + 6*x-2*z-1 + 4*x-3*y*z-1 + x-2*y-1*z-2 + 2*x-3*z-2 + x-4*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 2 irreducible and admissible
Image of facet 180 1 Lattice Minkowski decompositions of facet 180
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3759
Image of polytope 3759 PALP id: 3759
grdb id: 446933
Integer points: [ 1 0 0 2 -1 -2 -4 0 -2 1 -1 -3 0 -2 1 -1 -3 0 -2 -1 -1]
[ 0 1 0 -1 -1 2 2 0 1 -1 0 1 -1 0 0 1 2 0 1 0 1]
[ 0 0 1 -2 1 1 1 -1 0 -1 0 1 0 1 -1 0 1 0 1 1 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
11 rank 2, number 6 x + y + z + 2*x-1*y*z + x-2*y2*z + 2*x*z-1 + 4*x-1*y + 2*x-1*z + 4*x-2*y*z + 2*x-3*y2*z + x2*y-1*z-2 + 3*x*y-1*z-1 + 3*z-1 + 3*y-1 + 6*x-1 + 3*x-2*y + x-1*y-1*z + 3*x-2*z + 3*x-3*y*z + x-4*y2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 78 1 Lattice Minkowski decompositions of facet 78
Polytope 3760
Image of polytope 3760 PALP id: 3760
grdb id: 447135
Integer points: [ 1 0 0 -1 1 -1 -5 -4 -3 -2 -3 -2 -1 -1 0 -3 -2 -1 -1 0 1]
[ 0 1 0 1 -2 1 1 1 1 1 0 0 0 -1 -1 1 1 1 0 0 -1]
[ 0 0 1 -1 0 1 -3 -2 -1 0 -2 -1 0 -1 0 -2 -1 0 -1 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 148 1 none
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 80 1 none
Polytope 3761
Image of polytope 3761 PALP id: 3761
grdb id: 446913
Integer points: [ 1 0 0 -3 3 -3 3 -1 1 -2 0 2 -1 1 -1 1 -2 0 2 -1 1]
[ 0 1 0 1 -2 0 -3 -1 -2 0 -1 -2 0 -1 0 -1 1 0 -1 1 0]
[ 0 0 1 -3 3 -2 4 0 2 -1 1 3 0 2 -1 1 -2 0 2 -1 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x3*y-2*z3 + x3*y-3*z4 + 3*x2*y-1*z2 + 3*x2*y-2*z3 + 3*x*z + 3*x*y-1*z2 + x + y + 2*x*y-1*z + z + 3*x*y-2*z2 + 6*y-1*z + 3*x-1*y*z-1 + 3*x-1 + 2*x-1*z-1 + 3*x-1*y-1 + 3*x-2*y*z-2 + 3*x-2*z-1 + x-3*y*z-3 + x-3*z-2
34 rank 2, number 5 x3*y-2*z3 + x3*y-3*z4 + 3*x2*y-1*z2 + 3*x2*y-2*z3 + 3*x*z + 3*x*y-1*z2 + x + y + 4*x*y-1*z + z + 3*x*y-2*z2 + 6*y-1*z + 3*x-1*y*z-1 + 3*x-1 + 3*x-1*z-1 + 3*x-1*y-1 + 3*x-2*y*z-2 + 3*x-2*z-1 + x-3*y*z-3 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 9 2 irreducible and admissible
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 70 1 Lattice Minkowski decompositions of facet 70
Image of facet 60 2 Lattice Minkowski decompositions of facet 60
Polytope 3762
Image of polytope 3762 PALP id: 3762
grdb id: 447230
Integer points: [ 1 0 0 0 -1 -2 -6 -5 -4 -3 -2 -3 -2 -1 -4 -3 -2 -1 -1 0 -1]
[ 0 1 -1 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1]
[ 0 0 0 1 1 -2 -4 -3 -2 -1 0 -2 -1 0 -3 -2 -1 0 -1 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 236 1 none
Polytope 3763
Image of polytope 3763 PALP id: 3763
grdb id: 446171
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 1 0 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
[ 0 0 1 -1 -2 2 -2 -1 0 1 -2 -1 0 1 -1 0 -1 0 1 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + 2*y-1*z + 2*z-1 + x-1*y*z-1 + 4*y-1 + 3*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + 2*y-1*z-1 + 4*x-1*z-1 + 8*x-1*y-1 + 4*x-1*y-2*z + x-1*z-2 + 7*x-1*y-1*z-1 + 6*x-1*y-2 + 2*x-1*y-1*z-2 + 4*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Polytope 3764
Image of polytope 3764 PALP id: 3764
grdb id: 445117
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 1 1 0 -2 0 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 0 0 0 1]
[ 0 0 2 -2 -2 2 0 -1 -2 -1 0 1 -1 0 1 -1 0 -1 0 1 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 y*z2 + 2*y*z + x + y + 2*z + x-1*z2 + 4*x-1*z + 2*z-1 + 2*y-1 + 6*x-1 + 2*x-1*y-1*z + 2*y-1*z-1 + 4*x-1*z-1 + 6*x-1*y-1 + x-1*z-2 + 6*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-1*z-2 + 2*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3765
Image of polytope 3765 PALP id: 3765
grdb id: 445154
Integer points: [ 1 0 0 0 0 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0 0]
[ 0 1 0 1 -2 1 -2 0 -1 1 0 -1 -2 0 -1 1 0 -1 1 0 -1]
[ 0 0 1 -2 1 0 3 1 2 -1 0 1 2 -1 0 0 1 2 -1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*y*z-1 + 2*x-1*y + 2*y-1*z + 4*x-1*z + 2*x-1*y-1*z2 + y*z-2 + 3*z-1 + 2*x-1*y*z-1 + 3*y-1 + 6*x-1 + x-2*y + y-2*z + 6*x-1*y-1*z + 3*x-2*z + 2*x-1*y-2*z2 + 3*x-2*y-1*z2 + x-2*y-2*z3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Polytope 3766
Image of polytope 3766 PALP id: 3766
grdb id: 444809
Integer points: [ 1 0 0 -2 0 -3 -3 -1 -2 -1 0 -3 -2 -1 0 -2 -1 -1 0 -1 0]
[ 0 1 0 2 -3 2 0 1 1 0 -1 1 0 -1 -2 -1 -2 1 0 0 -1]
[ 0 0 1 -1 1 -2 -2 0 -1 0 1 -2 -1 0 1 -1 0 -1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 231 1 Lattice Minkowski decompositions of facet 231
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Polytope 3767
Image of polytope 3767 PALP id: 3767
grdb id: 446903
Integer points: [ 1 0 0 -1 -1 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 0 -1 -1 0 0 0]
[ 0 1 1 0 0 -2 -2 -2 -1 -1 -1 -1 0 0 0 1 -1 -1 0 0 0]
[ 0 0 2 -2 2 -2 0 -1 1 0 -1 -2 1 0 -1 1 0 -1 1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? y*z2 + 2*y*z + x + y + 2*z + x-1*z2 + 6*x-1*z + 2*z-1 + 8*x-1 + 4*x-1*z-1 + 2*x-1*y-1 + 2*x-2*y-1*z + x-1*z-2 + 2*x-1*y-1*z-1 + 7*x-2*y-1 + 6*x-2*y-1*z-1 + 2*x-2*y-1*z-2 + x-3*y-2 + 2*x-3*y-2*z-1 + x-3*y-2*z-2
31 rank 3, number 3 y*z2 + 2*y*z + x + y + 2*z + x-1*z2 + 4*x-1*z + 2*z-1 + 6*x-1 + 4*x-1*z-1 + 2*x-1*y-1 + 2*x-2*y-1*z + x-1*z-2 + 2*x-1*y-1*z-1 + 6*x-2*y-1 + 6*x-2*y-1*z-1 + 2*x-2*y-1*z-2 + x-3*y-2 + 2*x-3*y-2*z-1 + x-3*y-2*z-2
10 rank 1, V18 y*z2 + 2*y*z + x + y + 2*z + x-1*z2 + 4*x-1*z + 2*z-1 + 5*x-1 + 3*x-1*z-1 + 2*x-1*y-1 + 2*x-2*y-1*z + x-1*z-2 + 2*x-1*y-1*z-1 + 5*x-2*y-1 + 5*x-2*y-1*z-1 + 2*x-2*y-1*z-2 + x-3*y-2 + 2*x-3*y-2*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 3 Lattice Minkowski decompositions of facet 16
Image of facet 1 3 irreducible and admissible
Image of facet 251 1 Lattice Minkowski decompositions of facet 251
Polytope 3768
Image of polytope 3768 PALP id: 3768
grdb id: 445062
Integer points: [ 1 0 0 0 -1 -2 -2 0 -1 -1 -1 -1 -2 -2 -2 0 0 0 -1 -1 -1]
[ 0 1 -1 1 -2 -3 1 0 1 0 -1 -2 0 -1 -2 1 0 -1 1 0 -1]
[ 0 0 0 2 -2 -2 2 1 2 1 0 -1 1 0 -1 1 0 -1 1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 y*z2 + 2*y*z + 2*x-1*y*z2 + x + y + 2*z + 2*x-1*y*z + x-2*y*z2 + 6*x-1*z + y-1 + 4*x-1 + 4*x-2*z + 2*y-1*z-1 + 6*x-1*y-1 + 3*x-1*y-1*z-1 + 6*x-2*y-1 + 2*x-1*y-2*z-1 + x-1*y-2*z-2 + 4*x-2*y-2*z-1 + x-2*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 3 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3769
Image of polytope 3769 PALP id: 3769
grdb id: 444829
Integer points: [ 1 0 0 -2 1 -2 1 1 0 0 0 -1 -1 -1 -2 1 1 0 0 -1 -1]
[ 0 1 0 1 -2 -1 -4 -3 -3 -2 -1 -2 -1 0 0 -2 -1 -1 0 0 1]
[ 0 0 1 0 0 -2 -2 -1 -2 -1 0 -2 -1 0 -1 -1 0 -1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? x + y + z + 2*x*y-1 + 2*x-1*y + x*y-2 + 5*y-1 + 3*x-1 + x-2*y + 2*x*y-2*z-1 + 4*y-1*z-1 + 2*x-1*z-1 + 2*x*y-3*z-1 + 7*y-2*z-1 + 6*x-1*y-1*z-1 + 2*x-2*z-1 + x*y-4*z-2 + 3*y-3*z-2 + 3*x-1*y-2*z-2 + x-2*y-1*z-2
10 rank 1, V18 x + y + z + 2*x*y-1 + 2*x-1*y + x*y-2 + 3*y-1 + 2*x-1 + x-2*y + 2*x*y-2*z-1 + 4*y-1*z-1 + 2*x-1*z-1 + 2*x*y-3*z-1 + 5*y-2*z-1 + 5*x-1*y-1*z-1 + 2*x-2*z-1 + x*y-4*z-2 + 3*y-3*z-2 + 3*x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 199 1 Lattice Minkowski decompositions of facet 199
Polytope 3770
Image of polytope 3770 PALP id: 3770
grdb id: 446324
Integer points: [ 1 0 0 -1 -1 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -2 0 -4 -1 -2 -3 0 -1 -2 -3 0 -1 0 -1 -2 0 -1]
[ 0 0 1 -1 0 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y*z-1 + 2*y-1 + 3*x-1 + 3*x-1*z-1 + 4*x-1*y-1 + 4*x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 8*x-2*y-1*z-1 + x-3*z-2 + 7*x-2*y-2*z-1 + 4*x-3*y-1*z-2 + 2*x-2*y-3*z-1 + 6*x-3*y-2*z-2 + 4*x-3*y-3*z-2 + x-3*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Polytope 3771
Image of polytope 3771 PALP id: 3771
grdb id: 446183
Integer points: [ 1 0 0 0 0 -1 -4 -3 -2 -1 -3 -2 -1 0 -2 -1 -2 -1 0 -1 0]
[ 0 1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 0 1 0 -2 1 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + 2*z-1 + y-1 + 3*x-1 + x-1*y-1*z + 2*y-1*z-1 + 4*x-1*z-1 + 4*x-1*y-1 + y-1*z-2 + 7*x-1*y-1*z-1 + 2*x-2*z-1 + 3*x-2*y-1 + 4*x-1*y-1*z-2 + 8*x-2*y-1*z-1 + 6*x-2*y-1*z-2 + 3*x-3*y-1*z-1 + 4*x-3*y-1*z-2 + x-4*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Polytope 3772
Image of polytope 3772 PALP id: 3772
grdb id: 446195
Integer points: [ 1 0 0 0 1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
[ 0 1 0 0 -1 0 -4 -3 -2 -1 -3 -2 -1 0 -2 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 0 1 -3 -2 -1 0 -2 -1 0 1 -1 0 -2 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 80 1 none
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Polytope 3773
Image of polytope 3773 PALP id: 3773
grdb id: 446262
Integer points: [ 1 0 0 1 1 -3 1 1 0 -1 1 0 -1 -2 0 -1 -2 1 0 0 -1]
[ 0 1 0 -1 -2 0 -4 -2 -1 0 -3 -2 -1 0 -3 -2 -1 -1 0 -1 0]
[ 0 0 1 0 -2 1 -3 -1 0 1 -2 -1 0 1 -2 -1 0 -1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 64 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Polytope 3774
Image of polytope 3774 PALP id: 3774
grdb id: 446837
Integer points: [ 1 0 0 0 0 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 2 -1 4 0 1 2 3 0 1 2 3 -1 0 1 2 0 1]
[ 0 0 0 1 1 -2 3 -1 0 1 2 -1 0 1 2 -1 0 1 2 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x-2*y4*z3 + 2*x-1*y3*z2 + y2*z + 2*x-1*y2*z2 + 5*x-2*y3*z2 + 2*y*z + 6*x-1*y2*z + x + y + z + 6*x-1*y*z + 10*x-2*y2*z + 6*x-1*y + y-1 + 6*x-1 + 10*x-2*y + 2*x-1*z-1 + 2*x-1*y-1*z-1 + 5*x-2*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 129 2 Lattice Minkowski decompositions of facet 129
Polytope 3775
Image of polytope 3775 PALP id: 3775
grdb id: 445586
Integer points: [ 1 0 0 -1 -1 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 0]
[ 0 1 0 0 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 1 -1 2 -2 3 2 1 0 -1 2 1 0 -1 1 0 1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 218 1 none
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Polytope 3776
Image of polytope 3776 PALP id: 3776
grdb id: 444999
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0]
[ 0 1 1 -2 1 1 -2 -1 0 -1 0 1 0 1 -1 0 -1 0 1 0 1]
[ 0 0 3 -3 0 3 -3 -1 1 -2 0 2 -1 1 -1 1 -2 0 2 -1 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
34 rank 2, number 5 y*z3 + 3*y*z2 + x-1*y*z3 + 3*y*z + 3*x-1*y*z2 + x + y + 3*z + 3*x-1*y*z + x-1*y + 3*x-1*z + 3*z-1 + 6*x-1 + 3*y-1*z-1 + 3*x-1*z-1 + 3*y-1*z-2 + 3*x-1*y-1*z-1 + 3*x-1*y-1*z-2 + y-2*z-3 + x-1*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 9 3 irreducible and admissible
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 60 3 Lattice Minkowski decompositions of facet 60
Polytope 3777
Image of polytope 3777 PALP id: 3777
grdb id: 446276
Integer points: [ 1 0 0 -1 -2 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 2 -3 -4 -3 -2 -1 0 1 -2 -1 0 1 -2 -1 0 -1 0]
[ 0 0 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 -1 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Image of facet 8 1 none
Image of facet 13 1 irreducible and admissible
Image of facet 173 1 Lattice Minkowski decompositions of facet 173
Polytope 3778
Image of polytope 3778 PALP id: 3778
grdb id: 446380
Integer points: [ 1 0 0 -1 -1 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -2 0 -4 -3 -2 -1 -3 -2 -1 0 -1 0 -2 -1 0 -1 0]
[ 0 0 1 -1 2 -2 2 1 0 -1 2 1 0 -1 1 0 1 0 -1 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + 2*y-1*z + x-1*y*z-1 + 5*x-1 + 5*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-2*z + 3*x-2*z-1 + 8*x-2*y-1 + 7*x-2*y-2*z + 2*x-2*y-3*z2 + x-3*z-2 + 4*x-3*y-1*z-1 + 6*x-3*y-2 + 4*x-3*y-3*z + x-3*y-4*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 252 1 Lattice Minkowski decompositions of facet 252
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 3779
Image of polytope 3779 PALP id: 3779
grdb id: 444917
Integer points: [ 1 0 0 0 -2 -2 -5 -1 -3 -2 -1 -4 -3 -2 -1 -4 -3 -1 0 -2 -1]
[ 0 1 0 1 -2 1 -2 1 0 0 0 -1 -1 -1 -1 -2 -2 0 0 -1 -1]
[ 0 0 1 1 -1 -1 -4 0 -2 -1 0 -3 -2 -1 0 -3 -2 -1 0 -2 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 14 1 none
Image of facet 231 1 Lattice Minkowski decompositions of facet 231
Polytope 3780
Image of polytope 3780 PALP id: 3780
grdb id: 445061
Integer points: [ 1 0 0 0 -1 -3 -5 -2 -1 -4 -3 -2 -1 -4 -3 -2 -1 0 -2 -1 0]
[ 0 1 0 -1 -2 0 -2 0 0 -1 -1 -1 -1 -2 -2 -2 0 0 -1 -1 -1]
[ 0 0 1 1 0 -2 -4 -1 0 -3 -2 -1 0 -3 -2 -1 -1 0 -2 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + y-1*z + 2*y-1 + 3*x-1 + 2*x-1*z-1 + 5*x-1*y-1 + 4*x-1*y-1*z-1 + 3*x-2*z-1 + x-1*y-2 + 9*x-2*y-1*z-1 + 2*x-2*y-1*z-2 + x-3*z-2 + 4*x-2*y-2*z-1 + 7*x-3*y-1*z-2 + 6*x-3*y-2*z-2 + 2*x-4*y-1*z-3 + 4*x-4*y-2*z-3 + x-5*y-2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 198 1 Lattice Minkowski decompositions of facet 198
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 9 1 irreducible and admissible
Polytope 3781
Image of polytope 3781 PALP id: 3781
grdb id: 446309
Integer points: [ 1 0 0 0 -1 -2 -4 -1 -2 -3 0 -1 -2 -3 0 -1 -2 -1 0 -1 0]
[ 0 1 0 -3 -2 3 4 1 2 3 -1 0 1 2 -2 -1 0 2 0 1 -1]
[ 0 0 1 1 0 -2 -3 0 -1 -2 1 0 -1 -2 1 0 -1 -1 0 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + 2*x-1*y2*z-1 + 4*x-1*y + 3*y-1*z + x-2*y3*z-2 + 3*x-1*y*z-1 + 6*x-2*y2*z-1 + 2*y-1 + 9*x-1 + 3*y-2*z + 4*x-3*y3*z-2 + 9*x-2*y*z-1 + 6*x-1*y-1 + y-3*z + x-4*y4*z-3 + 3*x-3*y2*z-2 + 3*x-2*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Polytope 3782
Image of polytope 3782 PALP id: 3782
grdb id: 445152
Integer points: [ 1 0 0 0 0 -2 -2 0 0 -1 -1 -1 -1 -2 -2 0 0 0 -1 -1 -1]
[ 0 1 0 1 -2 -1 -4 0 -1 0 -1 -2 -3 -2 -3 1 0 -1 0 -1 -2]
[ 0 0 1 -2 1 0 3 -1 0 -1 0 1 2 1 2 -1 0 1 0 1 2]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + 2*y*z-1 + 2*y-1*z + y*z-2 + 3*z-1 + 3*y-1 + 2*x-1 + y-2*z + 4*x-1*y-1*z + 2*x-1*y-2*z2 + 2*x-1*z-1 + 6*x-1*y-1 + 6*x-1*y-2*z + 2*x-1*y-3*z2 + x-2*y-1 + 3*x-2*y-2*z + 3*x-2*y-3*z2 + x-2*y-4*z3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Polytope 3783
Image of polytope 3783 PALP id: 3783
grdb id: 446844
Integer points: [ 1 0 0 0 -1 -2 -6 -5 -4 -3 -2 -4 -3 -2 -1 -1 -3 -2 -1 -1 0]
[ 0 1 -1 0 0 -3 -5 -4 -3 -2 -1 -4 -3 -2 -1 -2 -2 -1 0 -1 0]
[ 0 0 0 1 1 -2 -4 -3 -2 -1 0 -3 -2 -1 0 -1 -2 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 73 1 none
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 201 1 Lattice Minkowski decompositions of facet 201
Polytope 3784
Image of polytope 3784 PALP id: 3784
grdb id: 446184
Integer points: [ 1 0 0 0 0 -2 -6 -5 -4 -3 -4 -3 -2 -1 -2 -1 -3 -2 -1 -1 0]
[ 0 1 -1 0 -1 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 0 0 1 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Image of facet 14 1 none
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Polytope 3785
Image of polytope 3785 PALP id: 3785
grdb id: 446193
Integer points: [ 1 0 0 0 0 -2 -6 -5 -4 -3 -4 -3 -2 -1 -2 -1 -3 -2 -1 -1 0]
[ 0 1 -1 0 1 1 -3 -2 -1 0 -2 -1 0 1 -1 0 -2 -1 0 -1 0]
[ 0 0 0 1 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 14 1 none
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Polytope 3786
Image of polytope 3786 PALP id: 3786
grdb id: 446194
Integer points: [ 1 0 0 0 0 -2 -6 -3 -4 -5 -1 -2 -3 -4 -1 -2 -1 -2 -3 0 -1]
[ 0 1 -1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]
[ 0 0 0 1 -1 0 -4 -1 -2 -3 0 -1 -2 -3 -1 -2 0 -1 -2 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + y*z-1 + 2*x-1*y + 4*x-1*y*z-1 + y-1 + 3*x-1 + x-2*y + 3*x-1*z-1 + 7*x-2*y*z-1 + 3*x-2*y*z-2 + 4*x-2*z-1 + 4*x-3*y*z-1 + 8*x-3*y*z-2 + 2*x-3*z-2 + 6*x-4*y*z-2 + 3*x-4*y*z-3 + 4*x-5*y*z-3 + x-6*y*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Polytope 3787
Image of polytope 3787 PALP id: 3787
grdb id: 446396
Integer points: [ 1 0 0 -1 -3 -3 -7 -6 -5 -4 -5 -4 -3 -2 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 -1 0 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
[ 0 0 1 1 -2 0 -4 -3 -2 -1 -3 -2 -1 0 -1 0 -2 -1 0 -1 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
16 ? x + y + z + 3*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + 4*x-2*z-1 + 5*x-2*y-1 + 4*x-2*y-1*z-1 + x-3*z-2 + 9*x-3*y-1*z-1 + x-3*y-2 + 2*x-3*y-1*z-2 + 7*x-4*y-1*z-2 + 4*x-4*y-2*z-1 + 2*x-5*y-1*z-3 + 6*x-5*y-2*z-2 + 4*x-6*y-2*z-3 + x-7*y-2*z-4
122 ? x + y + z + 4*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + 5*x-2*z-1 + 5*x-2*y-1 + 4*x-2*y-1*z-1 + x-3*z-2 + 10*x-3*y-1*z-1 + x-3*y-2 + 2*x-3*y-1*z-2 + 8*x-4*y-1*z-2 + 4*x-4*y-2*z-1 + 2*x-5*y-1*z-3 + 6*x-5*y-2*z-2 + 4*x-6*y-2*z-3 + x-7*y-2*z-4
50 ? x + y + z + 3*x-1 + x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + 3*x-2*z-1 + 4*x-2*y-1 + 4*x-2*y-1*z-1 + x-3*z-2 + 7*x-3*y-1*z-1 + x-3*y-2 + 2*x-3*y-1*z-2 + 6*x-4*y-1*z-2 + 4*x-4*y-2*z-1 + 2*x-5*y-1*z-3 + 6*x-5*y-2*z-2 + 4*x-6*y-2*z-3 + x-7*y-2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 253 1 Lattice Minkowski decompositions of facet 253
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 3788
Image of polytope 3788 PALP id: 3788
grdb id: 443493
Integer points: [ 1 0 0 0 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 1 -2 1 -2 -1 0 -1 0 1 -2 -1 0 1 -1 0 1 -1 0]
[ 0 0 1 -2 1 -2 1 0 -1 1 0 -1 1 0 -1 -2 1 0 -1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 x + y + z + 2*y*z-1 + 2*y-1*z + y*z-2 + 3*z-1 + 2*x-1*y*z-1 + 3*y-1 + 4*x-1 + y-2*z + 2*x-1*y-1*z + 2*x-1*y*z-2 + 6*x-1*z-1 + 6*x-1*y-1 + 2*x-1*y-2*z + x-2*y*z-2 + 3*x-2*z-1 + 3*x-2*y-1 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Polytope 3789
Image of polytope 3789 PALP id: 3789
grdb id: 294043
Integer points: [ 1 1 0 0 0 0 -2 -2 -1 -1 0 -2 -1 0 -1 0 0 1 -1 -1 0]
[ 0 2 0 2 -2 0 -2 0 -2 -1 -1 -1 -1 -1 0 0 1 1 0 1 1]
[ 0 0 1 1 -1 -1 1 1 0 1 0 1 0 -1 1 0 1 0 0 1 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
11 rank 2, number 6 x*y2 + y2*z + 2*x*y + 2*y*z + x + 2*y + z + 2*x-1*y*z + 4*x-1*z + z-1 + 2*y-1 + 2*x-1 + 2*x-1*y-1*z + x-2*z + 2*y-1*z-1 + 4*x-1*y-1 + 2*x-2*y-1*z + y-2*z-1 + 2*x-1*y-2 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 36 2 Lattice Minkowski decompositions of facet 36
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3790
Image of polytope 3790 PALP id: 3790
grdb id: 294031
Integer points: [ 1 0 1 -1 0 0 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0 0 1]
[ 0 1 0 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0]
[ 0 0 2 -1 2 -2 1 -3 0 -1 -2 1 0 -1 0 -1 -2 1 0 -1 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x*z2 + 2*x*z + x + y + 2*z + y-1*z2 + 4*y-1*z + 3*z-1 + x-1*y*z-1 + 6*y-1 + 2*x-1 + x-1*y-1*z + 4*y-1*z-1 + 4*x-1*z-1 + 4*x-1*y-1 + y-1*z-2 + 2*x-1*z-2 + 6*x-1*y-1*z-1 + 4*x-1*y-1*z-2 + x-1*y-1*z-3
7 rank 1, V12 x*z2 + 2*x*z + x + y + 3*z + y-1*z2 + 4*y-1*z + 2*z-1 + x-1*y*z-1 + 6*y-1 + 2*x-1 + x-1*y-1*z + 4*y-1*z-1 + 4*x-1*z-1 + 4*x-1*y-1 + y-1*z-2 + 2*x-1*z-2 + 6*x-1*y-1*z-1 + 4*x-1*y-1*z-2 + x-1*y-1*z-3
11 rank 2, number 6 x*z2 + 2*x*z + x + y + 2*z + y-1*z2 + 4*y-1*z + 2*z-1 + x-1*y*z-1 + 6*y-1 + 2*x-1 + x-1*y-1*z + 4*y-1*z-1 + 4*x-1*z-1 + 4*x-1*y-1 + y-1*z-2 + 2*x-1*z-2 + 6*x-1*y-1*z-1 + 4*x-1*y-1*z-2 + x-1*y-1*z-3
22 ? x*z2 + 2*x*z + x + y + 3*z + y-1*z2 + 4*y-1*z + 3*z-1 + x-1*y*z-1 + 6*y-1 + 2*x-1 + x-1*y-1*z + 4*y-1*z-1 + 4*x-1*z-1 + 4*x-1*y-1 + y-1*z-2 + 2*x-1*z-2 + 6*x-1*y-1*z-1 + 4*x-1*y-1*z-2 + x-1*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 134 1 Lattice Minkowski decompositions of facet 134
Image of facet 23 2 Lattice Minkowski decompositions of facet 23
Polytope 3791
Image of polytope 3791 PALP id: 3791
grdb id: 294041
Integer points: [ 1 1 0 0 1 1 -3 -3 -2 -1 -2 -1 -1 0 -1 0 1 -1 0 1 1]
[ 0 2 0 1 -1 2 -3 -2 -2 -1 -1 0 -2 -1 -1 0 1 0 1 0 1]
[ 0 0 1 1 -1 -1 1 1 1 1 1 1 0 0 0 0 0 0 0 -1 -1]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x*y2 + x*y2*z-1 + 2*x*y + y*z + 3*x*y*z-1 + x + 3*y + z + 3*x*z-1 + 3*x-1*z + x*y-1*z-1 + 3*y-1 + 2*x-1 + 3*x-1*y-1*z + 4*x-1*y-1 + 3*x-2*y-1*z + 2*x-1*y-2 + 3*x-2*y-2*z + x-3*y-2*z + x-3*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 3792
Image of polytope 3792 PALP id: 3792
grdb id: 294032
Integer points: [ 1 0 0 -3 2 0 0 -4 -1 -2 -3 1 0 -1 -2 1 -1 -2 1 0 -1]
[ 0 1 0 3 -3 -1 -1 3 0 1 2 -2 -1 0 1 -2 1 2 -1 0 1]
[ 0 0 1 1 -1 -1 1 1 1 1 1 0 0 0 0 -1 1 1 0 0 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 2 none
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3793
Image of polytope 3793 PALP id: 3793
grdb id: 292448
Integer points: [ 1 0 0 1 1 -2 1 -2 -1 0 -1 0 1 0 1 -2 -1 0 -1 0 -1]
[ 0 1 0 1 -1 0 -2 -2 -2 -2 -1 -1 -1 0 0 -1 -1 -1 0 0 0]
[ 0 0 1 -1 0 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x*y*z-1 + x + y + z + 3*x*z-1 + x*y-1 + 2*x-1*z + 3*x*y-1*z-1 + 3*z-1 + 4*y-1 + 3*x-1 + x-2*z + x*y-2*z-1 + 6*y-1*z-1 + 5*x-1*y-1 + 3*y-2*z-1 + 3*x-1*y-1*z-1 + 2*x-2*y-1 + 3*x-1*y-2*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Polytope 3794
Image of polytope 3794 PALP id: 3794
grdb id: 292940
Integer points: [ 1 0 0 0 0 1 -2 -2 -1 -2 -1 0 -1 -1 0 -1 0 1 -1 0 0]
[ 0 1 1 -1 -1 -2 1 1 0 1 0 -1 0 1 0 1 0 -1 1 0 1]
[ 0 0 2 0 -2 -2 2 0 1 1 0 -1 -1 2 1 1 0 -1 0 -1 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
22 ? y*z2 + 2*y*z + 2*x-1*y*z2 + x + y + 2*z + 4*x-1*y*z + x-2*y*z2 + 2*x-1*y + 2*x-1*z + 2*x-2*y*z + 2*x*y-1*z-1 + 2*z-1 + y-1 + 5*x-1 + x-2*y + 4*y-1*z-1 + 2*x-1*z-1 + x*y-2*z-2 + y-1*z-2
7 rank 1, V12 y*z2 + 2*y*z + 2*x-1*y*z2 + x + y + 2*z + 4*x-1*y*z + x-2*y*z2 + 2*x-1*y + 2*x-1*z + 2*x-2*y*z + 2*x*y-1*z-1 + 2*z-1 + y-1 + 4*x-1 + x-2*y + 3*y-1*z-1 + 2*x-1*z-1 + x*y-2*z-2 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 81 1 Lattice Minkowski decompositions of facet 81
Polytope 3795
Image of polytope 3795 PALP id: 3795
grdb id: 292458
Integer points: [ 1 0 0 2 1 -1 -2 -2 0 -1 0 -1 -2 -1 -2 1 1 0 -1 0 -1]
[ 0 1 0 -2 -2 1 1 1 -1 0 -1 0 1 0 1 -1 -1 0 1 0 1]
[ 0 0 1 -1 -1 -1 2 -1 0 1 -1 0 1 -1 0 0 -1 0 1 -1 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + 2*x-1*y*z + x-2*y*z2 + 2*x*y-1 + 3*x-1*y + 3*x-1*z + 3*x-2*y*z + x2*y-2*z-1 + 3*x*y-1*z-1 + 3*z-1 + x-1*y*z-1 + 3*y-1 + 6*x-1 + 3*x-2*y + x*y-2*z-1 + 3*y-1*z-1 + 3*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 3796
Image of polytope 3796 PALP id: 3796
grdb id: 293345
Integer points: [ 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 1 -2 0 -3 0 -1 -2 1 0 -1 -2 0 -1 -1 0 -1 0]
[ 0 0 1 -1 1 1 -2 1 1 1 1 0 0 0 0 -1 -1 1 0 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y*z + 2*x-1*y + 2*y-1*z + 4*x-1*z + 2*z-1 + x-1*y*z-1 + 3*y-1 + 7*x-1 + y-2*z + 6*x-1*y-1*z + 4*x-1*z-1 + 8*x-1*y-1 + 4*x-1*y-2*z + x-1*z-2 + 3*x-1*y-1*z-1 + 3*x-1*y-2 + x-1*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3797
Image of polytope 3797 PALP id: 3797
grdb id: 292762
Integer points: [ 1 0 0 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 1 -1 1 -1 -3 0 1 0 -1 -2 0 -1 -2 0 -1 0 -1 -2]
[ 0 0 1 1 -1 -1 1 -1 1 0 0 0 0 -1 -1 -1 0 0 -1 -1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 3*y-1 + 6*x-1 + x-1*y-1*z + 4*y-1*z-1 + 4*x-1*z-1 + 6*x-1*y-1 + 2*y-2*z-1 + 6*x-1*y-1*z-1 + 2*x-1*y-2 + 4*x-1*y-2*z-1 + x-1*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3798
Image of polytope 3798 PALP id: 3798
grdb id: 292446
Integer points: [ 1 0 0 -1 1 0 -2 -2 -1 0 -2 -1 0 -2 -1 -1 0 1 -1 0 -1]
[ 0 1 0 1 0 -1 0 -3 0 0 -1 -1 -1 -2 -2 0 0 0 -1 -1 -2]
[ 0 0 1 1 -2 1 1 1 0 -1 1 0 -1 1 0 1 0 -1 1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x-1*y*z + 2*x*z-1 + y-1*z + 3*x-1*z + x*z-2 + 3*z-1 + 4*y-1 + 3*x-1 + 4*x-1*y-1*z + x-2*z + 3*y-1*z-1 + 6*x-1*y-1 + 2*x-1*y-2*z + 3*x-2*y-1*z + 3*x-1*y-2 + 3*x-2*y-2*z + x-2*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Polytope 3799
Image of polytope 3799 PALP id: 3799
grdb id: 292443
Integer points: [ 1 0 0 0 -1 1 0 -3 -2 -1 -2 -1 0 -1 0 -2 -1 0 -1 0 1]
[ 0 1 0 1 1 -2 -2 1 0 -1 1 0 -1 1 0 1 0 -1 1 0 -1]
[ 0 0 1 -1 1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x-1*y*z + y*z-1 + 2*x*y-1 + 3*x-1*y + 3*z-1 + 3*x-1*y*z-1 + x*y-2 + 3*y-1 + 4*x-1 + 2*x-2*y + 3*y-1*z-1 + 6*x-1*z-1 + 3*x-2*y*z-1 + y-2*z-1 + 3*x-1*y-1*z-1 + 3*x-2*z-1 + x-3*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3800
Image of polytope 3800 PALP id: 3800
grdb id: 292802
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 1 -1 0 1 -1 1 1 1 1 0 0 0 0 -1 -1 1 0 0 0]
[ 0 0 2 -2 -2 -1 1 3 2 1 0 2 1 0 -1 0 -1 1 1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 198 1 Lattice Minkowski decompositions of facet 198
Image of facet 8 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3801
Image of polytope 3801 PALP id: 3801
grdb id: 292681
Integer points: [ 1 0 0 0 -1 -1 -2 -2 -2 -2 -2 -1 -1 -1 0 -1 -1 -1 0 0 0]
[ 0 1 0 -2 2 -2 -1 3 0 1 2 -1 0 1 -1 0 1 2 -1 0 1]
[ 0 0 1 -1 2 -2 -2 2 -1 0 1 -1 0 1 0 -1 0 1 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x-1*y2*z2 + x-2*y3*z2 + 2*y*z + 2*x-1*y2*z + x + y + z + 4*x-1*y*z + 4*x-2*y2*z + 4*x-1*y + 2*y-1 + 6*x-1 + 6*x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + y-2*z-1 + 4*x-1*y-1*z-1 + 4*x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
40 rank 2, number 10 x-1*y2*z2 + x-2*y3*z2 + 2*y*z + 2*x-1*y2*z + x + y + z + 5*x-1*y*z + 4*x-2*y2*z + 4*x-1*y + 2*y-1 + 8*x-1 + 6*x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + y-2*z-1 + 5*x-1*y-1*z-1 + 4*x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 3 irreducible and admissible
Image of facet 187 1 Lattice Minkowski decompositions of facet 187
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3802
Image of polytope 3802 PALP id: 3802
grdb id: 292451
Integer points: [ 1 0 0 0 1 -2 1 -2 0 0 -1 -1 -1 -2 -2 1 0 0 -1 -1 -1]
[ 0 1 0 0 -1 1 -2 -2 -2 -1 -2 -1 0 -1 0 -1 -1 0 -1 0 1]
[ 0 0 1 -1 -1 0 0 3 1 0 2 1 0 2 1 0 1 0 2 1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + 2*x*y-1 + 2*x-1*y + 4*y-1*z + 4*x-1*z + 2*x-1*y-1*z2 + x*y-1*z-1 + z-1 + x*y-2 + 4*y-1 + 3*x-1 + x-2*y + 3*y-2*z + 6*x-1*y-1*z + 3*x-2*z + 3*x-1*y-2*z2 + 3*x-2*y-1*z2 + x-2*y-2*z3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Image of facet 153 1 Lattice Minkowski decompositions of facet 153
Polytope 3803
Image of polytope 3803 PALP id: 3803
grdb id: 292445
Integer points: [ 1 0 1 0 0 -2 -3 -3 -2 -1 -3 -2 -1 -3 -2 -1 -1 0 -1 0 -1]
[ 0 1 -1 0 -1 2 2 -1 -1 -1 0 0 0 1 1 1 -1 -1 0 0 1]
[ 0 0 0 1 1 -1 -2 -2 -1 0 -2 -1 0 -2 -1 0 -1 0 -1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 174 1 Lattice Minkowski decompositions of facet 174
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Polytope 3804
Image of polytope 3804 PALP id: 3804
grdb id: 292764
Integer points: [ 1 0 0 0 -1 -2 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 1 0 -2 -4 -3 -2 -1 -2 -1 0 -3 -2 -1 0 -1 0 -1]
[ 0 0 1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
59 rank 2, number 16 x + y + z + z-1 + x-1*y*z-1 + 2*y-1 + 2*x-1 + 2*y-1*z-1 + 4*x-1*z-1 + 4*x-1*y-1 + y-2*z-1 + 7*x-1*y-1*z-1 + x-2*z-1 + 2*x-1*y-2 + 6*x-1*y-2*z-1 + 4*x-2*y-1*z-1 + 2*x-1*y-3*z-1 + 6*x-2*y-2*z-1 + 4*x-2*y-3*z-1 + x-2*y-4*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 180 1 Lattice Minkowski decompositions of facet 180
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3805
Image of polytope 3805 PALP id: 3805
grdb id: 292773
Integer points: [ 1 0 0 0 -1 0 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 1 -1 1 -3 0 -1 -2 0 -1 -2 1 0 -1 -2 0 -1 0]
[ 0 0 1 0 1 -2 0 -4 -1 -2 -3 0 -1 -2 0 -1 -2 -3 0 -1 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + x-1*y*z + 2*x-1*y + 2*z-1 + y-1 + 4*x-1 + x-2*y + 2*y-1*z-1 + 6*x-1*z-1 + y-1*z-2 + 5*x-1*y-1*z-1 + 4*x-2*z-1 + 6*x-1*y-1*z-2 + 2*x-1*y-2*z-2 + 6*x-2*y-1*z-2 + 2*x-1*y-2*z-3 + 4*x-2*y-2*z-3 + x-2*y-3*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3806
Image of polytope 3806 PALP id: 3806
grdb id: 293348
Integer points: [ 1 0 1 0 -1 -2 -1 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 1 -1 0 1 0 -2 -4 -1 -2 -3 0 -1 -2 -3 -1 -2 0 -1 0 -1]
[ 0 0 0 1 1 1 -2 -3 0 -1 -2 1 0 -1 -2 0 -1 0 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + x-1*y*z + x*y-1 + 2*x-1*z + 4*y-1 + 4*x-1 + x-2*z + 2*y-1*z-1 + 7*x-1*y-1 + 3*y-2*z-1 + 4*x-1*y-1*z-1 + 4*x-2*y-1 + 8*x-1*y-2*z-1 + x-1*y-2*z-2 + 6*x-2*y-2*z-1 + 3*x-1*y-3*z-2 + 4*x-2*y-3*z-2 + x-2*y-4*z-3
52 rank 2, number 52 x + y + z + x-1*y*z + x*y-1 + 2*x-1*z + 4*y-1 + 3*x-1 + x-2*z + 2*y-1*z-1 + 7*x-1*y-1 + 3*y-2*z-1 + 3*x-1*y-1*z-1 + 4*x-2*y-1 + 8*x-1*y-2*z-1 + x-1*y-2*z-2 + 6*x-2*y-2*z-1 + 3*x-1*y-3*z-2 + 4*x-2*y-3*z-2 + x-2*y-4*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 93 1 Lattice Minkowski decompositions of facet 93
Polytope 3807
Image of polytope 3807 PALP id: 3807
grdb id: 293896
Integer points: [ 1 0 0 1 1 1 -3 -4 -3 -2 -1 0 -2 -1 0 -2 -1 0 -1 0 1]
[ 0 1 0 -2 -2 -3 2 2 1 0 -1 -2 1 0 -1 1 0 -1 1 0 -1]
[ 0 0 1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 157 1 Lattice Minkowski decompositions of facet 157
Polytope 3808
Image of polytope 3808 PALP id: 3808
grdb id: 292765
Integer points: [ 1 0 1 0 0 0 -2 -4 -1 -3 -2 -1 0 -3 -2 -1 -1 0 -2 -1 0]
[ 0 1 -1 0 0 -2 2 2 1 2 1 0 -1 1 0 -1 1 0 1 0 -1]
[ 0 0 0 1 -1 1 -1 -3 0 -2 -1 0 1 -2 -1 0 -1 0 -2 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 80 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3809
Image of polytope 3809 PALP id: 3809
grdb id: 293354
Integer points: [ 1 0 1 0 0 -1 -1 -5 -2 -3 -4 -1 -2 -3 0 -1 -1 -2 -3 0 -1]
[ 0 1 -1 0 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 0 0 1 1 -1 1 -3 0 -1 -2 0 -1 -2 0 -1 0 -1 -2 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 148 1 none
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Polytope 3810
Image of polytope 3810 PALP id: 3810
grdb id: 293894
Integer points: [ 1 0 0 -1 1 -3 0 -5 -1 -2 -3 -4 0 -1 -2 -3 -1 -2 1 0 -1]
[ 0 1 0 0 2 -3 1 -4 0 -1 -2 -3 1 0 -1 -2 -1 -2 1 0 -1]
[ 0 0 1 -1 2 -2 2 -3 1 0 -1 -2 1 0 -1 -2 0 -1 1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 146 1 Lattice Minkowski decompositions of facet 146
Image of facet 181 1 Lattice Minkowski decompositions of facet 181
Image of facet 8 1 none
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3811
Image of polytope 3811 PALP id: 3811
grdb id: 287942
Integer points: [ 1 0 0 1 0 -2 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 0 2 -2 -2 -1 0 1 -1 0 1 -2 -1 0 1 -1 0 -1]
[ 0 0 1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*y-1 + 2*x-1*y + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 4*x-1 + 2*y-1*z-1 + 6*x-1*z-1 + 4*x-2*y*z-1 + 2*x-1*y-1 + y-2*z-1 + 6*x-1*y-1*z-1 + 6*x-2*z-1 + 2*x-1*y-2*z-1 + 4*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3812
Image of polytope 3812 PALP id: 3812
grdb id: 287299
Integer points: [ 1 0 0 -1 1 1 -2 1 -1 -1 0 0 0 1 1 -1 0 0 1 1 1]
[ 0 1 0 1 -1 0 0 -3 0 -1 0 -1 -2 -1 -2 0 0 -1 0 -1 -2]
[ 0 0 1 1 0 -2 1 -2 0 0 -1 -1 -1 -2 -2 1 0 0 -1 -1 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
51 rank 2, number 7 x + y + z + x-1*y*z + 2*x*z-1 + x*y-1 + 2*x-1*z + x*z-2 + 4*x*y-1*z-1 + 3*z-1 + 4*y-1 + 3*x-1 + x-2*z + 3*x*y-1*z-2 + 2*x*y-2*z-1 + 6*y-1*z-1 + 3*x-1*y-1 + 3*x*y-2*z-2 + 3*y-2*z-1 + x*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Polytope 3813
Image of polytope 3813 PALP id: 3813
grdb id: 290693
Integer points: [ 1 0 0 0 -2 -2 -3 -3 -3 -3 -3 -2 -2 -2 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 -2 2 2 -2 -1 0 1 -1 0 1 -1 0 1 -1 0 1 0]
[ 0 0 0 1 -1 -1 -2 -2 -2 -2 -2 -1 -1 -1 0 0 0 -1 -1 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
36 rank 3, number 7 x + y + z + 2*x-1*y + 2*x-1*y*z-1 + x-2*y2*z-1 + y-1 + 4*x-1 + 4*x-1*z-1 + 5*x-2*y*z-1 + 2*x-1*y-1 + x-3*y2*z-2 + 2*x-1*y-1*z-1 + 8*x-2*z-1 + 4*x-3*y*z-2 + 5*x-2*y-1*z-1 + 6*x-3*z-2 + x-2*y-2*z-1 + 4*x-3*y-1*z-2 + x-3*y-2*z-2
3 ? x + y + z + 2*x-1*y + 2*x-1*y*z-1 + x-2*y2*z-1 + y-1 + 5*x-1 + 4*x-1*z-1 + 6*x-2*y*z-1 + 2*x-1*y-1 + x-3*y2*z-2 + 2*x-1*y-1*z-1 + 10*x-2*z-1 + 4*x-3*y*z-2 + 6*x-2*y-1*z-1 + 6*x-3*z-2 + x-2*y-2*z-1 + 4*x-3*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 223 1 Lattice Minkowski decompositions of facet 223
Polytope 3814
Image of polytope 3814 PALP id: 3814
grdb id: 291585
Integer points: [ 1 0 0 0 -1 -2 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 2 2 -2 -3 1 0 -1 -2 1 0 -1 -2 1 0 -1 0 -1]
[ 0 0 1 1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 -1 -1 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 13 1 irreducible and admissible
Image of facet 157 1 Lattice Minkowski decompositions of facet 157
Polytope 3815
Image of polytope 3815 PALP id: 3815
grdb id: 288486
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 1 1 -2 -2 1 -1 0 -2 -1 0 1 -1 0 -1 0 1 -1 0]
[ 0 0 1 -2 -1 2 0 -3 1 0 1 0 -1 -2 -1 -2 1 0 -1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + 2*y*z-1 + 2*y-1*z + y*z-2 + 3*z-1 + x-1*y*z-1 + 2*y-1 + 3*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*y*z-2 + 6*x-1*z-1 + 6*x-1*y-1 + 2*x-1*y-2*z + x-1*y*z-3 + 3*x-1*z-2 + 3*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3816
Image of polytope 3816 PALP id: 3816
grdb id: 291693
Integer points: [ 1 0 0 0 0 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 -1 0 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0]
[ 0 0 1 0 -1 -2 2 -3 1 0 -1 -2 1 0 -1 1 0 -1 -2 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + 2*x-1*z + 2*z-1 + y-1 + 5*x-1 + 2*x-1*y-1*z + x-2*y-1*z2 + y-1*z-1 + 4*x-1*z-1 + 6*x-1*y-1 + 5*x-2*y-1*z + x-1*z-2 + 6*x-1*y-1*z-1 + 10*x-2*y-1 + 2*x-1*y-1*z-2 + 10*x-2*y-1*z-1 + 5*x-2*y-1*z-2 + x-2*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3817
Image of polytope 3817 PALP id: 3817
grdb id: 287226
Integer points: [ 1 0 -1 0 -1 0 -3 -3 -2 -1 -3 -2 -1 -3 -2 -1 -2 -1 0 -1 0]
[ 0 1 1 0 0 -1 -1 -4 -3 -2 -3 -2 -1 -2 -1 0 0 -2 -1 -1 0]
[ 0 0 0 1 -1 1 -2 -2 -1 0 -2 -1 0 -2 -1 0 -1 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 220 1 Lattice Minkowski decompositions of facet 220
Image of facet 14 1 none
Polytope 3818
Image of polytope 3818 PALP id: 3818
grdb id: 291701
Integer points: [ 1 0 -1 0 0 0 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 1 0 -1 -2 1 -4 -3 -2 -1 0 -2 -1 0 -3 -2 -1 0 -1 0]
[ 0 0 0 1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y + 2*y-1 + 4*x-1 + y-1*z-1 + 2*x-1*z-1 + x-2*y*z-1 + 5*x-1*y-1 + y-2*z-1 + 6*x-1*y-1*z-1 + 5*x-2*z-1 + 2*x-1*y-2 + 6*x-1*y-2*z-1 + 10*x-2*y-1*z-1 + 2*x-1*y-3*z-1 + 10*x-2*y-2*z-1 + 5*x-2*y-3*z-1 + x-2*y-4*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Polytope 3819
Image of polytope 3819 PALP id: 3819
grdb id: 287964
Integer points: [ 1 0 0 0 -1 -2 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 1 0 -2 -4 -3 -2 -1 -2 -1 0 -3 -2 -1 0 -1 0 -1]
[ 0 0 1 -1 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y + 2*y-1*z + 2*x-1*z + z-1 + 2*y-1 + 3*x-1 + y-2*z + 6*x-1*y-1*z + x-2*z + 4*x-1*y-1 + 6*x-1*y-2*z + 4*x-2*y-1*z + 2*x-1*y-2 + 2*x-1*y-3*z + 6*x-2*y-2*z + 4*x-2*y-3*z + x-2*y-4*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3820
Image of polytope 3820 PALP id: 3820
grdb id: 287137
Integer points: [ 1 0 0 0 -1 -1 -3 -3 -2 -1 -3 -2 -1 -3 -2 -1 -2 -1 0 -1 0]
[ 0 1 0 -1 2 -2 0 3 2 1 2 1 0 1 0 -1 -1 1 0 0 -1]
[ 0 0 1 1 -1 0 -2 -2 -1 0 -2 -1 0 -2 -1 0 -1 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y2*z-1 + 3*x-1*y + y-1*z + 3*x-1*y*z-1 + 3*x-2*y2*z-1 + 2*y-1 + 5*x-1 + x-3*y3*z-2 + 2*x-1*z-1 + 7*x-2*y*z-1 + 3*x-1*y-1 + 3*x-3*y2*z-2 + 6*x-2*z-1 + x-1*y-2 + 3*x-3*y*z-2 + 2*x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 220 1 Lattice Minkowski decompositions of facet 220
Polytope 3821
Image of polytope 3821 PALP id: 3821
grdb id: 287278
Integer points: [ 1 0 0 0 -1 -2 -2 -5 -1 -3 -2 -1 -4 -3 -2 -4 -3 -1 0 -2 -1]
[ 0 1 -1 0 1 1 -2 -2 -1 -2 -1 0 -2 -1 0 -1 0 -1 0 -1 0]
[ 0 0 0 1 0 -1 -1 -4 0 -2 -1 0 -3 -2 -1 -3 -2 -1 0 -2 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + x-1*y + y-1 + 3*x-1 + 3*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + 5*x-2*z-1 + 6*x-2*y-1*z-1 + 2*x-2*y-1*z-2 + 3*x-3*z-2 + x-2*y-2*z-1 + 7*x-3*y-1*z-2 + 3*x-3*y-2*z-2 + 3*x-4*y-1*z-3 + 3*x-4*y-2*z-3 + x-5*y-2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 220 1 Lattice Minkowski decompositions of facet 220
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Polytope 3822
Image of polytope 3822 PALP id: 3822
grdb id: 287241
Integer points: [ 1 0 0 0 -1 0 -1 -4 -2 -1 0 -3 -2 -1 -3 -2 0 -1 0 -2 -1]
[ 0 1 0 1 1 -1 -2 -2 -2 -1 0 -2 -1 0 -1 0 -1 -1 0 -1 0]
[ 0 0 1 -1 0 -1 0 3 1 0 -1 2 1 0 2 1 0 1 0 2 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + y*z-1 + x-1*y + 3*x-1*z + 2*z-1 + 2*y-1 + 5*x-1 + 4*x-1*y-1*z + 3*x-2*z + 2*x-2*y-1*z2 + y-1*z-1 + 5*x-1*y-1 + 7*x-2*y-1*z + 3*x-3*y-1*z2 + x-1*y-2 + 3*x-2*y-2*z + 3*x-3*y-2*z2 + x-4*y-2*z3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 174 1 Lattice Minkowski decompositions of facet 174
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3823
Image of polytope 3823 PALP id: 3823
grdb id: 112305
Integer points: [ 1 0 0 -1 1 0 -2 -1 -2 -2 -2 -1 -1 -1 0 0 -1 -1 0 0 1]
[ 0 1 0 1 -2 -1 1 0 1 1 1 0 0 0 -1 -1 1 1 0 0 -1]
[ 0 0 1 1 0 1 1 -2 -2 0 -1 1 0 -1 0 -1 0 -1 0 -1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
51 rank 2, number 7 x + y + z + x-1*y*z + 2*x*y-1 + 3*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + 2*z-1 + 2*x-1*y*z-1 + x*y-2 + 4*y-1 + 6*x-1 + 3*x-2*y + 2*y-1*z-1 + 5*x-1*z-1 + 3*x-2*y*z-1 + x-1*z-2 + x-2*y*z-2
18 rank 1, V14 x + y + z + x-1*y*z + 2*x*y-1 + 3*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + 2*z-1 + 2*x-1*y*z-1 + x*y-2 + 3*y-1 + 5*x-1 + 3*x-2*y + 2*y-1*z-1 + 4*x-1*z-1 + 3*x-2*y*z-1 + x-1*z-2 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 155 1 Lattice Minkowski decompositions of facet 155
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3824
Image of polytope 3824 PALP id: 3824
grdb id: 112517
Integer points: [ 1 0 0 -1 1 1 -1 0 -3 -2 -1 -2 -1 0 0 -2 -1 0 -1 0 1]
[ 0 1 0 1 -1 -2 1 -2 1 0 -1 1 0 -1 0 1 0 -1 1 0 -1]
[ 0 0 1 1 -1 0 -1 1 1 1 1 0 0 0 -1 1 1 1 0 0 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + 2*y-1*z + 4*x-1*z + 2*x-2*y*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + x*y-2 + 4*y-1 + 5*x-1 + 2*x-2*y + y-2*z + 3*x-1*y-1*z + 3*x-2*z + x-3*y*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3825
Image of polytope 3825 PALP id: 3825
grdb id: 112300
Integer points: [ 1 0 0 -1 1 1 0 0 -3 -2 -1 -2 -1 0 -1 0 -2 -1 0 -1 0]
[ 0 1 0 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 0 1 1 -1 0 1 -2 1 0 -1 1 0 -1 1 0 1 0 -1 1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + x-1*y*z + x*y-1 + y-1*z + 3*x-1*z + x*y-1*z-1 + 2*z-1 + 4*y-1 + 4*x-1 + 3*x-1*y-1*z + 2*x-2*z + 3*y-1*z-1 + 6*x-1*y-1 + 3*x-2*y-1*z + y-1*z-2 + 3*x-1*y-1*z-1 + 3*x-2*y-1 + x-3*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 153 1 Lattice Minkowski decompositions of facet 153
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3826
Image of polytope 3826 PALP id: 3826
grdb id: 112528
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 -2 1 -2 2 -3 2 -1 0 1 -2 -1 0 1 -1 0 1 -1 0]
[ 0 0 1 1 -2 2 -2 2 -3 1 0 -1 1 0 -1 -2 1 0 -1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
26 rank 2, number 8 x + y + z + y*z-1 + y-1*z + y*z-2 + x-1*y2*z-2 + 3*z-1 + 4*x-1*y*z-1 + 3*y-1 + 6*x-1 + y-2*z + 4*x-1*y-1*z + x-1*y-2*z2 + x-1*y2*z-3 + 5*x-1*y*z-2 + 10*x-1*z-1 + 10*x-1*y-1 + 5*x-1*y-2*z + x-1*y-3*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 146 1 Lattice Minkowski decompositions of facet 146
Image of facet 9 1 irreducible and admissible
Image of facet 10 2 Lattice Minkowski decompositions of facet 10
Image of facet 157 1 Lattice Minkowski decompositions of facet 157
Polytope 3827
Image of polytope 3827 PALP id: 3827
grdb id: 112423
Integer points: [ 1 0 0 0 1 0 -2 -2 -4 -1 -2 -3 0 -1 -2 -3 -1 -1 1 0 -1]
[ 0 1 -1 0 2 2 -1 -2 -2 1 0 -1 1 0 -1 -2 -1 0 1 0 -1]
[ 0 0 0 1 2 1 -2 -1 -3 0 -1 -2 1 0 -1 -2 0 -1 1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 x*y2*z2 + 2*x*y*z + y2*z + 4*y*z + x + y + z + 4*x-1*y + y-1 + 7*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + 6*x-2*z-1 + 6*x-2*y-1*z-1 + x-2*y-1*z-2 + x-2*y-2*z-1 + 4*x-3*y-1*z-2 + 2*x-3*y-2*z-2 + x-4*y-2*z-3
20 rank 1, V16 x*y2*z2 + 2*x*y*z + y2*z + 4*y*z + x + y + z + 4*x-1*y + y-1 + 7*x-1 + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 6*x-2*z-1 + 6*x-2*y-1*z-1 + x-2*y-1*z-2 + x-2*y-2*z-1 + 4*x-3*y-1*z-2 + 2*x-3*y-2*z-2 + x-4*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 180 1 Lattice Minkowski decompositions of facet 180
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 3828
Image of polytope 3828 PALP id: 3828
grdb id: 108694
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 -1 1 0 -2 -2 0 1 0 -1 0 -1 -2 -1 0 -1 0 -1]
[ 0 0 1 1 1 -1 -2 0 -2 1 0 0 0 -1 -1 -1 -2 0 0 -1 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 5*x-1 + x-1*y-1*z + 2*y-1*z-1 + 4*x-1*z-1 + 4*x-1*y-1 + x-1*z-2 + 5*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-1*z-2 + 2*x-1*y-2*z-1 + x-1*y-2*z-2
31 rank 3, number 3 x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 6*x-1 + x-1*y-1*z + 2*y-1*z-1 + 5*x-1*z-1 + 5*x-1*y-1 + x-1*z-2 + 6*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-1*z-2 + 2*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 224 1 Lattice Minkowski decompositions of facet 224
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 3829
Image of polytope 3829 PALP id: 3829
grdb id: 108209
Integer points: [ 1 0 0 1 -1 -2 1 1 -2 -1 0 -2 -1 0 -1 0 -1 0 1 -1 0]
[ 0 1 0 0 1 0 -1 -2 -2 -2 -2 -1 -1 -1 0 0 -1 -1 -1 0 0]
[ 0 0 1 -1 0 1 -2 -2 1 0 -1 1 0 -1 0 -1 1 0 -1 1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x*z-1 + x-1*y + 2*x-1*z + 2*x*y-1*z-1 + 2*z-1 + 4*y-1 + 4*x-1 + 2*x-1*y-1*z + x-2*z + x*y-1*z-2 + 5*y-1*z-1 + 6*x-1*y-1 + 2*x-2*y-1*z + x*y-2*z-2 + 3*y-2*z-1 + 3*x-1*y-2 + x-2*y-2*z
62 rank 2, number 9 x + y + z + x*z-1 + x-1*y + 2*x-1*z + 2*x*y-1*z-1 + 2*z-1 + 4*y-1 + 3*x-1 + 2*x-1*y-1*z + x-2*z + x*y-1*z-2 + 4*y-1*z-1 + 5*x-1*y-1 + 2*x-2*y-1*z + x*y-2*z-2 + 3*y-2*z-1 + 3*x-1*y-2 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 155 1 Lattice Minkowski decompositions of facet 155
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Polytope 3830
Image of polytope 3830 PALP id: 3830
grdb id: 107924
Integer points: [ 1 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 1 -1 -1 -2 -2 0 0 0 -1 -1 -1 -2 -2 0 0 -1 -1]
[ 0 0 1 1 0 -2 1 0 -3 -1 0 1 -2 -1 0 -2 -1 -1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + x-1*y + 2*x-1*z + 2*z-1 + 2*y-1 + 5*x-1 + x-1*y-1*z + 3*y-1*z-1 + 3*x-1*z-1 + 5*x-1*y-1 + y-1*z-2 + 7*x-1*y-1*z-1 + x-1*y-2 + 3*x-1*y-1*z-2 + 3*x-1*y-2*z-1 + 3*x-1*y-2*z-2 + x-1*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 174 1 Lattice Minkowski decompositions of facet 174
Polytope 3831
Image of polytope 3831 PALP id: 3831
grdb id: 108038
Integer points: [ 1 0 0 -1 1 1 -2 1 -2 0 -1 1 0 -1 1 0 0 -1 1 0 -1]
[ 0 1 0 1 0 -2 1 -3 0 -2 -1 -2 -1 0 -1 0 -1 0 -1 0 1]
[ 0 0 1 1 -1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
51 rank 2, number 7 x + y + z + x-1*y*z + x*z-1 + 2*x*y-1 + 2*x-1*y + 3*x*y-1*z-1 + 3*z-1 + x*y-2 + 4*y-1 + 4*x-1 + x-2*y + 3*x*y-2*z-1 + 6*y-1*z-1 + 3*x-1*z-1 + x*y-3*z-1 + 3*y-2*z-1 + 3*x-1*y-1*z-1 + x-2*z-1
18 rank 1, V14 x + y + z + x-1*y*z + x*z-1 + 2*x*y-1 + 2*x-1*y + 3*x*y-1*z-1 + 3*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + 3*x*y-2*z-1 + 6*y-1*z-1 + 3*x-1*z-1 + x*y-3*z-1 + 3*y-2*z-1 + 3*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Polytope 3832
Image of polytope 3832 PALP id: 3832
grdb id: 109121
Integer points: [ 1 0 0 0 -1 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 1 -1 1 -2 -3 0 1 0 -1 -2 0 -1 -2 0 -1 0 -1]
[ 0 0 1 -1 1 1 -1 -1 -1 1 0 0 0 0 -1 -1 -1 0 0 -1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + x-1*y*z + y*z-1 + 2*x-1*y + 2*x-1*z + 3*z-1 + x-1*y*z-1 + 2*y-1 + 6*x-1 + x-1*y-1*z + 3*y-1*z-1 + 4*x-1*z-1 + 6*x-1*y-1 + y-2*z-1 + 6*x-1*y-1*z-1 + 2*x-1*y-2 + 4*x-1*y-2*z-1 + x-1*y-3*z-1
20 rank 1, V16 x + y + z + x-1*y*z + y*z-1 + 2*x-1*y + 2*x-1*z + 3*z-1 + x-1*y*z-1 + 3*y-1 + 6*x-1 + x-1*y-1*z + 3*y-1*z-1 + 4*x-1*z-1 + 6*x-1*y-1 + y-2*z-1 + 6*x-1*y-1*z-1 + 2*x-1*y-2 + 4*x-1*y-2*z-1 + x-1*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3833
Image of polytope 3833 PALP id: 3833
grdb id: 108116
Integer points: [ 1 0 0 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 -1 1 0 1 0 -3 -2 -1 -2 -1 0 -1 0 -2 -1 -1 0 0]
[ 0 0 1 0 0 1 -1 -2 -2 -1 0 -2 -1 0 -2 -1 -1 0 -1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*y-1 + x-1*y + x-1*z + 2*z-1 + x-1*y*z-1 + 3*y-1 + 3*x-1 + 4*y-1*z-1 + 4*x-1*z-1 + 3*x-1*y-1 + x-1*z-2 + 2*y-2*z-1 + 6*x-1*y-1*z-1 + 3*x-1*y-1*z-2 + 3*x-1*y-2*z-1 + 3*x-1*y-2*z-2 + x-1*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 153 1 Lattice Minkowski decompositions of facet 153
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3834
Image of polytope 3834 PALP id: 3834
grdb id: 111798
Integer points: [ 1 0 0 -1 -1 -1 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -2 1 2 -2 -3 2 -2 -1 0 1 -1 0 1 -1 0 -1 0 1]
[ 0 0 1 1 -2 -2 2 2 -3 1 0 -1 -2 1 0 -1 0 -1 1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 5*x-1*y*z-1 + 8*x-1 + 5*x-1*y-1*z + x-1*y-2*z2 + x-1*y*z-2 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z + x-2*y2*z-3 + 5*x-2*y*z-2 + 10*x-2*z-1 + 10*x-2*y-1 + 5*x-2*y-2*z + x-2*y-3*z2
31 rank 3, number 3 x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 4*x-1*y*z-1 + 6*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + x-1*y*z-2 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z + x-2*y2*z-3 + 5*x-2*y*z-2 + 10*x-2*z-1 + 10*x-2*y-1 + 5*x-2*y-2*z + x-2*y-3*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 146 1 Lattice Minkowski decompositions of facet 146
Image of facet 9 1 irreducible and admissible
Image of facet 186 1 Lattice Minkowski decompositions of facet 186
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 3835
Image of polytope 3835 PALP id: 3835
grdb id: 111932
Integer points: [ 1 0 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 -1 1 1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 -1 -1 0 0]
[ 0 0 1 1 0 -1 -2 2 -3 1 0 -1 -2 1 0 -1 -2 0 -1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y + y-1*z + 2*x-1*z + x-1*y-1*z2 + 3*z-1 + x-1*y*z-1 + 3*y-1 + 6*x-1 + 5*x-1*y-1*z + 3*y-1*z-1 + 6*x-1*z-1 + 10*x-1*y-1 + y-1*z-2 + 2*x-1*z-2 + 10*x-1*y-1*z-1 + 5*x-1*y-1*z-2 + x-1*y-1*z-3
62 rank 2, number 9 x + y + z + x-1*y + y-1*z + 2*x-1*z + x-1*y-1*z2 + 2*z-1 + x-1*y*z-1 + 3*y-1 + 6*x-1 + 5*x-1*y-1*z + 3*y-1*z-1 + 6*x-1*z-1 + 10*x-1*y-1 + y-1*z-2 + 2*x-1*z-2 + 10*x-1*y-1*z-1 + 5*x-1*y-1*z-2 + x-1*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Image of facet 146 1 Lattice Minkowski decompositions of facet 146
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3836
Image of polytope 3836 PALP id: 3836
grdb id: 110185
Integer points: [ 1 0 1 0 0 -2 1 -2 1 -1 -2 -1 0 -1 0 -1 0 1 -1 0 1]
[ 0 1 -1 0 0 2 -2 0 -3 1 1 0 -1 -1 -2 1 0 -1 0 -1 -2]
[ 0 0 0 1 -1 1 -2 1 -2 0 1 0 -1 0 -1 1 0 -1 1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*x-1*y*z + x-2*y2*z + x*y-1 + 2*x-1*y + 2*x-1*z + 2*x-2*y*z + 2*x*y-1*z-1 + z-1 + 4*y-1 + 5*x-1 + x-2*z + 2*x*y-2*z-1 + 4*y-1*z-1 + 3*x-1*y-1 + x*y-2*z-2 + 3*y-2*z-1 + x*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3837
Image of polytope 3837 PALP id: 3837
grdb id: 108179
Integer points: [ 1 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 1 0 1 0 -1 -2 -4 0 -2 -1 0 -3 -2 -1 -3 -1 0 -2 -1]
[ 0 0 0 1 1 -1 1 -2 -2 1 0 0 0 -1 -1 -1 -2 0 0 -1 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y*z + x-1*y + 2*x-1*z + 3*y-1 + 4*x-1 + x-1*y-1*z + 2*y-1*z-1 + x-1*z-1 + 6*x-1*y-1 + 2*y-2*z-1 + 4*x-1*y-1*z-1 + 3*x-1*y-2 + 6*x-1*y-2*z-1 + x-1*y-2*z-2 + 3*x-1*y-3*z-1 + 2*x-1*y-3*z-2 + x-1*y-4*z-2
39 ? x + y + z + x-1*y*z + x-1*y + 2*x-1*z + 3*y-1 + 5*x-1 + x-1*y-1*z + 2*y-1*z-1 + x-1*z-1 + 7*x-1*y-1 + 2*y-2*z-1 + 5*x-1*y-1*z-1 + 3*x-1*y-2 + 7*x-1*y-2*z-1 + x-1*y-2*z-2 + 3*x-1*y-3*z-1 + 2*x-1*y-3*z-2 + x-1*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 225 1 Lattice Minkowski decompositions of facet 225
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3838
Image of polytope 3838 PALP id: 3838
grdb id: 103584
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 -1 0 -2 0 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 -1 1 1 1 -2 -2 0 -1 1 0 -1 -2 0 -1 0 -1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + y*z-1 + y-1*z + x-1*z + 2*z-1 + 3*y-1 + 3*x-1 + 2*x-1*y-1*z + 2*y-1*z-1 + 3*x-1*z-1 + 6*x-1*y-1 + x-1*y-2*z + x-1*z-2 + 6*x-1*y-1*z-1 + 3*x-1*y-2 + 2*x-1*y-1*z-2 + 3*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Polytope 3839
Image of polytope 3839 PALP id: 3839
grdb id: 105353
Integer points: [ 1 0 0 0 -1 -1 -1 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 0]
[ 0 1 -1 0 1 1 -2 1 -3 -2 -1 0 -2 -1 0 1 -1 0 -1 0 0]
[ 0 0 0 1 0 -1 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y + x-1*y*z-1 + y-1 + 4*x-1 + 3*x-1*z-1 + 2*x-2*y*z-1 + 3*x-1*y-1 + 3*x-1*y-1*z-1 + 7*x-2*z-1 + x-3*y*z-2 + x-1*y-2*z-1 + 8*x-2*y-1*z-1 + 4*x-3*z-2 + 3*x-2*y-2*z-1 + 6*x-3*y-1*z-2 + 4*x-3*y-2*z-2 + x-3*y-3*z-2
36 rank 3, number 7 x + y + z + x-1*y + x-1*y*z-1 + y-1 + 4*x-1 + 4*x-1*z-1 + 2*x-2*y*z-1 + 3*x-1*y-1 + 4*x-1*y-1*z-1 + 7*x-2*z-1 + x-3*y*z-2 + x-1*y-2*z-1 + 8*x-2*y-1*z-1 + 4*x-3*z-2 + 3*x-2*y-2*z-1 + 6*x-3*y-1*z-2 + 4*x-3*y-2*z-2 + x-3*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 93 1 Lattice Minkowski decompositions of facet 93
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Polytope 3840
Image of polytope 3840 PALP id: 3840
grdb id: 100388
Integer points: [ 1 0 0 0 -1 -1 -1 -3 -3 -2 -3 -2 -1 -3 -2 -1 -2 -1 0 -1 0]
[ 0 1 0 -1 1 1 -2 1 -2 -2 -1 -1 -1 0 0 0 1 -1 -1 0 0]
[ 0 0 1 1 0 -1 0 -2 -2 -1 -2 -1 0 -2 -1 0 -1 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + x-1*y + y-1*z + x-1*y*z-1 + 2*y-1 + 5*x-1 + 3*x-1*z-1 + 2*x-2*y*z-1 + 5*x-1*y-1 + 2*x-1*y-1*z-1 + 7*x-2*z-1 + x-1*y-2 + x-3*y*z-2 + 7*x-2*y-1*z-1 + 3*x-3*z-2 + 2*x-2*y-2*z-1 + 3*x-3*y-1*z-2 + x-3*y-2*z-2
17 rank 1, V22 x + y + z + x-1*y + y-1*z + x-1*y*z-1 + 2*y-1 + 4*x-1 + 3*x-1*z-1 + 2*x-2*y*z-1 + 4*x-1*y-1 + 2*x-1*y-1*z-1 + 6*x-2*z-1 + x-1*y-2 + x-3*y*z-2 + 6*x-2*y-1*z-1 + 3*x-3*z-2 + 2*x-2*y-2*z-1 + 3*x-3*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 225 1 Lattice Minkowski decompositions of facet 225
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3841
Image of polytope 3841 PALP id: 3841
grdb id: 102320
Integer points: [ 1 0 0 0 -1 0 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 0 -1 0 -1 -1 -1 -1 -1 0 0 -1 -1 -1 -1 0 0 -1]
[ 0 0 1 1 1 -1 -2 1 -3 0 -1 -2 0 -1 1 0 -1 -2 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + y-1*z + x-1*z + 2*z-1 + 2*y-1 + 3*x-1 + 2*x-1*y-1*z + y-1*z-1 + 3*x-1*z-1 + 6*x-1*y-1 + x-2*y-1*z + x-1*z-2 + 6*x-1*y-1*z-1 + 4*x-2*y-1 + 2*x-1*y-1*z-2 + 6*x-2*y-1*z-1 + 4*x-2*y-1*z-2 + x-2*y-1*z-3
39 ? x + y + z + y-1*z + x-1*z + 2*z-1 + 2*y-1 + 4*x-1 + 2*x-1*y-1*z + y-1*z-1 + 4*x-1*z-1 + 6*x-1*y-1 + x-2*y-1*z + x-1*z-2 + 6*x-1*y-1*z-1 + 4*x-2*y-1 + 2*x-1*y-1*z-2 + 6*x-2*y-1*z-1 + 4*x-2*y-1*z-2 + x-2*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 93 1 Lattice Minkowski decompositions of facet 93
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3842
Image of polytope 3842 PALP id: 3842
grdb id: 100550
Integer points: [ 1 0 0 0 0 0 -1 -1 -4 -2 -3 -1 -2 -3 0 -1 -2 -1 -2 0 -1]
[ 0 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 1 -1 1 -1 1 -2 -2 0 -1 0 -1 -2 0 -1 -2 0 -1 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + y-1*z + z-1 + 2*y-1 + 3*x-1 + x-1*y-1*z + y-1*z-1 + 3*x-1*z-1 + 5*x-1*y-1 + 5*x-1*y-1*z-1 + 2*x-2*z-1 + 3*x-2*y-1 + x-1*y-1*z-2 + 7*x-2*y-1*z-1 + 3*x-2*y-1*z-2 + 3*x-3*y-1*z-1 + 3*x-3*y-1*z-2 + x-4*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 174 1 Lattice Minkowski decompositions of facet 174
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Polytope 3843
Image of polytope 3843 PALP id: 3843
grdb id: 585895
Integer points: [ 1 0 0 -2 2 0 1 -2 2 -3 1 0 -1 0 -1 -2 1 1 0 -1 -1]
[ 0 1 0 2 -2 0 -2 1 -3 2 -2 -1 0 -1 0 1 -1 -1 0 1 1]
[ 0 0 1 1 -1 -1 -2 2 -2 2 -1 0 1 -1 0 1 0 -1 0 1 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
22 ? x + y + z + 3*x-1*y*z + x-2*y2*z + x-2*y*z2 + x-3*y2*z2 + 2*x*y-1 + 2*x-1*y + 4*x-1*z + 4*x-2*y*z + x2*y-2*z-1 + 3*x*y-1*z-1 + z-1 + 6*y-1 + 6*x-1 + 4*x*y-2*z-1 + 4*y-1*z-1 + x2*y-3*z-2 + x*y-2*z-2
7 rank 1, V12 x + y + z + 3*x-1*y*z + x-2*y2*z + x-2*y*z2 + x-3*y2*z2 + 2*x*y-1 + 2*x-1*y + 4*x-1*z + 4*x-2*y*z + x2*y-2*z-1 + 2*x*y-1*z-1 + z-1 + 6*y-1 + 6*x-1 + 4*x*y-2*z-1 + 4*y-1*z-1 + x2*y-3*z-2 + x*y-2*z-2
11 rank 2, number 6 x + y + z + 2*x-1*y*z + x-2*y2*z + x-2*y*z2 + x-3*y2*z2 + 2*x*y-1 + 2*x-1*y + 4*x-1*z + 4*x-2*y*z + x2*y-2*z-1 + 2*x*y-1*z-1 + z-1 + 6*y-1 + 6*x-1 + 4*x*y-2*z-1 + 4*y-1*z-1 + x2*y-3*z-2 + x*y-2*z-2
7 rank 1, V12 x + y + z + 2*x-1*y*z + x-2*y2*z + x-2*y*z2 + x-3*y2*z2 + 2*x*y-1 + 2*x-1*y + 4*x-1*z + 4*x-2*y*z + x2*y-2*z-1 + 3*x*y-1*z-1 + z-1 + 6*y-1 + 6*x-1 + 4*x*y-2*z-1 + 4*y-1*z-1 + x2*y-3*z-2 + x*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 24 2 Lattice Minkowski decompositions of facet 24
Image of facet 1 2 irreducible and admissible
Image of facet 59 2 Lattice Minkowski decompositions of facet 59
Image of facet 134 1 Lattice Minkowski decompositions of facet 134
Polytope 3844
Image of polytope 3844 PALP id: 3844
grdb id: 585890
Integer points: [ 1 0 1 0 -1 -1 0 0 -1 -1 -1 -1 0 0 -1 -1 -1 0 0 0 1]
[ 0 1 0 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0]
[ 0 0 2 1 -1 0 -2 1 -3 0 -1 -2 0 -1 0 -1 -2 1 0 -1 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x*z2 + 2*x*z + y*z + x + y + 2*z + x-1*y + y-1*z + 3*z-1 + x-1*y*z-1 + 3*y-1 + 2*x-1 + 3*y-1*z-1 + 4*x-1*z-1 + x-1*y-1 + y-1*z-2 + 2*x-1*z-2 + 3*x-1*y-1*z-1 + 3*x-1*y-1*z-2 + x-1*y-1*z-3
11 rank 2, number 6 x*z2 + 2*x*z + y*z + x + y + 2*z + x-1*y + y-1*z + 2*z-1 + x-1*y*z-1 + 3*y-1 + 2*x-1 + 3*y-1*z-1 + 4*x-1*z-1 + x-1*y-1 + y-1*z-2 + 2*x-1*z-2 + 3*x-1*y-1*z-1 + 3*x-1*y-1*z-2 + x-1*y-1*z-3
7 rank 1, V12 x*z2 + 2*x*z + y*z + x + y + 3*z + x-1*y + y-1*z + 2*z-1 + x-1*y*z-1 + 3*y-1 + 2*x-1 + 3*y-1*z-1 + 4*x-1*z-1 + x-1*y-1 + y-1*z-2 + 2*x-1*z-2 + 3*x-1*y-1*z-1 + 3*x-1*y-1*z-2 + x-1*y-1*z-3
22 ? x*z2 + 2*x*z + y*z + x + y + 3*z + x-1*y + y-1*z + 3*z-1 + x-1*y*z-1 + 3*y-1 + 2*x-1 + 3*y-1*z-1 + 4*x-1*z-1 + x-1*y-1 + y-1*z-2 + 2*x-1*z-2 + 3*x-1*y-1*z-1 + 3*x-1*y-1*z-2 + x-1*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 23 2 Lattice Minkowski decompositions of facet 23
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3845
Image of polytope 3845 PALP id: 3845
grdb id: 585897
Integer points: [ 1 1 0 0 0 0 -1 -1 -1 -1 -1 0 -1 0 -1 0 1 -1 0 -1 0]
[ 0 2 0 2 -2 0 -1 1 -3 -1 0 1 0 1 -1 0 1 -2 -1 -2 -1]
[ 0 0 1 1 -1 -1 1 1 -1 -1 1 1 0 0 0 0 0 0 0 -1 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
11 rank 2, number 6 x*y2 + y2*z + 2*x*y + 2*y*z + x + 2*y + z + x-1*y*z + 2*x-1*z + z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + 2*y-1*z-1 + 4*x-1*y-1 + y-2*z-1 + x-1*y-1*z-1 + 2*x-1*y-2 + 2*x-1*y-2*z-1 + x-1*y-3*z-1
7 rank 1, V12 x*y2 + y2*z + 2*x*y + 2*y*z + x + 3*y + z + x-1*y*z + 2*x-1*z + z-1 + 2*y-1 + 2*x-1 + x-1*y-1*z + 2*y-1*z-1 + 4*x-1*y-1 + y-2*z-1 + x-1*y-1*z-1 + 2*x-1*y-2 + 2*x-1*y-2*z-1 + x-1*y-3*z-1
7 rank 1, V12 x*y2 + y2*z + 2*x*y + 2*y*z + x + 2*y + z + x-1*y*z + 2*x-1*z + z-1 + 3*y-1 + 2*x-1 + x-1*y-1*z + 2*y-1*z-1 + 4*x-1*y-1 + y-2*z-1 + x-1*y-1*z-1 + 2*x-1*y-2 + 2*x-1*y-2*z-1 + x-1*y-3*z-1
22 ? x*y2 + y2*z + 2*x*y + 2*y*z + x + 3*y + z + x-1*y*z + 2*x-1*z + z-1 + 3*y-1 + 2*x-1 + x-1*y-1*z + 2*y-1*z-1 + 4*x-1*y-1 + y-2*z-1 + x-1*y-1*z-1 + 2*x-1*y-2 + 2*x-1*y-2*z-1 + x-1*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 15 4 Lattice Minkowski decompositions of facet 15
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 23 2 Lattice Minkowski decompositions of facet 23
Polytope 3846
Image of polytope 3846 PALP id: 3846
grdb id: 585232
Integer points: [ 1 0 0 -1 0 -2 1 -2 1 0 -1 -1 -1 0 0 1 -1 0 0 1 1]
[ 0 1 0 1 -1 1 -2 1 -2 -1 0 0 0 -1 -1 -2 1 0 0 -1 -1]
[ 0 0 1 1 1 1 0 0 -2 -2 1 0 -1 0 -1 -1 0 0 -1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
51 rank 2, number 7 x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + 2*x*y-1*z-1 + 2*z-1 + x*y-2 + 5*y-1 + 5*x-1 + x-2*y + 2*x*y-2*z-1 + 5*y-1*z-1 + 2*x-1*z-1 + x*y-2*z-2 + y-1*z-2
18 rank 1, V14 x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + 2*x*y-1*z-1 + 2*z-1 + x*y-2 + 4*y-1 + 4*x-1 + x-2*y + 2*x*y-2*z-1 + 4*y-1*z-1 + 2*x-1*z-1 + x*y-2*z-2 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 164 1 Lattice Minkowski decompositions of facet 164
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3847
Image of polytope 3847 PALP id: 3847
grdb id: 585514
Integer points: [ 1 0 0 0 2 -1 1 -1 -2 -2 0 -1 1 0 0 -1 -2 1 0 -1 -1]
[ 0 1 0 1 -1 1 -1 -1 1 -1 -1 -1 -1 -1 0 0 0 0 0 0 1]
[ 0 0 1 -1 -1 -1 -1 2 0 2 0 1 0 1 -1 0 1 -1 0 1 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + x2*y-1*z-1 + 2*x*z-1 + y*z-1 + 3*x*y-1 + 2*x-1*y + 3*y-1*z + 3*x-1*z + x-1*y-1*z2 + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 3*y-1 + 4*x-1 + x-2*y + 3*x-1*y-1*z + 2*x-2*z + x-2*y-1*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3848
Image of polytope 3848 PALP id: 3848
grdb id: 585544
Integer points: [ 1 0 0 1 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 0 0]
[ 0 1 0 -1 0 2 -2 2 1 -2 1 -1 0 1 -1 0 1 -1 0 -1 0]
[ 0 0 1 0 1 -1 1 -2 -2 1 0 1 0 -1 1 0 -1 0 -1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*y*z-1 + x-1*y2*z-1 + x*y-1 + 2*x-1*y + 2*y-1*z + x-1*z + x-1*y2*z-2 + 2*z-1 + 4*x-1*y*z-1 + 3*y-1 + 5*x-1 + y-2*z + 2*x-1*y-1*z + x-1*y*z-2 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3849
Image of polytope 3849 PALP id: 3849
grdb id: 585571
Integer points: [ 1 0 0 1 0 0 -1 0 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 1 -1 2 -1 2 -1 1 0 1 0 -1 1 0 -1 0 -1 0]
[ 0 0 1 0 -1 1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + y*z-1 + x-1*y2*z-1 + x*y-1 + 2*x-1*y + y-1*z + 2*z-1 + 4*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 4*x-1 + y-1*z-1 + 5*x-1*z-1 + 3*x-2*y*z-1 + 2*x-1*y-1 + 2*x-1*y-1*z-1 + 3*x-2*z-1 + x-2*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3850
Image of polytope 3850 PALP id: 3850
grdb id: 585038
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 -1 0 2 0 -2 -2 1 3 2 1 2 1 0 -1 0 -1 1 0 -1]
[ 0 0 0 1 1 -1 -1 -2 2 2 1 0 2 1 0 -1 1 0 1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x-1*y3*z2 + y2*z + 2*x-1*y2*z2 + 2*y*z + 3*x-1*y2*z + x-1*y*z2 + x + y + z + 6*x-1*y*z + 3*x-1*y + 3*x-1*z + y-1 + 7*x-1 + 2*y-1*z-1 + x-1*z-1 + 3*x-1*y-1 + 4*x-1*y-1*z-1 + x-1*y-2*z-1 + x-1*y-2*z-2
161 ? x-1*y3*z2 + y2*z + 2*x-1*y2*z2 + 3*y*z + 3*x-1*y2*z + x-1*y*z2 + x + y + z + 7*x-1*y*z + 3*x-1*y + 3*x-1*z + y-1 + 9*x-1 + 2*y-1*z-1 + x-1*z-1 + 3*x-1*y-1 + 5*x-1*y-1*z-1 + x-1*y-2*z-1 + x-1*y-2*z-2
40 rank 2, number 10 x-1*y3*z2 + y2*z + 2*x-1*y2*z2 + 2*y*z + 3*x-1*y2*z + x-1*y*z2 + x + y + z + 7*x-1*y*z + 3*x-1*y + 3*x-1*z + y-1 + 9*x-1 + 2*y-1*z-1 + x-1*z-1 + 3*x-1*y-1 + 5*x-1*y-1*z-1 + x-1*y-2*z-1 + x-1*y-2*z-2
40 rank 2, number 10 x-1*y3*z2 + y2*z + 2*x-1*y2*z2 + 3*y*z + 3*x-1*y2*z + x-1*y*z2 + x + y + z + 6*x-1*y*z + 3*x-1*y + 3*x-1*z + y-1 + 7*x-1 + 2*y-1*z-1 + x-1*z-1 + 3*x-1*y-1 + 4*x-1*y-1*z-1 + x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 178 1 Lattice Minkowski decompositions of facet 178
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 3851
Image of polytope 3851 PALP id: 3851
grdb id: 585519
Integer points: [ 1 0 0 -1 -1 -2 2 -2 2 0 0 1 1 -1 0 1 0 1 -1 -1 0]
[ 0 1 0 1 1 1 -1 0 -2 -2 0 -1 0 0 -1 -2 0 -1 -1 0 -1]
[ 0 0 1 1 0 1 -2 1 -3 -1 -1 -2 -1 0 -1 -2 0 -1 0 1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x-1*y*z + 2*x*z-1 + x-1*y + 2*x-1*z + x-2*y*z + x2*y-1*z-2 + 3*x*y-1*z-1 + 3*z-1 + 2*y-1 + 4*x-1 + x-2*z + 3*x*y-1*z-2 + 5*y-1*z-1 + 2*x-1*y-1 + x2*y-2*z-3 + 2*x*y-2*z-2 + y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3852
Image of polytope 3852 PALP id: 3852
grdb id: 585548
Integer points: [ 1 0 0 -1 2 2 0 -2 -1 -3 -2 -1 -1 0 1 1 -2 -1 0 0 1]
[ 0 1 0 1 -1 -1 -1 1 -1 1 1 1 0 0 0 -1 0 0 0 -1 -1]
[ 0 0 1 1 -1 -2 1 0 1 1 1 0 1 0 -1 0 1 0 -1 0 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + x-1*y*z + x2*y-1*z-1 + 2*x*z-1 + 2*x*y-1 + 2*x-1*y + y-1*z + 3*x-1*z + 2*x-2*y*z + x2*y-1*z-2 + 3*x*y-1*z-1 + 2*z-1 + 3*y-1 + 4*x-1 + x-2*y + x-1*y-1*z + 2*x-2*z + x-3*y*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3853
Image of polytope 3853 PALP id: 3853
grdb id: 584967
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 -2 2 0 2 -2 -3 1 0 -1 -2 1 0 -1 1 -1 1 0 -1]
[ 0 0 1 -1 1 -1 2 -2 -2 2 1 0 -1 1 0 -1 0 0 1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x-1*y2*z2 + 2*y*z + x-1*y2*z + x-1*y*z2 + x + y + z + 4*x-1*y*z + 2*x-1*y + 4*x-1*z + 2*y-1 + 6*x-1 + 2*y-1*z-1 + x-1*z-1 + 6*x-1*y-1 + y-2*z-1 + 4*x-1*y-1*z-1 + 4*x-1*y-2*z-1 + x-1*y-2*z-2 + x-1*y-3*z-2
40 rank 2, number 10 x-1*y2*z2 + 2*y*z + x-1*y2*z + x-1*y*z2 + x + y + z + 5*x-1*y*z + 2*x-1*y + 4*x-1*z + 2*y-1 + 8*x-1 + 2*y-1*z-1 + x-1*z-1 + 6*x-1*y-1 + y-2*z-1 + 5*x-1*y-1*z-1 + 4*x-1*y-2*z-1 + x-1*y-2*z-2 + x-1*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 187 1 Lattice Minkowski decompositions of facet 187
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Polytope 3854
Image of polytope 3854 PALP id: 3854
grdb id: 585566
Integer points: [ 1 0 0 0 0 -1 1 -1 0 -3 -1 -2 0 -1 -2 0 -1 -2 1 0 -1]
[ 0 1 0 1 -1 2 -2 0 -1 2 0 1 -1 0 1 0 1 2 -1 0 1]
[ 0 0 1 -1 1 -1 0 1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + y*z-1 + x-1*y2*z-1 + 2*x*y-1 + 3*x-1*y + y-1*z + x-1*z + 2*z-1 + 4*x-1*y*z-1 + 2*x-2*y2*z-1 + x*y-2 + 3*y-1 + 4*x-1 + 2*x-2*y + y-1*z-1 + 3*x-1*z-1 + 3*x-2*y*z-1 + x-3*y2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3855
Image of polytope 3855 PALP id: 3855
grdb id: 584997
Integer points: [ 1 0 0 0 1 -1 1 1 -2 -3 -2 -1 0 -1 0 1 -2 -1 0 -1 0]
[ 0 1 0 -1 -1 0 -2 -2 2 2 1 0 -1 1 0 -1 1 0 -1 1 0]
[ 0 0 1 1 -1 1 0 -1 -1 -1 0 0 0 0 0 0 -1 -1 -1 -1 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
51 rank 2, number 7 x + y + z + 2*x*y-1 + 3*x-1*y + y-1*z + x-1*z + x*y-1*z-1 + 3*z-1 + 3*x-1*y*z-1 + x-2*y2*z-1 + x*y-2 + 4*y-1 + 5*x-1 + 2*x-2*y + x*y-2*z-1 + 4*y-1*z-1 + 6*x-1*z-1 + 4*x-2*y*z-1 + x-3*y2*z-1
18 rank 1, V14 x + y + z + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + x*y-1*z-1 + 3*z-1 + 3*x-1*y*z-1 + x-2*y2*z-1 + x*y-2 + 4*y-1 + 5*x-1 + 2*x-2*y + x*y-2*z-1 + 4*y-1*z-1 + 6*x-1*z-1 + 4*x-2*y*z-1 + x-3*y2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 3856
Image of polytope 3856 PALP id: 3856
grdb id: 585686
Integer points: [ 1 0 0 -1 -2 2 -2 2 -3 3 -1 1 -2 0 2 -1 1 0 -1 1 0]
[ 0 1 0 1 1 -1 0 -2 1 -2 1 0 1 0 -1 0 -1 0 0 -1 -1]
[ 0 0 1 1 0 -2 1 -1 1 -2 0 -1 1 0 -1 1 0 -1 0 -1 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + x-1*y*z + 2*x2*y-1*z-1 + 2*x*z-1 + 2*x*y-1 + 2*x-1*y + 2*x-1*z + 2*x-2*y*z + x3*y-2*z-2 + x2*y-1*z-2 + x2*y-2*z-1 + 4*x*y-1*z-1 + 2*z-1 + 2*y-1 + 4*x-1 + x-2*y + x-2*z + x-3*y*z
11 rank 2, number 6 x + y + z + x-1*y*z + 2*x2*y-1*z-1 + 2*x*z-1 + 2*x*y-1 + 2*x-1*y + 2*x-1*z + 2*x-2*y*z + x3*y-2*z-2 + x2*y-1*z-2 + x2*y-2*z-1 + 3*x*y-1*z-1 + 2*z-1 + 2*y-1 + 3*x-1 + x-2*y + x-2*z + x-3*y*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 96 1 Lattice Minkowski decompositions of facet 96
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 15 4 Lattice Minkowski decompositions of facet 15
Polytope 3857
Image of polytope 3857 PALP id: 3857
grdb id: 579004
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 -1 1 -2 1 0 -2 1 1 0 0 0 -1 -1 -1 0 0 -1]
[ 0 0 1 -1 1 1 1 -2 -2 0 0 -1 1 0 -1 1 0 -1 0 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y*z + y*z-1 + 3*x-1*y + y-1*z + 3*x-1*z + 2*z-1 + 3*x-1*y*z-1 + 2*y-1 + 7*x-1 + 3*x-1*y-1*z + x-1*y*z-2 + 5*x-1*z-1 + 5*x-1*y-1 + x-1*y-2*z + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 174 1 Lattice Minkowski decompositions of facet 174
Polytope 3858
Image of polytope 3858 PALP id: 3858
grdb id: 579032
Integer points: [ 1 0 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 1 1 -1 -1 -2 -2 -2 -2 -1 -1 -1 0 0 0 -1 -1 0]
[ 0 0 1 -1 0 -1 -1 2 -1 2 0 1 -1 0 1 -1 0 1 0 1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + z-1 + x-1*y*z-1 + 3*y-1 + 5*x-1 + 5*x-1*y-1*z + x-1*y-2*z2 + y-1*z-1 + 3*x-1*z-1 + 7*x-1*y-1 + 3*x-1*y-2*z + 3*x-1*y-1*z-1 + 3*x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 174 1 Lattice Minkowski decompositions of facet 174
Polytope 3859
Image of polytope 3859 PALP id: 3859
grdb id: 580257
Integer points: [ 1 0 0 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 -1 1 -1 -1 1 -1 -1 -1 -1 0 0 0 0 1 -1 0 0]
[ 0 0 1 -1 1 0 -1 2 -2 -2 -1 0 1 -2 -1 0 1 -1 0 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + y*z-1 + x-1*y + y-1*z + 2*x-1*z + x-1*y-1*z2 + 2*z-1 + 2*x-1*y*z-1 + 2*y-1 + 6*x-1 + 4*x-1*y-1*z + x-1*y*z-2 + y-1*z-1 + 6*x-1*z-1 + 6*x-1*y-1 + 2*x-1*z-2 + 4*x-1*y-1*z-1 + x-1*y-1*z-2
20 rank 1, V16 x + y + z + y*z-1 + x-1*y + y-1*z + 2*x-1*z + x-1*y-1*z2 + 3*z-1 + 2*x-1*y*z-1 + 2*y-1 + 6*x-1 + 4*x-1*y-1*z + x-1*y*z-2 + y-1*z-1 + 6*x-1*z-1 + 6*x-1*y-1 + 2*x-1*z-2 + 4*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3860
Image of polytope 3860 PALP id: 3860
grdb id: 580376
Integer points: [ 1 0 0 0 0 0 -1 -1 -2 -2 -2 -2 -2 -1 -1 -1 0 -1 -1 -1 0]
[ 0 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 1 -1 -1 1 -2 2 2 -2 -1 0 1 -1 0 1 0 -1 0 1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + y-1*z + 2*x-1*z + x-1*y-1*z2 + z-1 + 2*y-1 + 4*x-1 + 5*x-1*y-1*z + x-2*y-1*z2 + y-1*z-1 + 2*x-1*z-1 + 8*x-1*y-1 + 4*x-2*y-1*z + 5*x-1*y-1*z-1 + 6*x-2*y-1 + x-1*y-1*z-2 + 4*x-2*y-1*z-1 + x-2*y-1*z-2
13 rank 2, number 12 x + y + z + y-1*z + 2*x-1*z + x-1*y-1*z2 + z-1 + 2*y-1 + 4*x-1 + 4*x-1*y-1*z + x-2*y-1*z2 + y-1*z-1 + 2*x-1*z-1 + 6*x-1*y-1 + 4*x-2*y-1*z + 4*x-1*y-1*z-1 + 6*x-2*y-1 + x-1*y-1*z-2 + 4*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 187 1 Lattice Minkowski decompositions of facet 187
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 3861
Image of polytope 3861 PALP id: 3861
grdb id: 580364
Integer points: [ 1 0 0 0 0 0 -1 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -1 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 0 1 -1 1 0 2 -2 2 -2 -1 0 1 -1 0 1 -1 0 1 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + y*z-1 + y-1*z + 2*x-1*z + x-1*y-1*z2 + 2*z-1 + y-1 + 5*x-1 + 4*x-1*y-1*z + x-2*y-1*z2 + 4*x-1*z-1 + 5*x-1*y-1 + 4*x-2*y-1*z + x-1*z-2 + 2*x-1*y-1*z-1 + 6*x-2*y-1 + 4*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 107 2 Lattice Minkowski decompositions of facet 107
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3862
Image of polytope 3862 PALP id: 3862
grdb id: 580301
Integer points: [ 1 0 0 0 -1 0 -1 0 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 1 -1 1 -1 1 -3 -2 -1 0 -2 -1 0 -2 -1 0 -1 0]
[ 0 0 1 -1 0 1 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y + y-1*z + z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + y-1*z-1 + 4*x-1*z-1 + x-2*y*z-1 + 5*x-1*y-1 + 5*x-1*y-1*z-1 + 4*x-2*z-1 + 2*x-1*y-2 + 2*x-1*y-2*z-1 + 6*x-2*y-1*z-1 + 4*x-2*y-2*z-1 + x-2*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 107 2 Lattice Minkowski decompositions of facet 107
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Polytope 3863
Image of polytope 3863 PALP id: 3863
grdb id: 582522
Integer points: [ 1 0 0 1 0 0 -1 -2 0 -2 0 -1 -1 -1 -2 -2 0 0 -1 -1 -1]
[ 0 1 0 0 1 -1 1 0 -1 -3 0 -2 -1 0 -2 -1 -1 0 -2 -1 0]
[ 0 0 1 -1 -1 1 0 1 -1 1 -1 0 0 0 1 1 0 0 1 1 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x*z-1 + y*z-1 + x-1*y + y-1*z + 2*x-1*z + 2*z-1 + 3*y-1 + 4*x-1 + 4*x-1*y-1*z + x-2*z + y-1*z-1 + 5*x-1*y-1 + 2*x-1*y-2*z + 3*x-2*y-1*z + 2*x-1*y-2 + 3*x-2*y-2*z + x-2*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3864
Image of polytope 3864 PALP id: 3864
grdb id: 582645
Integer points: [ 1 0 0 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 0 2 0 -2 -1 -3 0 1 -2 -1 0 1 -2 -1 -1 0 -1]
[ 0 0 1 -1 -1 -1 1 1 -1 1 -1 -1 0 0 0 0 1 1 0 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + y*z-1 + x-1*y2*z-1 + 2*x-1*y + 2*y-1*z + x-1*z + z-1 + 3*x-1*y*z-1 + 2*y-1 + 6*x-1 + y-2*z + 3*x-1*y-1*z + 3*x-1*z-1 + 6*x-1*y-1 + 3*x-1*y-2*z + x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-3*z
20 rank 1, V16 x + y + z + y*z-1 + x-1*y2*z-1 + 2*x-1*y + 2*y-1*z + x-1*z + z-1 + 3*x-1*y*z-1 + 3*y-1 + 6*x-1 + y-2*z + 3*x-1*y-1*z + 3*x-1*z-1 + 6*x-1*y-1 + 3*x-1*y-2*z + x-1*y-1*z-1 + 2*x-1*y-2 + x-1*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Polytope 3865
Image of polytope 3865 PALP id: 3865
grdb id: 580302
Integer points: [ 1 0 1 -1 0 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 -1 1 0 1 -2 0 0 -4 -1 -2 -3 0 -1 -2 -1 -2 -3 0 -1]
[ 0 0 0 0 1 1 -1 -1 1 -3 0 -1 -2 0 -1 -2 0 -1 -2 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + x*y-1 + x-1*y + x-1*z + 4*y-1 + 4*x-1 + x*y-2*z-1 + 3*y-1*z-1 + x-1*z-1 + 4*x-1*y-1 + 5*y-2*z-1 + 5*x-1*y-1*z-1 + 6*x-1*y-2*z-1 + 2*y-3*z-2 + 2*x-1*y-2*z-2 + 4*x-1*y-3*z-2 + x-1*y-4*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 107 2 Lattice Minkowski decompositions of facet 107
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3866
Image of polytope 3866 PALP id: 3866
grdb id: 29610
Integer points: [ 1 0 0 -1 1 0 1 1 -1 -2 -2 -1 -2 -1 0 -1 0 1 -1 0 0]
[ 0 1 0 1 -1 -1 -2 -2 1 1 1 0 1 0 -1 1 0 -1 0 -1 0]
[ 0 0 1 1 -1 1 0 -1 -1 1 -1 1 0 0 0 0 0 0 -1 -1 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
51 rank 2, number 7 x + y + z + x-1*y*z + 2*x*y-1 + 3*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + x*y-2 + 4*y-1 + 5*x-1 + 2*x-2*y + x*y-2*z-1 + 3*y-1*z-1 + 3*x-1*z-1 + x-2*y*z-1
18 rank 1, V14 x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + x*y-2 + 4*y-1 + 5*x-1 + 2*x-2*y + x*y-2*z-1 + 3*y-1*z-1 + 3*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 3867
Image of polytope 3867 PALP id: 3867
grdb id: 29624
Integer points: [ 1 0 0 1 1 1 1 -2 -2 1 -3 0 -1 -2 0 -1 0 -1 1 0 -1]
[ 0 1 0 0 -1 -1 -2 2 1 -2 2 -1 0 1 0 1 -1 0 -1 0 1]
[ 0 0 1 -1 0 -2 -1 1 2 -2 2 -1 0 1 -1 0 0 1 -1 0 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + 2*x-1*y*z + x-2*y2*z + x-2*y*z2 + x-3*y2*z2 + x*z-1 + x*y-1 + 3*x-1*y + 3*x-1*z + 4*x-2*y*z + 3*x*y-1*z-1 + 3*z-1 + 3*y-1 + 6*x-1 + x*y-1*z-2 + x*y-2*z-1 + 4*y-1*z-1 + x*y-2*z-2
7 rank 1, V12 x + y + z + 3*x-1*y*z + x-2*y2*z + x-2*y*z2 + x-3*y2*z2 + x*z-1 + x*y-1 + 3*x-1*y + 3*x-1*z + 4*x-2*y*z + 2*x*y-1*z-1 + 3*z-1 + 3*y-1 + 6*x-1 + x*y-1*z-2 + x*y-2*z-1 + 4*y-1*z-1 + x*y-2*z-2
11 rank 2, number 6 x + y + z + 2*x-1*y*z + x-2*y2*z + x-2*y*z2 + x-3*y2*z2 + x*z-1 + x*y-1 + 3*x-1*y + 3*x-1*z + 4*x-2*y*z + 2*x*y-1*z-1 + 3*z-1 + 3*y-1 + 6*x-1 + x*y-1*z-2 + x*y-2*z-1 + 4*y-1*z-1 + x*y-2*z-2
22 ? x + y + z + 3*x-1*y*z + x-2*y2*z + x-2*y*z2 + x-3*y2*z2 + x*z-1 + x*y-1 + 3*x-1*y + 3*x-1*z + 4*x-2*y*z + 3*x*y-1*z-1 + 3*z-1 + 3*y-1 + 6*x-1 + x*y-1*z-2 + x*y-2*z-1 + 4*y-1*z-1 + x*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 24 2 Lattice Minkowski decompositions of facet 24
Image of facet 90 2 Lattice Minkowski decompositions of facet 90
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Polytope 3868
Image of polytope 3868 PALP id: 3868
grdb id: 29628
Integer points: [ 1 0 1 0 0 -1 1 1 -2 0 -2 -1 0 -1 0 1 -1 0 1 -1 0]
[ 0 1 -1 0 0 2 -2 -3 3 -2 2 0 -1 1 -1 -2 1 0 -1 2 1]
[ 0 0 0 1 -1 2 -2 -2 2 -1 1 0 -1 0 0 -1 1 0 -1 1 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x-1*y2*z2 + x-2*y3*z2 + 2*y*z + 2*x-1*y2*z + x + y + z + 3*x-1*y*z + x-2*y2*z + x*y-1 + 2*x-1*y + 2*x*y-1*z-1 + z-1 + 2*y-1 + 2*x-1 + 2*x*y-2*z-1 + 3*y-1*z-1 + x*y-2*z-2 + y-2*z-1 + x*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Image of facet 15 4 Lattice Minkowski decompositions of facet 15
Polytope 3869
Image of polytope 3869 PALP id: 3869
grdb id: 28871
Integer points: [ 1 0 0 1 0 1 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 0 1 -1 1 -1 -1 1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 0 1 -1 -1 0 0 2 -1 -1 -1 0 1 -1 0 1 -1 0 1 -1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x*z-1 + y*z-1 + x*y-1 + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + x*y-1*z-1 + 3*z-1 + x-1*y*z-1 + 4*y-1 + 4*x-1 + 3*x-1*y-1*z + 2*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Polytope 3870
Image of polytope 3870 PALP id: 3870
grdb id: 28930
Integer points: [ 1 0 0 0 0 -1 1 1 -2 -2 1 -1 0 1 -1 0 1 -1 0 -1 0]
[ 0 1 0 1 -1 1 -1 0 0 -1 -1 -1 -1 -1 0 0 0 -1 -1 0 0]
[ 0 0 1 -1 1 0 0 -2 1 1 -2 1 0 -1 1 0 -1 0 -1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*x*z-1 + y*z-1 + x*y-1 + x-1*y + y-1*z + 2*x-1*z + x*z-2 + 2*x*y-1*z-1 + 3*z-1 + 4*y-1 + 3*x-1 + 2*x-1*y-1*z + x-2*z + x*y-1*z-2 + 3*y-1*z-1 + 3*x-1*y-1 + x-2*y-1*z
51 rank 2, number 7 x + y + z + 2*x*z-1 + y*z-1 + x*y-1 + x-1*y + y-1*z + 2*x-1*z + x*z-2 + 2*x*y-1*z-1 + 4*z-1 + 4*y-1 + 4*x-1 + 2*x-1*y-1*z + x-2*z + x*y-1*z-2 + 3*y-1*z-1 + 3*x-1*y-1 + x-2*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3871
Image of polytope 3871 PALP id: 3871
grdb id: 28869
Integer points: [ 1 0 0 1 1 -1 -1 0 -1 1 -1 -1 -1 -1 -1 0 0 0 0 0 1]
[ 0 1 0 0 -1 1 0 -1 -1 -1 -1 -1 -1 0 0 -1 -1 -1 0 0 -1]
[ 0 0 1 -1 0 0 1 1 1 -2 -2 0 -1 0 -1 0 -1 -2 0 -1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x*z-1 + x*y-1 + x-1*y + y-1*z + x-1*z + 2*x*y-1*z-1 + 3*z-1 + 4*y-1 + 3*x-1 + x-1*y-1*z + x*y-1*z-2 + 5*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1 + 2*y-1*z-2 + 3*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3872
Image of polytope 3872 PALP id: 3872
grdb id: 28187
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 -1 -1 2 -2 1 -2 2 -1 0 -1 0 1 0 1 -1 0 1]
[ 0 0 1 -1 0 -2 1 -1 2 -2 2 0 1 -1 0 1 -1 0 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x-1*y2*z2 + 2*y*z + x-1*y2*z + x-1*y*z2 + x + y + z + 4*x-1*y*z + 3*x-1*y + 3*x-1*z + z-1 + y-1 + 6*x-1 + 2*y-1*z-1 + 3*x-1*z-1 + 3*x-1*y-1 + 4*x-1*y-1*z-1 + x-1*y-1*z-2 + x-1*y-2*z-1 + x-1*y-2*z-2
40 rank 2, number 10 x-1*y2*z2 + 2*y*z + x-1*y2*z + x-1*y*z2 + x + y + z + 5*x-1*y*z + 3*x-1*y + 3*x-1*z + z-1 + y-1 + 8*x-1 + 2*y-1*z-1 + 3*x-1*z-1 + 3*x-1*y-1 + 5*x-1*y-1*z-1 + x-1*y-1*z-2 + x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 188 1 Lattice Minkowski decompositions of facet 188
Polytope 3873
Image of polytope 3873 PALP id: 3873
grdb id: 5953
Integer points: [ 1 0 0 -1 0 -2 2 0 2 1 -1 -2 -1 -1 0 1 1 -1 0 0 1]
[ 0 1 0 1 -1 1 -1 1 -1 0 -1 0 1 0 0 0 -1 0 0 -1 -1]
[ 0 0 1 1 1 1 -1 -1 -2 -2 1 1 0 1 0 -1 0 0 -1 0 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + x-1*y*z + x2*y-1*z-1 + 3*x*z-1 + y*z-1 + 2*x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + x2*y-1*z-2 + x*z-2 + 3*x*y-1*z-1 + 3*z-1 + 3*y-1 + 3*x-1 + x-1*y-1*z + x-2*z
11 rank 2, number 6 x + y + z + x-1*y*z + x2*y-1*z-1 + 2*x*z-1 + y*z-1 + 2*x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + x2*y-1*z-2 + x*z-2 + 3*x*y-1*z-1 + 3*z-1 + 3*y-1 + 3*x-1 + x-1*y-1*z + x-2*z
7 rank 1, V12 x + y + z + x-1*y*z + x2*y-1*z-1 + 2*x*z-1 + y*z-1 + 2*x*y-1 + 2*x-1*y + y-1*z + 3*x-1*z + x-2*y*z + x2*y-1*z-2 + x*z-2 + 3*x*y-1*z-1 + 3*z-1 + 3*y-1 + 3*x-1 + x-1*y-1*z + x-2*z
22 ? x + y + z + x-1*y*z + x2*y-1*z-1 + 3*x*z-1 + y*z-1 + 2*x*y-1 + 2*x-1*y + y-1*z + 3*x-1*z + x-2*y*z + x2*y-1*z-2 + x*z-2 + 3*x*y-1*z-1 + 3*z-1 + 3*y-1 + 3*x-1 + x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 24 2 Lattice Minkowski decompositions of facet 24
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 3874
Image of polytope 3874 PALP id: 3874
grdb id: 5954
Integer points: [ 1 0 0 -2 -2 -3 3 2 2 0 0 -1 2 1 1 1 0 -1 -1 -1 -2]
[ 0 1 0 2 1 2 -2 -1 -2 0 -1 0 -1 0 -1 -1 0 1 1 0 1]
[ 0 0 1 1 2 2 -2 -2 -1 -1 0 0 -1 -1 -1 0 0 0 1 1 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
11 rank 2, number 6 x + y + z + 2*x-1*y*z + x-2*y2*z + x-2*y*z2 + x-3*y2*z2 + 2*x2*y-1*z-1 + 2*x*z-1 + 2*x*y-1 + 2*x-1*y + 2*x-1*z + 2*x-2*y*z + x3*y-2*z-2 + x2*y-1*z-2 + x2*y-2*z-1 + 2*x*y-1*z-1 + z-1 + y-1 + x-1
22 ? x + y + z + 3*x-1*y*z + x-2*y2*z + x-2*y*z2 + x-3*y2*z2 + 2*x2*y-1*z-1 + 2*x*z-1 + 2*x*y-1 + 2*x-1*y + 2*x-1*z + 2*x-2*y*z + x3*y-2*z-2 + x2*y-1*z-2 + x2*y-2*z-1 + 3*x*y-1*z-1 + z-1 + y-1 + x-1
7 rank 1, V12 x + y + z + 2*x-1*y*z + x-2*y2*z + x-2*y*z2 + x-3*y2*z2 + 2*x2*y-1*z-1 + 2*x*z-1 + 2*x*y-1 + 2*x-1*y + 2*x-1*z + 2*x-2*y*z + x3*y-2*z-2 + x2*y-1*z-2 + x2*y-2*z-1 + 3*x*y-1*z-1 + z-1 + y-1 + x-1
7 rank 1, V12 x + y + z + 3*x-1*y*z + x-2*y2*z + x-2*y*z2 + x-3*y2*z2 + 2*x2*y-1*z-1 + 2*x*z-1 + 2*x*y-1 + 2*x-1*y + 2*x-1*z + 2*x-2*y*z + x3*y-2*z-2 + x2*y-1*z-2 + x2*y-2*z-1 + 2*x*y-1*z-1 + z-1 + y-1 + x-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 24 2 Lattice Minkowski decompositions of facet 24
Image of facet 15 6 Lattice Minkowski decompositions of facet 15
Polytope 3875
Image of polytope 3875 PALP id: 3875
grdb id: 5946
Integer points: [ 1 0 0 1 1 -1 0 0 1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 0 -1 1 -1 1 -1 1 -1 -1 -1 0 0 0 1 -1 -1 0 0]
[ 0 0 1 -1 0 1 1 -1 -1 -1 1 -1 0 -1 0 1 0 -1 0 -1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x-1*y*z + x*z-1 + y*z-1 + x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x*y-1*z-1 + 3*z-1 + x-1*y*z-1 + 3*y-1 + 4*x-1 + x-1*y-1*z + 2*y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 4 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Polytope 3876
Image of polytope 3876 PALP id: 3876
grdb id: 544849
Integer points: [ 1 0 1 -6 -1 -2 -3 -4 -5 0 -1 -2 -3 -4 0 -1 -2 0 -1 -2 1 0]
[ 0 1 0 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 0 2 -3 2 1 0 -1 -2 2 1 0 -1 -2 1 0 -1 1 0 -1 1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 254 1 Lattice Minkowski decompositions of facet 254
Image of facet 73 1 none
Polytope 3877
Image of polytope 3877 PALP id: 3877
grdb id: 544841
Integer points: [ 1 0 0 -4 -9 -8 -7 -6 -5 -6 -5 -4 -3 -2 -3 -2 -1 -4 -3 -2 -1 0]
[ 0 1 0 -1 -6 -5 -4 -3 -2 -4 -3 -2 -1 0 -2 -1 0 -3 -2 -1 -1 0]
[ 0 0 1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 14 1 none
Image of facet 254 1 Lattice Minkowski decompositions of facet 254
Image of facet 73 1 none
Polytope 3878
Image of polytope 3878 PALP id: 3878
grdb id: 523456
Integer points: [ 1 1 0 0 -1 -3 -2 -1 -2 -1 0 -1 0 -2 -1 0 -1 0 0 0 0 1]
[ 0 2 0 3 -4 -6 -3 0 -4 -1 2 -2 1 -5 -2 1 -3 0 -1 -1 -2 1]
[ 0 0 1 1 -2 -2 -1 0 -1 0 1 0 1 -2 -1 0 -1 0 0 -1 -1 0]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
27 ? y3*z + x*y2 + 3*y2*z + 2*x*y + 3*y*z + x + 2*y + z + 2*y-1 + 3*x-1 + 2*y-1*z-1 + 6*x-1*y-1 + 2*y-2*z-1 + 3*x-1*y-2 + 4*x-1*y-2*z-1 + 4*x-1*y-3*z-1 + 3*x-2*y-3*z-1 + x-1*y-4*z-2 + 3*x-2*y-4*z-1 + 2*x-2*y-5*z-2 + x-3*y-6*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 78 2 Lattice Minkowski decompositions of facet 78
Polytope 3879
Image of polytope 3879 PALP id: 3879
grdb id: 523342
Integer points: [ 1 0 1 -3 -1 -3 -2 -3 -2 -1 0 -3 -2 -1 0 -2 -1 -1 0 -1 0 1]
[ 0 1 0 1 -2 -2 -2 -1 -1 -1 -1 0 0 0 0 1 1 -1 -1 0 0 0]
[ 0 0 2 -3 2 0 1 -1 0 1 2 -2 -1 0 1 -2 -1 0 1 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 14 1 none
Image of facet 255 1 Lattice Minkowski decompositions of facet 255
Polytope 3880
Image of polytope 3880 PALP id: 3880
grdb id: 523449
Integer points: [ 1 0 0 -2 0 -2 0 0 -1 -1 -1 -1 -1 -2 -2 -2 -2 0 0 -1 -1 -1]
[ 0 1 0 0 -3 -5 -2 -1 -4 -3 -2 -1 0 -4 -3 -2 -1 -1 0 -2 -1 0]
[ 0 0 1 1 -2 -4 -1 0 -3 -2 -1 0 1 -3 -2 -1 0 -1 0 -2 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 9 1 irreducible and admissible
Image of facet 216 1 Lattice Minkowski decompositions of facet 216
Image of facet 73 1 none
Polytope 3881
Image of polytope 3881 PALP id: 3881
grdb id: 523178
Integer points: [ 1 0 0 -2 0 -4 -1 -2 -3 0 -1 -2 -3 0 -1 -2 0 -1 -1 0 -1 0]
[ 0 1 0 3 -4 4 1 2 3 -1 0 1 2 -2 -1 0 -3 -2 2 0 1 -1]
[ 0 0 1 -2 1 -3 0 -1 -2 1 0 -1 -2 1 0 -1 1 0 -1 0 -1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 64 1 none
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 13 1 irreducible and admissible
Image of facet 206 1 Lattice Minkowski decompositions of facet 206
Polytope 3882
Image of polytope 3882 PALP id: 3882
grdb id: 523385
Integer points: [ 1 0 0 -2 -1 -5 -4 -3 -2 -4 -3 -2 -1 -3 -2 -1 -1 -2 -1 0 -1 0]
[ 0 1 0 1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 1 -1 -1 -1 0 0]
[ 0 0 1 -2 2 -2 -1 0 1 -2 -1 0 1 -2 -1 0 -1 -1 0 1 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 14 1 none
Image of facet 256 1 Lattice Minkowski decompositions of facet 256
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 3883
Image of polytope 3883 PALP id: 3883
grdb id: 523398
Integer points: [ 1 0 0 -1 -2 -5 -1 -3 -2 -1 -4 -3 -2 -1 -4 -3 -2 -1 0 -2 -1 0]
[ 0 1 0 -2 2 2 1 2 1 0 2 1 0 -1 1 0 -1 1 0 1 0 -1]
[ 0 0 1 0 -1 -4 0 -2 -1 0 -3 -2 -1 0 -3 -2 -1 -1 0 -2 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 242 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 3884
Image of polytope 3884 PALP id: 3884
grdb id: 523285
Integer points: [ 1 0 0 0 -1 -6 -5 -4 -3 -2 -4 -3 -2 -1 -2 -1 0 -3 -2 -1 -1 0]
[ 0 1 0 -2 0 -5 -4 -3 -2 -1 -4 -3 -2 -1 -3 -2 -1 -2 -1 0 -1 0]
[ 0 0 1 -1 1 -4 -3 -2 -1 0 -3 -2 -1 0 -2 -1 0 -2 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 227 1 Lattice Minkowski decompositions of facet 227
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 73 1 none
Polytope 3885
Image of polytope 3885 PALP id: 3885
grdb id: 523268
Integer points: [ 1 0 0 -3 -2 -7 -6 -5 -4 -3 -5 -4 -3 -2 -1 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 0 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
[ 0 0 1 -2 1 -4 -3 -2 -1 0 -3 -2 -1 0 1 -1 0 -2 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 73 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 257 1 Lattice Minkowski decompositions of facet 257
Polytope 3886
Image of polytope 3886 PALP id: 3886
grdb id: 523387
Integer points: [ 1 0 0 0 -1 -4 -1 -2 -3 0 -1 -2 -3 0 -1 -2 0 -1 -2 0 -1 0]
[ 0 1 0 -3 2 5 -1 1 3 -2 0 2 4 -1 1 3 -1 1 3 0 2 1]
[ 0 0 1 -2 2 2 -1 0 1 -1 0 1 2 0 1 2 -1 0 1 0 1 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x-1*y2*z2 + 3*x-2*y3*z2 + 3*x-3*y4*z2 + x-4*y5*z2 + 2*y*z + 4*x-1*y2*z + 2*x-2*y3*z + x + y + z + 6*x-1*y*z + 9*x-2*y2*z + 4*x-3*y3*z + 4*x-1*y + 3*y-1 + 9*x-1 + 6*x-2*y + 2*y-1*z-1 + 3*y-2*z-1 + 4*x-1*y-1*z-1 + y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Image of facet 9 1 irreducible and admissible
Polytope 3887
Image of polytope 3887 PALP id: 3887
grdb id: 523284
Integer points: [ 1 0 0 0 -1 -6 -5 -4 -3 -2 -4 -3 -2 -1 -2 -1 -3 -2 -1 0 -1 0]
[ 0 1 -1 0 -2 3 2 1 0 -1 2 1 0 -1 1 0 2 1 0 -1 1 0]
[ 0 0 0 1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 218 1 none
Image of facet 14 1 none
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Polytope 3888
Image of polytope 3888 PALP id: 3888
grdb id: 523283
Integer points: [ 1 0 1 0 -1 -10 -8 -6 -4 -2 -7 -5 -3 -1 -4 -2 0 -5 -3 -1 -2 0]
[ 0 1 -1 0 -2 -5 -4 -3 -2 -1 -4 -3 -2 -1 -3 -2 -1 -2 -1 0 -1 0]
[ 0 0 0 1 -1 -4 -3 -2 -1 0 -3 -2 -1 0 -2 -1 0 -2 -1 0 -1 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 244 1 none
Image of facet 73 1 none
Polytope 3889
Image of polytope 3889 PALP id: 3889
grdb id: 523278
Integer points: [ 1 0 0 -2 -1 -11 -9 -7 -5 -3 -8 -6 -4 -2 -5 -3 -1 -5 -3 -1 -2 0]
[ 0 1 0 0 -1 -6 -5 -4 -3 -2 -4 -3 -2 -1 -2 -1 0 -3 -2 -1 -1 0]
[ 0 0 1 -1 1 -4 -3 -2 -1 0 -3 -2 -1 0 -2 -1 0 -2 -1 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 73 1 none
Image of facet 258 1 none
Image of facet 14 1 none
Polytope 3890
Image of polytope 3890 PALP id: 3890
grdb id: 442981
Integer points: [ 1 0 0 0 -2 1 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0 1]
[ 0 1 0 0 2 -2 -2 -1 0 1 -2 -1 0 1 -2 -1 -1 0 1 -1 0 -1]
[ 0 0 1 -1 -1 2 -1 -1 -1 -1 0 0 0 0 1 1 -1 -1 -1 0 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*x-1*y + 4*y-1*z + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + 4*y-1 + 7*x-1 + 3*y-2*z + 4*x-1*z-1 + 4*x-2*y*z-1 + 8*x-1*y-1 + 2*x-1*y-1*z-1 + 6*x-2*z-1 + 3*x-1*y-2 + 4*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Polytope 3891
Image of polytope 3891 PALP id: 3891
grdb id: 442978
Integer points: [ 1 0 0 0 1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0 1]
[ 0 1 0 0 -2 2 -2 -1 0 1 -2 -1 0 1 -2 -1 -1 0 1 -1 0 -1]
[ 0 0 1 -1 0 -1 3 2 1 0 2 1 0 -1 1 0 2 1 0 1 0 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Image of facet 80 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3892
Image of polytope 3892 PALP id: 3892
grdb id: 442983
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 1 -1 0 -4 -3 -2 -1 -3 -2 -1 0 -2 -1 0 -2 -1 0 -1 0]
[ 0 0 1 -1 1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + 2*z-1 + x-1*y*z-1 + 3*y-1 + 2*x-1 + x-1*y-1*z + 4*y-1*z-1 + 4*x-1*z-1 + 4*x-1*y-1 + x-1*z-2 + 2*y-2*z-1 + 8*x-1*y-1*z-1 + 3*x-1*y-2 + 4*x-1*y-1*z-2 + 8*x-1*y-2*z-1 + 6*x-1*y-2*z-2 + 3*x-1*y-3*z-1 + 4*x-1*y-3*z-2 + x-1*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 213 1 Lattice Minkowski decompositions of facet 213
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 3893
Image of polytope 3893 PALP id: 3893
grdb id: 442730
Integer points: [ 1 0 0 1 -1 -1 -4 -3 -2 -3 -2 -1 -2 -1 0 0 -2 -1 -1 0 0 1]
[ 0 1 0 -2 1 -2 1 1 1 0 0 0 -1 -1 -1 -2 1 1 0 0 -1 -1]
[ 0 0 1 0 1 -2 -2 -1 0 -2 -1 0 -2 -1 0 -1 -1 0 -1 0 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 220 1 Lattice Minkowski decompositions of facet 220
Image of facet 14 1 none
Polytope 3894
Image of polytope 3894 PALP id: 3894
grdb id: 443054
Integer points: [ 1 0 0 0 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 2 -2 -1 4 0 1 2 3 -1 0 1 2 0 1 2 3 -1 0 1]
[ 0 0 1 1 -2 -2 3 -1 0 1 2 -1 0 1 2 -1 0 1 2 -1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x-2*y4*z3 + 2*x-1*y3*z2 + y2*z + 2*x-1*y2*z2 + 5*x-2*y3*z2 + 2*y*z + 6*x-1*y2*z + x + y + z + 5*x-1*y*z + 10*x-2*y2*z + 6*x-1*y + 6*x-1 + 10*x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + 4*x-1*y-1*z-1 + 5*x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 150 1 Lattice Minkowski decompositions of facet 150
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3895
Image of polytope 3895 PALP id: 3895
grdb id: 442754
Integer points: [ 1 0 0 -1 -2 0 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0 0]
[ 0 1 0 2 3 -3 -1 0 1 2 -2 -1 0 1 -2 -1 0 1 2 -1 0 1]
[ 0 0 1 2 2 -2 -2 -1 0 1 -2 -1 0 1 -1 0 -1 0 1 -1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x-1*y2*z2 + x-2*y3*z2 + 2*y*z + 2*x-1*y2*z + x + y + z + 5*x-1*y*z + 4*x-2*y2*z + 4*x-1*y + 3*y-1 + 9*x-1 + 6*x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + 3*y-2*z-1 + 7*x-1*y-1*z-1 + 4*x-2*z-1 + y-3*z-2 + 2*x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 198 1 Lattice Minkowski decompositions of facet 198
Image of facet 9 1 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3896
Image of polytope 3896 PALP id: 3896
grdb id: 442766
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 1 1 -1 -1 1 1 1 1 0 0 0 0 0 -1 -1 -1 1 0 0 0]
[ 0 0 2 3 -3 1 -1 0 1 2 -2 -1 0 1 2 -2 -1 0 1 -1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 2 none
Image of facet 1 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 13 1 irreducible and admissible
Image of facet 214 1 Lattice Minkowski decompositions of facet 214
Polytope 3897
Image of polytope 3897 PALP id: 3897
grdb id: 442952
Integer points: [ 1 0 0 -2 1 -3 1 0 -1 -2 1 0 -1 -2 0 -1 1 0 -1 1 0 -1]
[ 0 1 0 1 -2 0 -4 -3 -2 -1 -3 -2 -1 0 -1 0 -2 -1 0 -1 0 1]
[ 0 0 1 -2 2 -2 2 1 0 -1 2 1 0 -1 1 0 1 0 -1 1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*x*y-2*z + 4*y-1*z + 2*x*y-3*z2 + 2*x-1*y*z-1 + 4*y-1 + 3*x-1 + 7*y-2*z + x*y-4*z2 + 3*x-1*z-1 + 8*x-1*y-1 + 4*y-3*z + x-2*y*z-2 + 3*x-2*z-1 + 6*x-1*y-2 + 4*x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Polytope 3898
Image of polytope 3898 PALP id: 3898
grdb id: 442848
Integer points: [ 1 0 1 0 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
[ 0 1 -1 0 -2 1 -4 -3 -2 -1 0 -3 -2 -1 0 -2 -1 -1 0 1 -1 0]
[ 0 0 0 1 -2 2 -3 -2 -1 0 1 -2 -1 0 1 -1 0 -1 0 1 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 218 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3899
Image of polytope 3899 PALP id: 3899
grdb id: 442953
Integer points: [ 1 0 0 -2 1 -1 -4 -1 -2 -3 0 -1 -2 -3 0 -1 -2 -1 1 0 -1 0]
[ 0 1 0 3 -2 -2 4 1 2 3 -1 0 1 2 -2 -1 0 2 -1 0 1 -1]
[ 0 0 1 -2 2 0 -3 0 -1 -2 1 0 -1 -2 1 0 -1 -1 1 0 -1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*x-1*y2*z-1 + 4*x-1*y + 4*y-1*z + x-2*y3*z-2 + 3*x-1*y*z-1 + 6*x-2*y2*z-1 + 2*y-1 + 8*x-1 + 2*y-2*z + 4*x-3*y3*z-2 + 8*x-2*y*z-1 + 4*x-1*y-1 + x-4*y4*z-3 + 3*x-3*y2*z-2 + 3*x-2*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 213 1 Lattice Minkowski decompositions of facet 213
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3900
Image of polytope 3900 PALP id: 3900
grdb id: 442762
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 0 0 -1 -1 -1 -1 0 0 0 -1 0 0]
[ 0 1 1 0 -2 -2 0 0 0 0 1 1 -1 -1 -1 -1 0 0 0 -2 -1 -1]
[ 0 0 3 2 -4 -2 -2 1 0 -1 2 1 0 -1 -2 -3 1 0 -1 -3 -1 -2]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
11 rank 2, number 6 y*z3 + 3*y*z2 + 3*y*z + x + y + 2*z + x-1*z2 + 4*x-1*z + 2*z-1 + 6*x-1 + 2*y-1*z-1 + 4*x-1*z-1 + 2*x-1*y-1 + 2*y-1*z-2 + x-1*z-2 + 6*x-1*y-1*z-1 + 6*x-1*y-1*z-2 + 2*x-1*y-1*z-3 + x-1*y-2*z-2 + 2*x-1*y-2*z-3 + x-1*y-2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3901
Image of polytope 3901 PALP id: 3901
grdb id: 443055
Integer points: [ 1 0 0 0 0 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -2 1 -4 -3 -2 -1 0 -3 -2 -1 0 -1 -2 -1 0 1 -1 0]
[ 0 0 1 -1 1 -2 3 2 1 0 -1 2 1 0 -1 0 2 1 0 -1 1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 236 1 none
Polytope 3902
Image of polytope 3902 PALP id: 3902
grdb id: 442714
Integer points: [ 1 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 1]
[ 0 2 0 3 -1 2 -4 0 -2 1 -1 -3 0 -2 1 -1 2 0 -2 1 -1 1]
[ 0 0 1 1 1 1 -2 0 -1 1 0 -1 1 0 0 -1 1 0 -1 1 0 0]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 y3*z + x*y2 + 3*y2*z + 2*x*y + 3*y*z + x-1*y2*z + x + 3*y + z + 3*x-1*y*z + 3*x-1*z + 3*y-1 + 3*x-1 + x-1*y-1*z + 2*y-1*z-1 + 6*x-1*y-1 + 2*y-2*z-1 + 3*x-1*y-2 + 3*x-1*y-2*z-1 + 3*x-1*y-3*z-1 + x-1*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 3903
Image of polytope 3903 PALP id: 3903
grdb id: 443014
Integer points: [ 1 0 0 1 -2 -3 -5 -4 -4 -3 -2 -1 -3 -2 -1 0 -1 -2 -1 -1 0 1]
[ 0 1 0 -2 2 0 2 1 2 1 0 -1 2 1 0 -1 1 1 0 1 0 -1]
[ 0 0 1 2 -1 -2 -4 -3 -3 -2 -1 0 -2 -1 0 1 0 -2 -1 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*x-1*y + 4*y-1*z + 3*x-1*y*z-1 + x-2*y2*z-1 + 6*x-1 + 2*x-1*z-1 + 6*x-2*y*z-1 + 2*x-1*y-1 + 2*x-2*y*z-2 + 3*x-3*y2*z-2 + 6*x-2*z-1 + 6*x-3*y*z-2 + 3*x-4*y2*z-3 + x-3*z-2 + 2*x-4*y*z-3 + x-5*y2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 246 1 Lattice Minkowski decompositions of facet 246
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3904
Image of polytope 3904 PALP id: 3904
grdb id: 442850
Integer points: [ 1 0 0 0 0 -1 -6 -5 -4 -3 -2 -4 -3 -2 -1 -2 -1 -3 -2 -1 -1 0]
[ 0 1 -1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]
[ 0 0 0 1 -1 1 -4 -3 -2 -1 0 -3 -2 -1 0 -2 -1 -2 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 218 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Polytope 3905
Image of polytope 3905 PALP id: 3905
grdb id: 442956
Integer points: [ 1 0 0 1 0 -4 -6 -1 -2 -3 -4 -5 0 -1 -2 -3 -1 -2 -3 1 0 -1]
[ 0 1 0 2 1 -4 -5 0 -1 -2 -3 -4 1 0 -1 -2 -1 -2 -3 1 0 -1]
[ 0 0 1 2 2 -3 -4 1 0 -1 -2 -3 1 0 -1 -2 0 -1 -2 1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 171 1 Lattice Minkowski decompositions of facet 171
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 13 1 irreducible and admissible
Image of facet 173 1 Lattice Minkowski decompositions of facet 173
Polytope 3906
Image of polytope 3906 PALP id: 3906
grdb id: 442435
Integer points: [ 1 0 0 -1 -2 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -2 2 2 -2 -1 0 1 -2 -1 0 1 -1 0 1 -1 0 1 -1 0]
[ 0 0 1 0 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
146 ? x + y + z + 2*x-1*y + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 5*x-1 + 4*x-1*z-1 + 6*x-2*y*z-1 + 3*x-1*y-1 + x-3*y2*z-2 + 2*x-1*y-1*z-1 + 10*x-2*z-1 + x-1*y-2 + 4*x-3*y*z-2 + 7*x-2*y-1*z-1 + 6*x-3*z-2 + 2*x-2*y-2*z-1 + 4*x-3*y-1*z-2 + x-3*y-2*z-2
59 rank 2, number 16 x + y + z + 2*x-1*y + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 3*x-1 + 4*x-1*z-1 + 4*x-2*y*z-1 + 2*x-1*y-1 + x-3*y2*z-2 + 2*x-1*y-1*z-1 + 7*x-2*z-1 + x-1*y-2 + 4*x-3*y*z-2 + 6*x-2*y-1*z-1 + 6*x-3*z-2 + 2*x-2*y-2*z-1 + 4*x-3*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 245 1 Lattice Minkowski decompositions of facet 245
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3907
Image of polytope 3907 PALP id: 3907
grdb id: 442311
Integer points: [ 1 0 0 0 -1 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 1 0 -4 -1 -2 -3 0 -1 -2 -3 0 -1 -2 0 -1 -2 0 -1]
[ 0 0 1 1 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Image of facet 14 1 none
Polytope 3908
Image of polytope 3908 PALP id: 3908
grdb id: 441580
Integer points: [ 1 0 0 -2 -1 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 -1 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 -1 0]
[ 0 0 1 -2 2 -2 3 -1 0 1 2 -1 0 1 2 -1 0 1 -1 0 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + 3*x-1*z + x-1*y-1*z2 + 5*x-1 + 4*x-1*y-1*z + 3*x-2*y-1*z2 + 2*x-1*z-1 + 5*x-1*y-1 + 10*x-2*y-1*z + x-3*y-2*z3 + 2*x-1*y-1*z-1 + 12*x-2*y-1 + 5*x-3*y-2*z2 + 6*x-2*y-1*z-1 + 10*x-3*y-2*z + x-2*y-1*z-2 + 10*x-3*y-2 + 5*x-3*y-2*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 227 1 Lattice Minkowski decompositions of facet 227
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Polytope 3909
Image of polytope 3909 PALP id: 3909
grdb id: 442425
Integer points: [ 1 0 0 -2 -1 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -2 0 -4 -3 -2 -1 -3 -2 -1 0 -1 0 1 -2 -1 0 -1 0]
[ 0 0 1 -2 2 -2 2 1 0 -1 2 1 0 -1 1 0 -1 1 0 -1 1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + 2*y-1*z + 2*x-1*y*z-1 + 6*x-1 + 5*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-2*z + x-2*y*z-2 + 6*x-2*z-1 + 11*x-2*y-1 + 8*x-2*y-2*z + 2*x-2*y-3*z2 + x-3*z-2 + 4*x-3*y-1*z-1 + 6*x-3*y-2 + 4*x-3*y-3*z + x-3*y-4*z2
59 rank 2, number 16 x + y + z + 2*y-1*z + 2*x-1*y*z-1 + 5*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 4*x-1*y-1 + 2*x-1*y-2*z + x-2*y*z-2 + 5*x-2*z-1 + 9*x-2*y-1 + 7*x-2*y-2*z + 2*x-2*y-3*z2 + x-3*z-2 + 4*x-3*y-1*z-1 + 6*x-3*y-2 + 4*x-3*y-3*z + x-3*y-4*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 259 1 Lattice Minkowski decompositions of facet 259
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 3910
Image of polytope 3910 PALP id: 3910
grdb id: 442225
Integer points: [ 1 0 0 -1 -2 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 2 2 -3 -4 -3 -2 -1 0 1 -2 -1 0 1 -2 -1 0 1 -1 0]
[ 0 0 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 -1 -1 -1 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 260 1 Lattice Minkowski decompositions of facet 260
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Image of facet 8 1 none
Image of facet 43 1 irreducible and admissible
Polytope 3911
Image of polytope 3911 PALP id: 3911
grdb id: 442307
Integer points: [ 1 0 0 0 0 -1 -4 -1 -2 -3 0 -1 -2 -3 0 -1 -2 0 -1 -2 0 -1]
[ 0 1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 0 1 1 -2 2 2 -1 0 1 -1 0 1 2 0 1 2 -1 0 1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + y-1*z + 3*x-1*z + x-1*y-1*z2 + 2*z-1 + 3*y-1 + 4*x-1 + 6*x-1*y-1*z + 2*x-2*z + 3*x-2*y-1*z2 + 3*y-1*z-1 + 9*x-1*y-1 + 9*x-2*y-1*z + 3*x-3*y-1*z2 + y-1*z-2 + 4*x-1*y-1*z-1 + 6*x-2*y-1 + 4*x-3*y-1*z + x-4*y-1*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 9 1 irreducible and admissible
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Polytope 3912
Image of polytope 3912 PALP id: 3912
grdb id: 442325
Integer points: [ 1 0 0 -1 -1 -2 -5 -4 -3 -2 -4 -3 -2 -1 -3 -2 -1 -2 -1 0 -1 0]
[ 0 1 0 1 -2 1 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 0 1 0 0 -1 -4 -3 -2 -1 -3 -2 -1 0 -2 -1 0 -2 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? x + y + z + x-1*y + 2*y-1 + 3*x-1 + 3*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + 4*x-1*y-1*z-1 + 5*x-2*z-1 + x-1*y-2 + 7*x-2*y-1*z-1 + 2*x-2*y-1*z-2 + 3*x-3*z-2 + 4*x-2*y-2*z-1 + 8*x-3*y-1*z-2 + 6*x-3*y-2*z-2 + 3*x-4*y-1*z-3 + 4*x-4*y-2*z-3 + x-5*y-2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 248 1 Lattice Minkowski decompositions of facet 248
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 3913
Image of polytope 3913 PALP id: 3913
grdb id: 442583
Integer points: [ 1 0 0 -1 -1 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 0 0 -1 -1 0 0 0]
[ 0 1 1 0 0 -2 -2 -2 -1 -1 -1 -1 0 0 0 1 1 -1 -1 0 0 0]
[ 0 0 3 2 -2 -2 -4 -3 0 -1 -2 -3 1 0 -1 2 1 -1 -2 1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 y*z3 + 3*y*z2 + 3*y*z + x + y + 2*z + x-1*z2 + 5*x-1*z + 2*z-1 + 8*x-1 + 5*x-1*z-1 + x-1*z-2 + 2*x-1*y-1*z-1 + 2*x-2*y-1 + 2*x-1*y-1*z-2 + 6*x-2*y-1*z-1 + 6*x-2*y-1*z-2 + 2*x-2*y-1*z-3 + x-3*y-2*z-2 + 2*x-3*y-2*z-3 + x-3*y-2*z-4
40 rank 2, number 10 y*z3 + 3*y*z2 + 3*y*z + x + y + 2*z + x-1*z2 + 6*x-1*z + 2*z-1 + 10*x-1 + 6*x-1*z-1 + x-1*z-2 + 2*x-1*y-1*z-1 + 2*x-2*y-1 + 2*x-1*y-1*z-2 + 7*x-2*y-1*z-1 + 7*x-2*y-1*z-2 + 2*x-2*y-1*z-3 + x-3*y-2*z-2 + 2*x-3*y-2*z-3 + x-3*y-2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 3 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 261 1 Lattice Minkowski decompositions of facet 261
Image of facet 9 1 irreducible and admissible
Polytope 3914
Image of polytope 3914 PALP id: 3914
grdb id: 442337
Integer points: [ 1 0 0 1 1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 1 0 0 -1 0 -4 -3 -2 -1 -3 -2 -1 0 -2 -1 0 -2 -1 0 -1 0]
[ 0 0 1 -1 0 -1 3 2 1 0 2 1 0 -1 1 0 -1 2 1 0 1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Image of facet 80 1 none
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3915
Image of polytope 3915 PALP id: 3915
grdb id: 442320
Integer points: [ 1 0 -1 0 -2 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 1 0 0 -2 -6 -5 -4 -3 -4 -3 -2 -1 -2 -1 0 -3 -2 -1 -1 0]
[ 0 0 0 1 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Image of facet 247 1 Lattice Minkowski decompositions of facet 247
Polytope 3916
Image of polytope 3916 PALP id: 3916
grdb id: 442316
Integer points: [ 1 0 -1 0 -2 -1 -5 -2 -3 -4 -1 -2 -3 -4 -1 -2 -3 0 -1 -2 0 -1]
[ 0 1 1 0 0 -2 -6 -3 -4 -5 -1 -2 -3 -4 0 -1 -2 -1 -2 -3 0 -1]
[ 0 0 0 1 -1 0 -4 -1 -2 -3 0 -1 -2 -3 0 -1 -2 0 -1 -2 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 249 1 none
Polytope 3917
Image of polytope 3917 PALP id: 3917
grdb id: 442338
Integer points: [ 1 0 1 0 0 -2 -6 -3 -4 -5 -1 -2 -3 -4 0 -1 -2 -1 -2 -3 0 -1]
[ 0 1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 0 0 1 -1 0 -4 -1 -2 -3 0 -1 -2 -3 0 -1 -2 0 -1 -2 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x*y-1 + 3*y-1 + 3*x-1 + y-1*z-1 + 3*x-1*z-1 + 3*x-1*y-1 + 6*x-1*y-1*z-1 + 4*x-2*z-1 + x-2*y-1 + 9*x-2*y-1*z-1 + 3*x-2*y-1*z-2 + 2*x-3*z-2 + 4*x-3*y-1*z-1 + 9*x-3*y-1*z-2 + 6*x-4*y-1*z-2 + 3*x-4*y-1*z-3 + 4*x-5*y-1*z-3 + x-6*y-1*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3918
Image of polytope 3918 PALP id: 3918
grdb id: 441575
Integer points: [ 1 0 0 -1 -2 -3 -7 -3 -4 -5 -6 -2 -3 -4 -5 -1 -2 -1 -2 -3 0 -1]
[ 0 1 0 0 -1 -2 -6 -2 -3 -4 -5 -1 -2 -3 -4 0 -1 -1 -2 -3 0 -1]
[ 0 0 1 1 1 -2 -4 0 -1 -2 -3 0 -1 -2 -3 0 -1 0 -1 -2 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 250 1 none
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Polytope 3919
Image of polytope 3919 PALP id: 3919
grdb id: 442321
Integer points: [ 1 0 0 -1 -1 -3 -7 -6 -5 -4 -5 -4 -3 -2 -3 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 1 -1 0 -4 -3 -2 -1 -3 -2 -1 0 -2 -1 0 -2 -1 0 -1 0]
[ 0 0 1 -1 1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 14 1 none
Image of facet 262 1 Lattice Minkowski decompositions of facet 262
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 3920
Image of polytope 3920 PALP id: 3920
grdb id: 440627
Integer points: [ 1 0 0 0 -1 0 -4 -2 -1 0 -3 -2 -1 0 -3 -2 -1 -1 0 -2 -1 0]
[ 0 1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 0 1 1 1 -2 -2 0 0 0 -1 -1 -1 -1 -2 -2 -2 0 0 -1 -1 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + y-1*z + 2*z-1 + 3*y-1 + 3*x-1 + x-1*y-1*z + 3*y-1*z-1 + 4*x-1*z-1 + 6*x-1*y-1 + y-1*z-2 + 9*x-1*y-1*z-1 + 2*x-2*z-1 + 3*x-2*y-1 + 4*x-1*y-1*z-2 + 9*x-2*y-1*z-1 + 6*x-2*y-1*z-2 + 3*x-3*y-1*z-1 + 4*x-3*y-1*z-2 + x-4*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 9 1 irreducible and admissible
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Polytope 3921
Image of polytope 3921 PALP id: 3921
grdb id: 283511
Integer points: [ 1 0 1 -2 1 1 0 0 0 0 0 1 1 1 -1 -1 -1 0 0 0 1 -1]
[ 0 1 0 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 1]
[ 0 0 2 -2 3 -1 2 -2 -1 0 1 0 1 2 -2 -1 0 -1 0 1 1 -1]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x*z2 + x*y-1*z3 + 2*x*z + 4*x*y-1*z2 + x + y + 6*x*y-1*z + 3*z + y-1*z2 + 4*x*y-1 + 4*y-1*z + x*y-1*z-1 + 3*z-1 + 2*x-1*y*z-1 + 6*y-1 + 2*x-1 + 4*y-1*z-1 + 4*x-1*z-1 + y-1*z-2 + 2*x-1*z-2 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Image of facet 134 1 Lattice Minkowski decompositions of facet 134
Polytope 3922
Image of polytope 3922 PALP id: 3922
grdb id: 283523
Integer points: [ 1 0 0 -1 2 -1 0 -3 -2 -1 0 -1 0 1 -2 -1 -2 -1 0 1 0 1]
[ 0 1 0 1 -2 1 -2 1 1 0 -1 1 0 -1 0 -1 1 0 -1 -2 0 -1]
[ 0 0 1 1 -1 -1 1 1 1 1 1 0 0 0 1 1 0 0 0 0 -1 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
11 rank 2, number 6 x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + 2*y-1*z + 4*x-1*z + 2*x-2*y*z + x2*y-2*z-1 + 3*x*y-1*z-1 + 3*z-1 + x-1*y*z-1 + 2*x*y-2 + 6*y-1 + 6*x-1 + 2*x-2*y + y-2*z + 3*x-1*y-1*z + 3*x-2*z + x-3*y*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Polytope 3923
Image of polytope 3923 PALP id: 3923
grdb id: 283558
Integer points: [ 1 0 0 -1 -2 2 2 -3 -2 -1 0 1 -2 -1 0 1 -1 0 1 -1 0 1]
[ 0 1 0 1 1 -3 -4 1 0 -1 -2 -3 1 0 -1 -2 0 -1 -2 1 0 -1]
[ 0 0 1 1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 -1 -1 -1 0 0 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 2 none
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 157 1 Lattice Minkowski decompositions of facet 157
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Polytope 3924
Image of polytope 3924 PALP id: 3924
grdb id: 283515
Integer points: [ 1 0 0 0 1 -2 0 -4 -1 -2 -3 0 -1 -2 -3 -1 0 -1 -2 1 0 -1]
[ 0 1 0 0 -2 2 -2 2 -1 0 1 -1 0 1 2 1 -1 0 1 -1 0 1]
[ 0 0 1 -1 -2 1 -1 3 0 1 2 -1 0 1 2 0 0 1 2 -1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 3*x-1*y*z + x-2*y2*z + 2*x-2*y*z2 + 2*x-3*y2*z2 + x-4*y2*z3 + 2*x-1*y + 4*x-1*z + 6*x-2*y*z + 4*x-3*y*z2 + 2*x*y-1*z-1 + z-1 + 2*y-1 + 7*x-1 + 6*x-2*z + 4*y-1*z-1 + 4*x-1*y-1 + x*y-2*z-2 + y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 1 irreducible and admissible
Image of facet 180 1 Lattice Minkowski decompositions of facet 180
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3925
Image of polytope 3925 PALP id: 3925
grdb id: 283518
Integer points: [ 1 0 1 -2 2 -3 2 -4 1 0 -1 -2 -3 0 -1 -2 1 0 -1 1 0 -1]
[ 0 1 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0 0]
[ 0 0 2 -2 2 -2 3 -3 2 1 0 -1 -2 1 0 -1 1 0 -1 1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
26 rank 2, number 8 x2*y-1*z3 + x2*y-1*z2 + x*z2 + x*z + 6*x*y-1*z2 + x + y + 4*x*y-1*z + 4*z + 15*y-1*z + 6*y-1 + 6*x-1 + x-1*z-1 + 20*x-1*y-1 + 4*x-1*y-1*z-1 + 4*x-2*z-1 + 15*x-2*y-1*z-1 + x-2*y-1*z-2 + x-3*z-2 + 6*x-3*y-1*z-2 + x-4*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 10 2 Lattice Minkowski decompositions of facet 10
Image of facet 13 2 irreducible and admissible
Image of facet 173 2 Lattice Minkowski decompositions of facet 173
Polytope 3926
Image of polytope 3926 PALP id: 3926
grdb id: 283519
Integer points: [ 1 1 -1 -1 0 0 1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 1 1 1]
[ 0 2 -2 0 0 3 -2 -4 -2 -3 -1 -3 -1 1 -2 0 2 -1 1 0 -1 1]
[ 0 0 0 0 1 1 -2 -2 -1 -1 0 -2 -1 0 -1 0 1 0 1 -1 -1 0]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
49 rank 2, number 4 y3*z + x*y2 + 3*y2*z + 2*x*y + 3*y*z + x + 3*y + z + 2*x*z-1 + 2*x*y-1*z-1 + 4*y-1 + x-1 + 4*y-1*z-1 + 2*x-1*y-1 + x*y-2*z-2 + 5*y-2*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 2*y-3*z-2 + 2*x-1*y-3*z-1 + x-1*y-4*z-2
9 rank 1, V10 y3*z + x*y2 + 3*y2*z + 2*x*y + 3*y*z + x + 3*y + z + 2*x*z-1 + 2*x*y-1*z-1 + 3*y-1 + x-1 + 4*y-1*z-1 + 2*x-1*y-1 + x*y-2*z-2 + 4*y-2*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 2*y-3*z-2 + 2*x-1*y-3*z-1 + x-1*y-4*z-2
49 rank 2, number 4 y3*z + x*y2 + 3*y2*z + 2*x*y + 3*y*z + x + 4*y + z + 2*x*z-1 + 2*x*y-1*z-1 + 3*y-1 + x-1 + 5*y-1*z-1 + 2*x-1*y-1 + x*y-2*z-2 + 4*y-2*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 2*y-3*z-2 + 2*x-1*y-3*z-1 + x-1*y-4*z-2
72 ? y3*z + x*y2 + 3*y2*z + 2*x*y + 3*y*z + x + 4*y + z + 2*x*z-1 + 2*x*y-1*z-1 + 4*y-1 + x-1 + 5*y-1*z-1 + 2*x-1*y-1 + x*y-2*z-2 + 5*y-2*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 2*y-3*z-2 + 2*x-1*y-3*z-1 + x-1*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 81 2 Lattice Minkowski decompositions of facet 81
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Polytope 3927
Image of polytope 3927 PALP id: 3927
grdb id: 282264
Integer points: [ 1 0 1 0 1 -2 0 -2 -1 -1 0 -1 0 -1 0 1 -1 0 1 0 0 1]
[ 0 1 0 1 -2 1 -2 0 1 0 0 1 1 0 0 0 -1 -1 -1 0 -1 -1]
[ 0 0 2 -2 2 -2 1 -1 -1 0 1 -2 -1 -1 0 1 0 1 2 -1 0 1]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x*z2 + 2*x*z + 2*x*y-1*z2 + x + y + 2*x*y-1*z + 3*z + x*y-2*z2 + 2*y*z-1 + 4*y-1*z + y*z-2 + 3*z-1 + 2*x-1*y*z-1 + 3*y-1 + 3*x-1 + y-2*z + 2*x-1*y*z-2 + 4*x-1*z-1 + 2*x-1*y-1 + x-2*y*z-2 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3928
Image of polytope 3928 PALP id: 3928
grdb id: 282712
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 1 0 -2 0 1 1 1 1 1 0 0 0 -1 -1 -1 1 0 0 0 -1]
[ 0 0 2 -2 -2 2 3 -1 2 1 0 1 0 -1 0 -1 -2 1 1 0 -1 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 y*z2 + x-1*y*z3 + 2*y*z + 4*x-1*y*z2 + x + y + 2*z + 6*x-1*y*z + x-1*z2 + 4*x-1*y + 5*x-1*z + 2*z-1 + x-1*y*z-1 + 8*x-1 + 2*y-1*z-1 + 5*x-1*z-1 + 2*x-1*y-1 + x-1*z-2 + 4*x-1*y-1*z-1 + 2*x-1*y-1*z-2 + x-1*y-2*z-2
51 rank 2, number 7 y*z2 + x-1*y*z3 + 2*y*z + 4*x-1*y*z2 + x + y + 2*z + 6*x-1*y*z + x-1*z2 + 4*x-1*y + 6*x-1*z + 2*z-1 + x-1*y*z-1 + 10*x-1 + 2*y-1*z-1 + 6*x-1*z-1 + 2*x-1*y-1 + x-1*z-2 + 5*x-1*y-1*z-1 + 2*x-1*y-1*z-2 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 223 1 Lattice Minkowski decompositions of facet 223
Polytope 3929
Image of polytope 3929 PALP id: 3929
grdb id: 283324
Integer points: [ 1 0 0 0 -1 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 -1 0 -2 2 3 -2 2 1 0 -1 1 0 -1 2 1 0 -1 1 0 -1]
[ 0 0 0 1 2 -2 -2 3 -1 0 1 2 -1 0 1 -1 0 1 2 -1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + 2*y*z-1 + 2*x-1*y2*z-1 + 6*x-1*y + 2*y-1*z + 6*x-1*z + 2*x-1*y-1*z2 + x-1*y2*z-2 + x-2*y3*z-2 + 3*x-1*y*z-1 + 5*x-2*y2*z-1 + y-1 + 4*x-1 + 10*x-2*y + 3*x-1*y-1*z + 10*x-2*z + x-1*y-2*z2 + 5*x-2*y-1*z2 + x-2*y-2*z3
151 ? x + y + z + 2*y*z-1 + 2*x-1*y2*z-1 + 6*x-1*y + 2*y-1*z + 6*x-1*z + 2*x-1*y-1*z2 + x-1*y2*z-2 + x-2*y3*z-2 + 4*x-1*y*z-1 + 5*x-2*y2*z-1 + y-1 + 7*x-1 + 10*x-2*y + 5*x-1*y-1*z + 10*x-2*z + x-1*y-2*z2 + 5*x-2*y-1*z2 + x-2*y-2*z3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 160 1 Lattice Minkowski decompositions of facet 160
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Polytope 3930
Image of polytope 3930 PALP id: 3930
grdb id: 282243
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 1 1 -1 1 1 -2 -2 -1 0 -2 -1 0 1 -1 0 0 -1 0 1 -1 0]
[ 0 0 2 -2 1 3 -2 0 -1 0 -1 0 1 2 1 2 -1 -1 0 1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 y*z2 + x-1*y*z3 + 2*y*z + 2*x-1*y*z2 + x + y + 3*z + x-1*y*z + 3*x-1*z2 + 6*x-1*z + 2*z-1 + 2*y-1 + 3*x-1 + 3*x-1*y-1*z + 2*y-1*z-1 + 6*x-1*y-1 + y-1*z-2 + 3*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3931
Image of polytope 3931 PALP id: 3931
grdb id: 281904
Integer points: [ 1 0 0 1 -1 -2 1 -2 0 0 0 -1 -1 -1 -2 -2 1 0 0 -1 -1 -1]
[ 0 1 0 -1 1 1 -2 -2 -2 -1 0 -2 -1 0 -1 0 -1 -1 0 -1 0 1]
[ 0 0 1 -1 -1 0 0 3 1 0 -1 2 1 0 2 1 0 1 0 2 1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*x*y-1 + 2*x-1*y + 4*y-1*z + 4*x-1*z + 2*x-1*y-1*z2 + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + x*y-2 + 5*y-1 + 5*x-1 + x-2*y + 3*y-2*z + 7*x-1*y-1*z + 3*x-2*z + 3*x-1*y-2*z2 + 3*x-2*y-1*z2 + x-2*y-2*z3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 174 1 Lattice Minkowski decompositions of facet 174
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Polytope 3932
Image of polytope 3932 PALP id: 3932
grdb id: 281846
Integer points: [ 1 0 0 1 0 -1 -2 -2 -1 -1 -1 0 0 0 1 -2 -2 -1 -1 -1 0 0]
[ 0 1 0 -2 -2 2 0 3 0 1 2 -1 0 1 -1 1 2 -1 0 1 -1 0]
[ 0 0 1 0 1 -2 1 -2 1 0 -1 1 0 -1 0 0 -1 1 0 -1 0 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
11 rank 2, number 6 x + y + z + 2*y*z-1 + 2*x-1*y2*z-1 + 2*x*y-1 + 4*x-1*y + 2*y-1*z + 2*x-1*z + x-1*y2*z-2 + x-2*y3*z-2 + 2*z-1 + 4*x-1*y*z-1 + 3*x-2*y2*z-1 + x*y-2 + 3*y-1 + 5*x-1 + 3*x-2*y + y-2*z + 2*x-1*y-1*z + x-2*z
7 rank 1, V12 x + y + z + 2*y*z-1 + 2*x-1*y2*z-1 + 2*x*y-1 + 4*x-1*y + 2*y-1*z + 2*x-1*z + x-1*y2*z-2 + x-2*y3*z-2 + 2*z-1 + 5*x-1*y*z-1 + 3*x-2*y2*z-1 + x*y-2 + 4*y-1 + 6*x-1 + 3*x-2*y + y-2*z + 2*x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 155 1 Lattice Minkowski decompositions of facet 155
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3933
Image of polytope 3933 PALP id: 3933
grdb id: 283208
Integer points: [ 1 0 0 -2 1 -3 -1 -3 -2 0 -1 -2 -3 0 -1 -2 -1 0 -1 1 0 -1]
[ 0 1 0 2 -2 2 -2 0 -1 -2 -1 0 1 -1 0 1 1 -1 0 -1 0 1]
[ 0 0 1 -1 2 -2 0 -2 -1 1 0 -1 -2 1 0 -1 0 0 -1 1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*x-1*y + 3*y-1*z + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 5*x-1 + 2*y-2*z + 2*x-1*z-1 + 4*x-2*y*z-1 + 5*x-1*y-1 + x-3*y2*z-2 + 5*x-2*z-1 + x-1*y-2 + 2*x-3*y*z-2 + 2*x-2*y-1*z-1 + x-3*z-2
20 rank 1, V16 x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*x-1*y + 4*y-1*z + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 6*x-1 + 2*y-2*z + 2*x-1*z-1 + 4*x-2*y*z-1 + 6*x-1*y-1 + x-3*y2*z-2 + 6*x-2*z-1 + x-1*y-2 + 2*x-3*y*z-2 + 2*x-2*y-1*z-1 + x-3*z-2
40 rank 2, number 10 x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*x-1*y + 4*y-1*z + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 8*x-1 + 2*y-2*z + 2*x-1*z-1 + 6*x-2*y*z-1 + 6*x-1*y-1 + x-3*y2*z-2 + 7*x-2*z-1 + x-1*y-2 + 2*x-3*y*z-2 + 2*x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 3 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 251 1 Lattice Minkowski decompositions of facet 251
Polytope 3934
Image of polytope 3934 PALP id: 3934
grdb id: 282251
Integer points: [ 1 0 0 -1 2 -1 0 -3 -2 -1 -2 -1 0 -2 -1 0 1 -1 0 1 0 1]
[ 0 1 0 1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0 0 -1 -1]
[ 0 0 1 1 -2 1 -2 1 0 -1 1 0 -1 1 0 -1 -2 1 0 -1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x-1*y*z + 2*x*z-1 + 2*x-1*z + x2*y-1*z-2 + 3*x*y-1*z-1 + 2*z-1 + 3*y-1 + 4*x-1 + x-1*y-1*z + 2*x-2*z + 2*x*y-1*z-2 + 6*y-1*z-1 + 6*x-1*y-1 + 2*x-2*y-1*z + y-1*z-2 + 3*x-1*y-1*z-1 + 3*x-2*y-1 + x-3*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Polytope 3935
Image of polytope 3935 PALP id: 3935
grdb id: 281906
Integer points: [ 1 0 0 1 -2 1 -2 1 -1 0 -1 0 1 0 1 -1 0 1 -1 0 1 1]
[ 0 1 0 -1 1 0 0 -3 -1 -2 0 -1 -2 0 -1 0 -1 -2 1 0 -1 0]
[ 0 0 1 0 2 -2 1 -2 0 -1 0 -1 -2 -1 -2 1 0 -1 1 0 -1 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + 2*x-1*y*z + x-2*y*z2 + 2*x*z-1 + x*y-1 + 3*x-1*z + x*z-2 + 4*x*y-1*z-1 + 3*z-1 + 4*y-1 + 3*x-1 + x-2*z + 3*x*y-1*z-2 + 2*x*y-2*z-1 + 6*y-1*z-1 + 3*x-1*y-1 + 3*x*y-2*z-2 + 3*y-2*z-1 + x*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 82 1 Lattice Minkowski decompositions of facet 82
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3936
Image of polytope 3936 PALP id: 3936
grdb id: 281910
Integer points: [ 1 0 0 1 -2 1 1 -2 -1 0 -1 0 1 0 1 -2 -1 0 -1 0 1 -1]
[ 0 1 0 0 2 -2 -3 0 -1 -2 0 -1 -2 0 -1 1 0 -1 1 0 -1 1]
[ 0 0 1 -1 1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + 2*x-1*y*z + x-2*y2*z + x*z-1 + 2*x*y-1 + 3*x-1*y + 3*x*y-1*z-1 + 3*z-1 + x*y-2 + 4*y-1 + 5*x-1 + 2*x-2*y + 3*x*y-2*z-1 + 6*y-1*z-1 + 3*x-1*z-1 + x*y-3*z-1 + 3*y-2*z-1 + 3*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3937
Image of polytope 3937 PALP id: 3937
grdb id: 282088
Integer points: [ 1 0 0 2 -2 -2 2 0 -1 0 1 1 -2 -1 0 1 -1 0 1 -1 -1 0]
[ 0 1 0 -2 1 1 -3 -1 0 -1 -2 -1 1 0 -1 -2 1 0 -1 0 1 0]
[ 0 0 1 -1 0 2 -2 -2 1 0 -1 0 1 0 -1 -2 1 0 -1 -1 0 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + 2*x-1*y*z + x-2*y*z2 + 2*x*y-1 + 2*x-1*y + 4*x-1*z + 2*x-2*y*z + x2*y-2*z-1 + 3*x*y-1*z-1 + 2*z-1 + 6*y-1 + 6*x-1 + x-2*y + 4*x*y-2*z-1 + 6*y-1*z-1 + 2*x-1*z-1 + x2*y-3*z-2 + 2*x*y-2*z-2 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3938
Image of polytope 3938 PALP id: 3938
grdb id: 281831
Integer points: [ 1 0 0 -1 1 -2 1 -2 1 0 0 0 -1 -1 -1 -2 1 1 0 0 -1 -1]
[ 0 1 0 1 -2 1 -4 -1 -3 -3 -2 -1 -2 -1 0 0 -2 -1 -1 0 0 1]
[ 0 0 1 1 0 0 -2 -2 -1 -2 -1 0 -2 -1 0 -1 -1 0 -1 0 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + x*y-2 + 4*y-1 + 4*x-1 + x-2*y + 2*x*y-2*z-1 + 4*y-1*z-1 + 2*x-1*z-1 + 2*x*y-3*z-1 + 6*y-2*z-1 + 6*x-1*y-1*z-1 + 2*x-2*z-1 + x*y-4*z-2 + 3*y-3*z-2 + 3*x-1*y-2*z-2 + x-2*y-1*z-2
40 rank 2, number 10 x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + x*y-2 + 5*y-1 + 5*x-1 + x-2*y + 2*x*y-2*z-1 + 4*y-1*z-1 + 2*x-1*z-1 + 2*x*y-3*z-1 + 7*y-2*z-1 + 7*x-1*y-1*z-1 + 2*x-2*z-1 + x*y-4*z-2 + 3*y-3*z-2 + 3*x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 225 1 Lattice Minkowski decompositions of facet 225
Polytope 3939
Image of polytope 3939 PALP id: 3939
grdb id: 282905
Integer points: [ 1 0 0 0 1 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
[ 0 1 0 0 -1 1 0 -4 -1 -2 -3 0 -1 -2 -3 -1 -2 0 -1 -2 0 -1]
[ 0 0 1 -1 0 1 1 -3 0 -1 -2 1 0 -1 -2 0 -1 0 -1 -2 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + x*y-1 + 2*x-1*z + z-1 + 4*y-1 + 4*x-1 + x-2*z + 3*y-1*z-1 + 7*x-1*y-1 + 3*y-2*z-1 + 5*x-1*y-1*z-1 + 4*x-2*y-1 + 8*x-1*y-2*z-1 + 2*x-1*y-2*z-2 + 6*x-2*y-2*z-1 + 3*x-1*y-3*z-2 + 4*x-2*y-3*z-2 + x-2*y-4*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Polytope 3940
Image of polytope 3940 PALP id: 3940
grdb id: 282906
Integer points: [ 1 0 0 0 1 -1 0 -4 -3 -2 -1 -3 -2 -1 0 -2 -1 -2 -1 0 -1 0]
[ 0 1 0 0 -1 1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
[ 0 0 1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*y-1 + z-1 + x-1*y*z-1 + 3*y-1 + 3*x-1 + 2*y-1*z-1 + 4*x-1*z-1 + 4*x-1*y-1 + y-2*z-1 + 7*x-1*y-1*z-1 + 3*x-2*z-1 + 2*x-2*y-1 + 4*x-1*y-2*z-1 + 8*x-2*y-1*z-1 + 6*x-2*y-2*z-1 + 3*x-3*y-1*z-1 + 4*x-3*y-2*z-1 + x-4*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Polytope 3941
Image of polytope 3941 PALP id: 3941
grdb id: 282805
Integer points: [ 1 0 -1 0 -2 1 -3 1 0 -1 -2 1 0 -1 -2 0 -1 1 0 -1 1 0]
[ 0 1 1 0 1 -2 0 -4 -3 -2 -1 -3 -2 -1 0 -1 0 -2 -1 0 -1 0]
[ 0 0 0 1 -1 2 -2 2 1 0 -1 2 1 0 -1 1 0 1 0 -1 1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + 2*x*y-1*z + z + x*y-2*z2 + x-1*y + 2*x*y-2*z + 5*y-1*z + 2*x*y-3*z2 + 4*y-1 + 5*x-1 + 7*y-2*z + x*y-4*z2 + 2*x-1*z-1 + x-2*y*z-1 + 8*x-1*y-1 + 4*y-3*z + 3*x-2*z-1 + 6*x-1*y-2 + 4*x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 252 1 Lattice Minkowski decompositions of facet 252
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 3942
Image of polytope 3942 PALP id: 3942
grdb id: 281839
Integer points: [ 1 0 -1 0 -2 1 -1 -4 0 -2 -1 0 -3 -2 -1 -3 -2 0 1 -1 0 -1]
[ 0 1 1 0 1 -2 -2 1 -2 -1 -1 -1 0 0 0 1 1 -1 -1 0 0 1]
[ 0 0 0 1 -2 2 0 -3 1 -1 0 1 -2 -1 0 -2 -1 0 1 -1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + 2*x*y-1*z + z + x*y-2*z2 + x-1*y + 3*y-1*z + 2*x-1*y*z-1 + 2*y-1 + 5*x-1 + 2*y-2*z + 3*x-1*z-1 + 3*x-2*y*z-1 + 6*x-1*y-1 + x-2*y*z-2 + 7*x-2*z-1 + x-1*y-2 + 3*x-3*y*z-2 + 3*x-2*y-1*z-1 + 3*x-3*z-2 + x-4*y*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 220 1 Lattice Minkowski decompositions of facet 220
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 3943
Image of polytope 3943 PALP id: 3943
grdb id: 282871
Integer points: [ 1 0 0 -1 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 2 0 2 -3 -4 -1 -2 -3 1 0 -1 -2 1 0 -1 -2 0 -1 1]
[ 0 0 1 -1 1 -2 1 1 1 1 1 0 0 0 0 -1 -1 1 1 0 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*y*z-1 + x-1*y2*z-1 + 2*x-1*y + 3*y-1*z + x-1*z + x-1*y2*z-2 + 4*x-1*y*z-1 + 3*y-1 + 7*x-1 + 3*y-2*z + 4*x-1*y-1*z + 3*x-1*z-1 + 8*x-1*y-1 + y-3*z + 6*x-1*y-2*z + 3*x-1*y-2 + 4*x-1*y-3*z + x-1*y-4*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Image of facet 9 1 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 3944
Image of polytope 3944 PALP id: 3944
grdb id: 282143
Integer points: [ 1 0 0 0 1 -2 0 -4 -3 -2 -1 -2 -1 0 -3 -2 -1 0 -1 0 1 -1]
[ 0 1 0 0 -2 2 -2 2 1 0 -1 1 0 -1 2 1 0 -1 1 0 -1 1]
[ 0 0 1 -1 0 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + 2*x*y-1 + 2*x-1*y + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + x*y-2 + 3*y-1 + 4*x-1 + 2*x-2*y + 2*y-1*z-1 + 6*x-1*z-1 + 6*x-2*y*z-1 + 2*x-3*y2*z-1 + y-2*z-1 + 4*x-1*y-1*z-1 + 6*x-2*z-1 + 4*x-3*y*z-1 + x-4*y2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3945
Image of polytope 3945 PALP id: 3945
grdb id: 281909
Integer points: [ 1 0 0 1 -2 1 1 1 -1 0 -1 0 1 0 1 -1 0 1 0 1 1 1]
[ 0 1 0 0 2 -2 -1 -4 0 -2 1 -1 -3 0 -2 1 -1 -3 0 -2 -1 -1]
[ 0 0 1 -1 1 0 -2 -2 0 -1 0 -1 -2 -1 -2 1 0 -1 0 -1 -1 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + 2*x-1*y*z + x-2*y2*z + x*z-1 + 2*x*y-1 + 3*x-1*y + 4*x*y-1*z-1 + 3*z-1 + x*y-2 + 4*y-1 + 3*x-1 + x*y-1*z-2 + 5*x*y-2*z-1 + 6*y-1*z-1 + 3*x*y-2*z-2 + 2*x*y-3*z-1 + 3*y-2*z-1 + 3*x*y-3*z-2 + x*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3946
Image of polytope 3946 PALP id: 3946
grdb id: 283322
Integer points: [ 1 0 -1 0 -2 2 -3 2 -2 -1 0 1 -2 -1 0 1 -1 0 1 -1 0 1]
[ 0 1 1 0 1 -3 1 -4 0 -1 -2 -3 1 0 -1 -2 0 -1 -2 1 0 -1]
[ 0 0 0 1 -2 2 -2 3 -1 0 1 2 -1 0 1 2 -1 0 1 -1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
51 rank 2, number 7 x + y + 3*x*y-1*z + z + x2*y-3*z2 + 2*x*y-2*z2 + x2*y-4*z3 + x-1*y + 4*x*y-2*z + 6*y-1*z + 5*x*y-3*z2 + 2*x-1*y*z-1 + 6*y-1 + 6*x-1 + 10*y-2*z + 4*x-1*z-1 + 2*x-2*y*z-1 + 10*x-1*y-1 + x-2*y*z-2 + 5*x-2*z-1 + x-3*y*z-2
18 rank 1, V14 x + y + 2*x*y-1*z + z + x2*y-3*z2 + 2*x*y-2*z2 + x2*y-4*z3 + x-1*y + 4*x*y-2*z + 6*y-1*z + 5*x*y-3*z2 + 2*x-1*y*z-1 + 6*y-1 + 6*x-1 + 10*y-2*z + 4*x-1*z-1 + 2*x-2*y*z-1 + 10*x-1*y-1 + x-2*y*z-2 + 5*x-2*z-1 + x-3*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 157 1 Lattice Minkowski decompositions of facet 157
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 13 1 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3947
Image of polytope 3947 PALP id: 3947
grdb id: 283006
Integer points: [ 1 0 1 -3 -3 1 -5 1 0 -1 -2 -3 -4 0 -1 -2 0 -1 -2 1 0 -1]
[ 0 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0 0]
[ 0 0 2 -2 -2 2 -3 3 2 1 0 -1 -2 1 0 -1 1 0 -1 1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x*z2 + x*y-1*z3 + 2*x*z + x*y-1*z2 + x + y + 4*z + 6*y-1*z2 + 4*y-1*z + 6*x-1 + 15*x-1*y-1*z + 2*x-1*z-1 + 6*x-1*y-1 + 4*x-2*z-1 + 20*x-2*y-1 + 4*x-2*y-1*z-1 + x-3*z-2 + 15*x-3*y-1*z-1 + x-3*y-1*z-2 + 6*x-4*y-1*z-2 + x-5*y-1*z-3
151 ? x*z2 + x*y-1*z3 + 2*x*z + x*y-1*z2 + x + y + 5*z + 6*y-1*z2 + 4*y-1*z + 8*x-1 + 15*x-1*y-1*z + 2*x-1*z-1 + 6*x-1*y-1 + 5*x-2*z-1 + 20*x-2*y-1 + 4*x-2*y-1*z-1 + x-3*z-2 + 15*x-3*y-1*z-1 + x-3*y-1*z-2 + 6*x-4*y-1*z-2 + x-5*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 13 1 irreducible and admissible
Image of facet 173 1 Lattice Minkowski decompositions of facet 173
Image of facet 183 1 Lattice Minkowski decompositions of facet 183
Polytope 3948
Image of polytope 3948 PALP id: 3948
grdb id: 283327
Integer points: [ 1 0 1 -1 1 -3 0 -5 -1 -2 -3 -4 0 -1 -2 -3 0 -1 -2 1 0 -1]
[ 0 1 1 -1 2 -2 2 -3 1 0 -1 -2 1 0 -1 -2 0 0 -1 1 0 -1]
[ 0 0 2 0 2 -3 1 -4 0 -1 -2 -3 1 0 -1 -2 1 -1 -2 1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 146 1 Lattice Minkowski decompositions of facet 146
Image of facet 9 1 irreducible and admissible
Image of facet 8 1 none
Image of facet 201 1 Lattice Minkowski decompositions of facet 201
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3949
Image of polytope 3949 PALP id: 3949
grdb id: 282904
Integer points: [ 1 0 0 0 1 -1 -1 -5 -2 -3 -4 -1 -2 -3 0 -1 -1 -2 -3 0 -1 1]
[ 0 1 0 -1 -2 2 0 4 1 2 3 0 1 2 -1 0 1 2 3 0 1 -1]
[ 0 0 1 1 0 -1 1 -3 0 -1 -2 0 -1 -2 0 -1 0 -1 -2 0 -1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 148 1 none
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Polytope 3950
Image of polytope 3950 PALP id: 3950
grdb id: 278148
Integer points: [ 1 0 0 0 0 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
[ 0 1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 0 1 1 -2 2 2 -2 -1 0 1 -2 -1 0 1 -1 0 -1 0 1 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + y-1*z + 2*x-1*z + x-1*y-1*z2 + 2*z-1 + 3*y-1 + 4*x-1 + 5*x-1*y-1*z + x-2*y-1*z2 + 3*y-1*z-1 + 2*x-1*z-1 + 9*x-1*y-1 + 4*x-2*y-1*z + y-1*z-2 + 7*x-1*y-1*z-1 + 6*x-2*y-1 + 2*x-1*y-1*z-2 + 4*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 198 1 Lattice Minkowski decompositions of facet 198
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 3951
Image of polytope 3951 PALP id: 3951
grdb id: 277734
Integer points: [ 1 0 0 -1 -1 0 -3 -3 -2 -1 -3 -2 -1 0 -3 -2 -1 -2 -1 0 -1 0]
[ 0 1 0 1 1 -2 1 -2 -2 -2 -1 -1 -1 -1 0 0 0 1 -1 -1 0 0]
[ 0 0 1 0 -1 1 -2 -2 -1 0 -2 -1 0 1 -2 -1 0 -1 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 231 1 Lattice Minkowski decompositions of facet 231
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Polytope 3952
Image of polytope 3952 PALP id: 3952
grdb id: 280147
Integer points: [ 1 0 1 -1 0 1 1 -3 -2 -1 0 -2 -1 0 1 -1 0 -2 -1 0 -1 0]
[ 0 1 -1 1 0 -1 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 0 0 0 1 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 14 1 none
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Polytope 3953
Image of polytope 3953 PALP id: 3953
grdb id: 278160
Integer points: [ 1 0 0 0 0 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 0 -2 2 -2 2 -1 0 1 -1 0 1 -2 -1 0 1 -1 0 1 -1]
[ 0 0 1 -1 1 -2 1 -3 0 -1 -2 1 0 -1 1 0 -1 -2 1 0 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + z-1 + 4*x-1*y*z-1 + 2*y-1 + 5*x-1 + y-2*z + 2*x-1*y-1*z + 2*x-1*y*z-2 + 6*x-1*z-1 + 6*x-1*y-1 + 2*x-1*y-2*z + x-2*y2*z-3 + 4*x-2*y*z-2 + 6*x-2*z-1 + 4*x-2*y-1 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3954
Image of polytope 3954 PALP id: 3954
grdb id: 281543
Integer points: [ 1 0 0 0 0 0 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 -1 2 -3 1 0 -1 -2 1 0 -1 -2 1 0 -1 -2 0 -1]
[ 0 0 1 -1 1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 -1 -1 -1 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + 2*x-1*y + y-1*z + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 6*x-1 + y-1*z-1 + 6*x-1*z-1 + 5*x-2*y*z-1 + 6*x-1*y-1 + 6*x-1*y-1*z-1 + 10*x-2*z-1 + 2*x-1*y-2 + 2*x-1*y-2*z-1 + 10*x-2*y-1*z-1 + 5*x-2*y-2*z-1 + x-2*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 129 2 Lattice Minkowski decompositions of facet 129
Polytope 3955
Image of polytope 3955 PALP id: 3955
grdb id: 280470
Integer points: [ 1 0 0 -1 -1 -2 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -2 1 0 -4 -3 -2 -1 -3 -2 -1 0 -1 0 -2 -1 0 -1 0]
[ 0 0 1 0 0 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
85 rank 3, number 8 x + y + z + x-1*y + 2*y-1 + 4*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 5*x-1*y-1 + 4*x-1*y-1*z-1 + 5*x-2*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 10*x-2*y-1*z-1 + x-3*z-2 + 8*x-2*y-2*z-1 + 4*x-3*y-1*z-2 + 2*x-2*y-3*z-1 + 6*x-3*y-2*z-2 + 4*x-3*y-3*z-2 + x-3*y-4*z-2
38 ? x + y + z + x-1*y + 2*y-1 + 3*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 3*x-1*y-1 + 4*x-1*y-1*z-1 + 4*x-2*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 7*x-2*y-1*z-1 + x-3*z-2 + 6*x-2*y-2*z-1 + 4*x-3*y-1*z-2 + 2*x-2*y-3*z-1 + 6*x-3*y-2*z-2 + 4*x-3*y-3*z-2 + x-3*y-4*z-2
36 rank 3, number 7 x + y + z + x-1*y + 2*y-1 + 3*x-1 + 2*x-1*z-1 + x-2*y*z-1 + 4*x-1*y-1 + 4*x-1*y-1*z-1 + 5*x-2*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 9*x-2*y-1*z-1 + x-3*z-2 + 7*x-2*y-2*z-1 + 4*x-3*y-1*z-2 + 2*x-2*y-3*z-1 + 6*x-3*y-2*z-2 + 4*x-3*y-3*z-2 + x-3*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 253 1 Lattice Minkowski decompositions of facet 253
Polytope 3956
Image of polytope 3956 PALP id: 3956
grdb id: 278176
Integer points: [ 1 0 0 1 1 0 -2 -4 -1 0 -3 -2 -1 0 -1 0 -3 -2 -1 -2 -1 0]
[ 0 1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 -1 -1 -1 0 0 0]
[ 0 0 1 0 -1 -2 0 -2 0 0 -1 -1 -1 -1 0 0 -2 -2 -2 -1 -1 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x*y-1 + x*y-1*z-1 + 2*z-1 + 3*y-1 + 2*x-1 + 5*y-1*z-1 + 4*x-1*z-1 + 3*x-1*y-1 + y-1*z-2 + 9*x-1*y-1*z-1 + 2*x-2*z-1 + x-2*y-1 + 4*x-1*y-1*z-2 + 7*x-2*y-1*z-1 + 6*x-2*y-1*z-2 + 2*x-3*y-1*z-1 + 4*x-3*y-1*z-2 + x-4*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 198 1 Lattice Minkowski decompositions of facet 198
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 3957
Image of polytope 3957 PALP id: 3957
grdb id: 280321
Integer points: [ 1 0 1 0 -2 1 0 -4 -1 -2 -3 0 -1 -2 -3 0 -1 0 -1 -2 0 -1]
[ 0 1 -1 0 1 -2 -3 1 -2 -1 0 -2 -1 0 1 -1 0 -1 0 1 0 1]
[ 0 0 0 1 0 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*y-1 + 2*x-1*y + 3*y-1 + 4*x-1 + x-2*y + x*y-2*z-1 + 4*y-1*z-1 + 5*x-1*z-1 + 2*x-2*y*z-1 + 3*y-2*z-1 + 8*x-1*y-1*z-1 + 7*x-2*z-1 + 2*x-3*y*z-1 + y-3*z-2 + 4*x-1*y-2*z-2 + 6*x-2*y-1*z-2 + 4*x-3*z-2 + x-4*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Polytope 3958
Image of polytope 3958 PALP id: 3958
grdb id: 277552
Integer points: [ 1 0 0 -1 0 -1 -3 -3 -2 -1 -3 -2 -1 0 -3 -2 -1 -2 -1 0 -1 0]
[ 0 1 0 2 -2 -2 3 0 2 1 2 1 0 -1 1 0 -1 -1 1 0 0 -1]
[ 0 0 1 -1 1 0 -2 -2 -1 0 -2 -1 0 1 -2 -1 0 -1 -1 0 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y2*z-1 + 3*x-1*y + 2*y-1*z + 3*x-1*y*z-1 + 3*x-2*y2*z-1 + 2*y-1 + 7*x-1 + y-2*z + x-3*y3*z-2 + 2*x-1*z-1 + 8*x-2*y*z-1 + 5*x-1*y-1 + 3*x-3*y2*z-2 + 7*x-2*z-1 + x-1*y-2 + 3*x-3*y*z-2 + 2*x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 231 1 Lattice Minkowski decompositions of facet 231
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 3959
Image of polytope 3959 PALP id: 3959
grdb id: 277791
Integer points: [ 1 0 0 0 0 -2 -2 -5 -1 -3 -2 -1 -4 -3 -2 -1 -4 -3 -1 0 -2 -1]
[ 0 1 -1 0 -1 2 -1 2 1 2 1 0 2 1 0 -1 1 0 1 0 1 0]
[ 0 0 0 1 1 -1 -1 -4 0 -2 -1 0 -3 -2 -1 0 -3 -2 -1 0 -2 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + 2*x-1*y + y-1*z + 3*x-1*y*z-1 + x-2*y2*z-1 + y-1 + 5*x-1 + 3*x-1*z-1 + 7*x-2*y*z-1 + 2*x-1*y-1 + 2*x-2*y*z-2 + 3*x-3*y2*z-2 + 7*x-2*z-1 + 8*x-3*y*z-2 + x-2*y-1*z-1 + 3*x-4*y2*z-3 + 3*x-3*z-2 + 3*x-4*y*z-3 + x-5*y2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Image of facet 231 1 Lattice Minkowski decompositions of facet 231
Polytope 3960
Image of polytope 3960 PALP id: 3960
grdb id: 281524
Integer points: [ 1 0 0 0 0 -1 -2 -6 -2 -3 -4 -5 -1 -2 -3 -4 -1 -1 -2 -3 0 -1]
[ 0 1 -1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]
[ 0 0 0 1 1 1 -2 -4 0 -1 -2 -3 0 -1 -2 -3 -1 0 -1 -2 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
38 ? y*z + x + y + z + x-1*y*z + 5*x-1*y + 2*x-1*y*z-1 + y-1 + 4*x-1 + 5*x-2*y + 2*x-1*z-1 + 9*x-2*y*z-1 + x-2*y*z-2 + 5*x-2*z-1 + 10*x-3*y*z-1 + 7*x-3*y*z-2 + 2*x-3*z-2 + 10*x-4*y*z-2 + 2*x-4*y*z-3 + 5*x-5*y*z-3 + x-6*y*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 201 1 Lattice Minkowski decompositions of facet 201
Polytope 3961
Image of polytope 3961 PALP id: 3961
grdb id: 98314
Integer points: [ 1 0 0 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 1]
[ 0 1 0 -2 2 2 1 0 -2 1 -1 0 1 -1 0 0 1 -1 0 -2 -1 -1]
[ 0 0 1 2 -2 -1 0 -2 0 -2 -1 -1 -1 0 0 -1 -1 0 0 1 1 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*y*z-1 + x-1*y2*z-1 + x-1*y + 3*y-1*z + x-1*y2*z-2 + 2*z-1 + 4*x-1*y*z-1 + 4*y-1 + 3*x-1 + 2*y-2*z + 2*x-1*y*z-2 + 5*x-1*z-1 + 3*x-1*y-1 + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Polytope 3962
Image of polytope 3962 PALP id: 3962
grdb id: 98196
Integer points: [ 1 0 1 0 -2 1 -3 -3 1 0 -1 -2 0 -1 -2 -1 1 0 -1 1 0 -1]
[ 0 1 -1 0 2 -2 2 1 -3 -2 -1 0 -1 0 1 1 -2 -1 0 -1 0 1]
[ 0 0 0 1 -1 2 -2 -2 2 1 0 -1 1 0 -1 0 1 0 -1 1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + 2*x*y-1*z + z + x*y-2*z2 + x*y-1 + 2*x-1*y + 2*x*y-2*z + 4*y-1*z + x*y-3*z2 + 2*x-1*y*z-1 + x-2*y2*z-1 + 4*y-1 + 6*x-1 + 4*y-2*z + 2*x-1*z-1 + 4*x-2*y*z-1 + 6*x-1*y-1 + x-3*y2*z-2 + 4*x-2*z-1 + x-3*y*z-2
51 rank 2, number 7 x + y + 2*x*y-1*z + z + x*y-2*z2 + x*y-1 + 2*x-1*y + 2*x*y-2*z + 5*y-1*z + x*y-3*z2 + 2*x-1*y*z-1 + x-2*y2*z-1 + 4*y-1 + 8*x-1 + 4*y-2*z + 2*x-1*z-1 + 5*x-2*y*z-1 + 6*x-1*y-1 + x-3*y2*z-2 + 4*x-2*z-1 + x-3*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 187 1 Lattice Minkowski decompositions of facet 187
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3963
Image of polytope 3963 PALP id: 3963
grdb id: 98325
Integer points: [ 1 0 1 1 -2 0 -1 1 -2 -1 -1 0 -1 0 -1 0 1 0 1 0 0 1]
[ 0 1 1 0 -2 1 -2 1 -1 0 0 1 -1 0 -1 0 1 0 1 -1 -1 0]
[ 0 0 0 2 -3 2 -2 3 -2 0 -1 1 -1 1 -2 0 2 -1 1 0 -1 1]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
49 rank 2, number 4 x*y*z3 + 3*x*y*z2 + 3*x*y*z + x*z2 + y*z2 + x*y + 2*x*z + 2*y*z + x + y + 4*z + 3*z-1 + 2*y-1 + 2*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + 4*x-1*y-1*z-1 + 3*x-1*y-1*z-2 + x-1*y-2*z-2 + x-2*y-1*z-2 + x-2*y-2*z-3
9 rank 1, V10 x*y*z3 + 3*x*y*z2 + 3*x*y*z + x*z2 + y*z2 + x*y + 2*x*z + 2*y*z + x + y + 3*z + 3*z-1 + 2*y-1 + 2*x-1 + 2*y-1*z-1 + 2*x-1*z-1 + 3*x-1*y-1*z-1 + 3*x-1*y-1*z-2 + x-1*y-2*z-2 + x-2*y-1*z-2 + x-2*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 96 1 Lattice Minkowski decompositions of facet 96
Image of facet 44 4 Lattice Minkowski decompositions of facet 44
Polytope 3964
Image of polytope 3964 PALP id: 3964
grdb id: 98326
Integer points: [ 1 1 -1 -1 0 3 0 3 -3 -1 -2 0 -1 -2 1 0 -1 2 1 0 2 1]
[ 0 2 -2 0 0 3 1 4 -4 -1 -2 1 -2 -3 1 0 -1 3 2 -1 2 1]
[ 0 0 0 0 1 1 1 1 -2 -1 -1 0 -1 -1 0 0 0 1 1 0 1 1]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x3*y4*z + x3*y3*z + 3*x2*y3*z + 3*x2*y2*z + 3*x*y2*z + x*y2 + 3*x*y*z + 3*x*y + y*z + x + 2*y + z + 2*y-1 + x-1 + 3*x-1*y-1 + 2*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-2*z-1 + 2*x-2*y-2*z-1 + 2*x-2*y-3*z-1 + x-3*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Polytope 3965
Image of polytope 3965 PALP id: 3965
grdb id: 93823
Integer points: [ 1 0 0 1 1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 1 0 -1 0 -1 -1 2 -1 -1 -1 0 0 0 1 1 -1 -1 -1 0 0 1]
[ 0 0 1 0 -1 2 -1 -1 -1 0 1 -1 0 1 -1 0 -1 0 1 -1 0 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + x*z-1 + 2*y*z-1 + x-1*y2*z-1 + x*y-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + x*y-1*z-1 + 4*z-1 + 3*x-1*y*z-1 + 4*y-1 + 6*x-1 + 3*x-1*y-1*z + 2*y-1*z-1 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 3966
Image of polytope 3966 PALP id: 3966
grdb id: 95245
Integer points: [ 1 0 0 0 1 -2 1 -2 0 -1 -1 0 0 0 1 1 -1 -1 -1 0 0 1]
[ 0 1 0 -2 0 1 -2 0 1 0 1 -1 0 1 -1 0 -1 0 1 -1 0 -1]
[ 0 0 1 1 -2 0 0 1 -2 1 0 1 0 -1 0 -1 1 0 -1 0 -1 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + 2*x*z-1 + 2*y*z-1 + 2*x*y-1 + 2*x-1*y + 2*y-1*z + 2*x-1*z + x*z-2 + y*z-2 + 2*x*y-1*z-1 + 4*z-1 + 2*x-1*y*z-1 + x*y-2 + 4*y-1 + 4*x-1 + x-2*y + y-2*z + 2*x-1*y-1*z + x-2*z
22 ? x + y + z + 2*x*z-1 + 2*y*z-1 + 2*x*y-1 + 2*x-1*y + 2*y-1*z + 2*x-1*z + x*z-2 + y*z-2 + 2*x*y-1*z-1 + 5*z-1 + 2*x-1*y*z-1 + x*y-2 + 5*y-1 + 5*x-1 + x-2*y + y-2*z + 2*x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 16 3 Lattice Minkowski decompositions of facet 16
Image of facet 164 1 Lattice Minkowski decompositions of facet 164
Image of facet 15 3 Lattice Minkowski decompositions of facet 15
Polytope 3967
Image of polytope 3967 PALP id: 3967
grdb id: 93948
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 -1 1 1 -2 1 -2 0 -1 -1 -1 0 0 0 1 1 -1 0 0 0 1]
[ 0 0 0 2 2 -1 -1 -2 -2 0 -1 -2 1 0 -1 1 0 -1 1 0 -1 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 y*z2 + 2*y*z + x-1*y*z2 + x + y + 2*z + 3*x-1*y*z + 3*x-1*y + 3*x-1*z + 2*z-1 + x-1*y*z-1 + y-1 + 7*x-1 + 2*y-1*z-1 + 5*x-1*z-1 + 3*x-1*y-1 + x-1*z-2 + 5*x-1*y-1*z-1 + 2*x-1*y-1*z-2 + x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 174 1 Lattice Minkowski decompositions of facet 174
Polytope 3968
Image of polytope 3968 PALP id: 3968
grdb id: 96299
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 0 1 -1 -1 -2 -2 -2 -2 -2 -1 -1 -1 0 0 0 -1 -1 -1 0]
[ 0 0 1 -1 0 -2 2 2 -2 -1 0 1 -1 0 1 -1 0 1 -1 0 1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
31 rank 3, number 3 x + y + z + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + z-1 + 4*y-1 + 5*x-1 + 6*x-1*y-1*z + x-1*y-2*z2 + 2*y-1*z-1 + 2*x-1*z-1 + 10*x-1*y-1 + 4*x-1*y-2*z + 6*x-1*y-1*z-1 + 6*x-1*y-2 + x-1*y-1*z-2 + 4*x-1*y-2*z-1 + x-1*y-2*z-2
10 rank 1, V18 x + y + z + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + z-1 + 4*y-1 + 4*x-1 + 5*x-1*y-1*z + x-1*y-2*z2 + 2*y-1*z-1 + 2*x-1*z-1 + 8*x-1*y-1 + 4*x-1*y-2*z + 5*x-1*y-1*z-1 + 6*x-1*y-2 + x-1*y-1*z-2 + 4*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 223 1 Lattice Minkowski decompositions of facet 223
Polytope 3969
Image of polytope 3969 PALP id: 3969
grdb id: 94721
Integer points: [ 1 0 0 1 -1 1 -1 1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 1]
[ 0 1 0 0 1 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0 -1]
[ 0 0 1 -1 0 0 2 -2 -2 -1 0 1 -1 0 1 -2 -1 0 1 -1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x*z-1 + x*y-1 + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + 2*x*y-1*z-1 + 3*z-1 + 6*y-1 + 4*x-1 + 4*x-1*y-1*z + x*y-1*z-2 + 6*y-1*z-1 + 2*x-1*z-1 + 6*x-1*y-1 + 2*y-1*z-2 + 4*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3970
Image of polytope 3970 PALP id: 3970
grdb id: 96497
Integer points: [ 1 0 0 -1 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 -1 0 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 0 0]
[ 0 0 1 0 1 1 -2 1 -3 0 -1 -2 1 0 -1 -2 0 -1 0 -1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y + y-1*z + x-1*z + 2*z-1 + 3*y-1 + 4*x-1 + 2*x-1*y-1*z + 3*y-1*z-1 + 3*x-1*z-1 + 7*x-1*y-1 + x-1*y-2*z + y-1*z-2 + 8*x-1*y-1*z-1 + 4*x-1*y-2 + 3*x-1*y-1*z-2 + 6*x-1*y-2*z-1 + 4*x-1*y-2*z-2 + x-1*y-2*z-3
31 rank 3, number 3 x + y + z + x-1*y + y-1*z + x-1*z + 2*z-1 + 4*y-1 + 4*x-1 + 2*x-1*y-1*z + 4*y-1*z-1 + 3*x-1*z-1 + 7*x-1*y-1 + x-1*y-2*z + y-1*z-2 + 8*x-1*y-1*z-1 + 4*x-1*y-2 + 3*x-1*y-1*z-2 + 6*x-1*y-2*z-1 + 4*x-1*y-2*z-2 + x-1*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 93 1 Lattice Minkowski decompositions of facet 93
Polytope 3971
Image of polytope 3971 PALP id: 3971
grdb id: 94626
Integer points: [ 1 0 0 -1 1 -2 1 1 -3 0 -1 -2 0 -1 1 0 -1 -2 1 0 -1 0]
[ 0 1 0 1 -1 1 -2 -3 1 -2 -1 0 -1 0 -2 -1 0 1 -1 0 1 0]
[ 0 0 1 -1 -1 0 0 -1 -1 -1 -1 -1 0 0 -1 -1 -1 -1 0 0 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 x + y + z + 2*x*y-1 + 2*x-1*y + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + x*y-2 + 4*y-1 + 4*x-1 + x-2*y + 2*x*y-2*z-1 + 6*y-1*z-1 + 6*x-1*z-1 + 2*x-2*y*z-1 + x*y-3*z-1 + 4*y-2*z-1 + 6*x-1*y-1*z-1 + 4*x-2*z-1 + x-3*y*z-1
20 rank 1, V16 x + y + z + 2*x*y-1 + 2*x-1*y + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + 2*x*y-2*z-1 + 6*y-1*z-1 + 6*x-1*z-1 + 2*x-2*y*z-1 + x*y-3*z-1 + 4*y-2*z-1 + 6*x-1*y-1*z-1 + 4*x-2*z-1 + x-3*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 93 1 Lattice Minkowski decompositions of facet 93
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3972
Image of polytope 3972 PALP id: 3972
grdb id: 93843
Integer points: [ 1 0 0 -1 1 0 -2 1 1 1 0 1 0 -1 0 -1 1 1 0 1 0 -1]
[ 0 1 0 0 0 -1 1 -2 -2 -2 -1 -2 -1 0 -1 0 -1 -1 0 -1 0 1]
[ 0 0 1 1 -1 1 0 0 -3 -1 0 -2 -1 0 -2 -1 0 -1 0 -2 -1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x*z-1 + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + 4*x*y-1*z-1 + 4*z-1 + x*y-2 + 4*y-1 + 3*x-1 + x-2*y + 2*x*y-1*z-2 + 3*x*y-2*z-1 + 6*y-1*z-1 + 3*x-1*z-1 + 3*x*y-2*z-2 + 3*y-1*z-2 + x*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Image of facet 153 1 Lattice Minkowski decompositions of facet 153
Polytope 3973
Image of polytope 3973 PALP id: 3973
grdb id: 94699
Integer points: [ 1 0 0 0 0 -1 0 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 -1 -1 -1 0 0]
[ 0 1 0 1 -1 1 -1 1 -3 -2 -1 0 -2 -1 0 1 0 -2 -1 0 -1 0]
[ 0 0 1 -1 1 1 -1 1 1 1 1 1 0 0 0 0 -1 1 1 1 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + x-1*y*z + y*z-1 + 2*x-1*y + y-1*z + 4*x-1*z + x-2*y*z + 2*z-1 + 2*y-1 + 6*x-1 + 5*x-1*y-1*z + 4*x-2*z + y-1*z-1 + 6*x-1*y-1 + 2*x-1*y-2*z + 6*x-2*y-1*z + 2*x-1*y-2 + 4*x-2*y-2*z + x-2*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3974
Image of polytope 3974 PALP id: 3974
grdb id: 93844
Integer points: [ 1 0 0 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 -1 1 0 1 0 -3 -1 0 1 -2 -1 0 -2 -1 -1 0 -2 -1 0]
[ 0 0 1 0 1 1 -1 -2 -2 0 0 0 -1 -1 -1 -2 -2 0 0 -1 -1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y*z + x*y-1 + 2*x-1*y + x-1*z + 2*z-1 + x-1*y*z-1 + 3*y-1 + 5*x-1 + 4*y-1*z-1 + 5*x-1*z-1 + 3*x-1*y-1 + x-1*z-2 + 2*y-2*z-1 + 7*x-1*y-1*z-1 + 3*x-1*y-1*z-2 + 3*x-1*y-2*z-1 + 3*x-1*y-2*z-2 + x-1*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 174 1 Lattice Minkowski decompositions of facet 174
Polytope 3975
Image of polytope 3975 PALP id: 3975
grdb id: 94624
Integer points: [ 1 0 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 1 1 -1 -2 1 -3 0 -1 -2 1 0 -1 -2 0 0 -1 1 0 -1]
[ 0 0 1 -2 0 2 1 -2 2 -1 0 1 -1 0 1 2 1 -1 0 -1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
51 rank 2, number 7 x + y + z + 2*y*z-1 + x-1*y + 3*y-1*z + 2*x-1*z + x-1*y-1*z2 + y*z-2 + 3*z-1 + 2*x-1*y*z-1 + 3*y-1 + 6*x-1 + y-2*z + 6*x-1*y-1*z + 2*x-1*y-2*z2 + x-1*y*z-2 + 4*x-1*z-1 + 6*x-1*y-1 + 4*x-1*y-2*z + x-1*y-3*z2
18 rank 1, V14 x + y + z + 2*y*z-1 + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + y*z-2 + 3*z-1 + 2*x-1*y*z-1 + 3*y-1 + 6*x-1 + y-2*z + 6*x-1*y-1*z + 2*x-1*y-2*z2 + x-1*y*z-2 + 4*x-1*z-1 + 6*x-1*y-1 + 4*x-1*y-2*z + x-1*y-3*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3976
Image of polytope 3976 PALP id: 3976
grdb id: 95280
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 0 -1 -1 -1 -1 0 0 0 -1 -1 0]
[ 0 1 1 -1 -1 1 1 -2 -2 0 -1 0 1 0 -1 -2 1 0 -1 0 -1 0]
[ 0 0 2 0 -2 2 0 -1 -3 1 0 1 1 0 -1 -2 1 0 -1 -1 -2 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
51 rank 2, number 7 y*z2 + 2*y*z + x-1*y*z2 + x + y + 2*z + 2*x-1*y*z + x-1*y + 3*x-1*z + 2*z-1 + y-1 + 6*x-1 + 3*y-1*z-1 + 3*x-1*z-1 + 3*x-1*y-1 + y-1*z-2 + 6*x-1*y-1*z-1 + 3*x-1*y-1*z-2 + x-1*y-2*z-1 + 2*x-1*y-2*z-2 + x-1*y-2*z-3
18 rank 1, V14 y*z2 + 2*y*z + x-1*y*z2 + x + y + 2*z + 2*x-1*y*z + x-1*y + 3*x-1*z + 2*z-1 + y-1 + 6*x-1 + 2*y-1*z-1 + 3*x-1*z-1 + 3*x-1*y-1 + y-1*z-2 + 6*x-1*y-1*z-1 + 3*x-1*y-1*z-2 + x-1*y-2*z-1 + 2*x-1*y-2*z-2 + x-1*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Polytope 3977
Image of polytope 3977 PALP id: 3977
grdb id: 93838
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 0 1 0 -1 -1 -4 -2 -3 -1 -2 -3 0 -1 -2 0 -1 -2 0 -1]
[ 0 0 1 -1 0 1 1 -2 -2 0 -1 0 -1 -2 0 -1 -2 -1 0 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y + x-1*z + z-1 + 3*y-1 + 3*x-1 + x-1*y-1*z + 3*y-1*z-1 + 2*x-1*z-1 + 5*x-1*y-1 + 2*y-2*z-1 + 6*x-1*y-1*z-1 + 3*x-1*y-2 + x-1*y-1*z-2 + 7*x-1*y-2*z-1 + 3*x-1*y-2*z-2 + 3*x-1*y-3*z-1 + 3*x-1*y-3*z-2 + x-1*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 220 1 Lattice Minkowski decompositions of facet 220
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Polytope 3978
Image of polytope 3978 PALP id: 3978
grdb id: 89065
Integer points: [ 1 0 0 0 0 -1 0 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 -1 1 -1 1 -3 -2 -1 0 -2 -1 0 -2 -1 0 1 -1 0 0]
[ 0 0 1 -1 1 0 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + y*z-1 + x-1*y + y-1*z + 2*z-1 + 2*x-1*y*z-1 + 2*y-1 + 4*x-1 + y-1*z-1 + 6*x-1*z-1 + x-2*y*z-1 + 5*x-1*y-1 + 6*x-1*y-1*z-1 + 4*x-2*z-1 + 2*x-1*y-2 + 2*x-1*y-2*z-1 + 6*x-2*y-1*z-1 + 4*x-2*y-2*z-1 + x-2*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 3979
Image of polytope 3979 PALP id: 3979
grdb id: 91442
Integer points: [ 1 0 0 0 0 -1 -1 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 -1 2 -1 -1 3 2 1 0 2 1 0 -1 1 0 -1 1 0 0]
[ 0 0 0 1 1 -1 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y2*z-1 + 3*x-1*y + y-1*z + 4*x-1*y*z-1 + 3*x-2*y2*z-1 + y-1 + 6*x-1 + x-3*y3*z-2 + 4*x-1*z-1 + 9*x-2*y*z-1 + 3*x-1*y-1 + 4*x-3*y2*z-2 + x-1*y-1*z-1 + 9*x-2*z-1 + 6*x-3*y*z-2 + 3*x-2*y-1*z-1 + 4*x-3*z-2 + x-3*y-1*z-2
13 rank 2, number 12 x + y + z + x-1*y2*z-1 + 3*x-1*y + y-1*z + 3*x-1*y*z-1 + 3*x-2*y2*z-1 + y-1 + 6*x-1 + x-3*y3*z-2 + 3*x-1*z-1 + 9*x-2*y*z-1 + 3*x-1*y-1 + 4*x-3*y2*z-2 + x-1*y-1*z-1 + 9*x-2*z-1 + 6*x-3*y*z-2 + 3*x-2*y-1*z-1 + 4*x-3*z-2 + x-3*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 5 irreducible and admissible
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 93 1 Lattice Minkowski decompositions of facet 93
Polytope 3980
Image of polytope 3980 PALP id: 3980
grdb id: 574886
Integer points: [ 1 0 0 -1 0 0 -2 1 1 1 -1 0 -1 0 1 -1 0 1 0 1 1 1]
[ 0 1 0 1 -1 1 1 0 -2 -2 0 -1 1 0 -1 0 -1 -2 0 -1 0 -1]
[ 0 0 1 1 1 -1 1 -2 0 -2 0 -1 0 -1 -2 1 0 -1 0 -1 -1 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + x-1*y*z + 2*x*z-1 + y*z-1 + 2*x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + x*z-2 + 4*x*y-1*z-1 + 4*z-1 + x*y-2 + 4*y-1 + 3*x-1 + 2*x*y-1*z-2 + 2*x*y-2*z-1 + 3*y-1*z-1 + x*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Polytope 3981
Image of polytope 3981 PALP id: 3981
grdb id: 574884
Integer points: [ 1 0 0 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 -1 1 -1 1 -1 1 -1 1 1 0 0 0 0 -1 -1 0 0 -1 -1]
[ 0 0 1 0 -1 1 1 1 -2 -2 0 -1 1 0 -1 -2 0 -1 0 -1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x-1*y*z + y*z-1 + x*y-1 + 3*x-1*y + y-1*z + 2*x-1*z + 3*z-1 + 3*x-1*y*z-1 + 3*y-1 + 6*x-1 + x-1*y-1*z + x-1*y*z-2 + 2*y-1*z-1 + 6*x-1*z-1 + 3*x-1*y-1 + 2*x-1*z-2 + 3*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3982
Image of polytope 3982 PALP id: 3982
grdb id: 573895
Integer points: [ 1 0 0 1 1 -1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 -1 0 1 1 -2 1 -2 1 1 0 0 0 -1 -1 1 0 0 -1 -1]
[ 0 0 1 0 -1 1 -2 1 -2 1 0 -1 1 0 -1 1 0 -1 0 -1 1 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + x-1*y*z + x*z-1 + 2*y*z-1 + x*y-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + y*z-2 + 4*z-1 + 3*x-1*y*z-1 + 4*y-1 + 6*x-1 + y-2*z + 3*x-1*y-1*z + x-1*y*z-2 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z
11 rank 2, number 6 x + y + z + x-1*y*z + x*z-1 + 2*y*z-1 + x*y-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + y*z-2 + 3*z-1 + 3*x-1*y*z-1 + 3*y-1 + 6*x-1 + y-2*z + 3*x-1*y-1*z + x-1*y*z-2 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Polytope 3983
Image of polytope 3983 PALP id: 3983
grdb id: 574977
Integer points: [ 1 0 0 -1 2 0 0 -2 0 -2 1 -1 0 1 -1 0 1 -1 0 -2 -1 -1]
[ 0 1 0 1 -1 1 -1 1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 1]
[ 0 0 1 1 -1 -1 1 1 -1 1 -1 0 0 0 1 -1 -1 0 0 1 1 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + x-1*y*z + x2*y-1*z-1 + 2*x*z-1 + y*z-1 + 2*x*y-1 + 2*x-1*y + y-1*z + 3*x-1*z + x-2*y*z + 2*x*y-1*z-1 + 2*z-1 + 4*y-1 + 4*x-1 + 2*x-1*y-1*z + 2*x-2*z + y-1*z-1 + 2*x-1*y-1 + x-2*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 36 2 Lattice Minkowski decompositions of facet 36
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3984
Image of polytope 3984 PALP id: 3984
grdb id: 574842
Integer points: [ 1 0 0 1 1 -1 1 0 -2 -2 0 -1 0 -1 -2 -1 0 1 0 -1 0 -1]
[ 0 1 0 0 -1 2 -2 -2 0 2 0 1 -1 0 1 -1 1 -1 0 1 -1 0]
[ 0 0 1 -1 -1 -1 0 1 1 -1 -1 -1 0 0 0 1 -1 0 0 0 1 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + x*z-1 + 2*y*z-1 + x-1*y2*z-1 + 2*x*y-1 + 3*x-1*y + 2*y-1*z + 2*x-1*z + x*y-1*z-1 + 3*z-1 + 3*x-1*y*z-1 + x-2*y2*z-1 + x*y-2 + 4*y-1 + 5*x-1 + 2*x-2*y + y-2*z + 2*x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 3985
Image of polytope 3985 PALP id: 3985
grdb id: 574262
Integer points: [ 1 0 0 1 -1 0 -2 1 -3 1 0 -1 -2 0 -1 -2 1 0 -1 1 0 -1]
[ 0 1 0 -1 1 0 1 -2 1 -3 -2 -1 0 -1 0 1 -2 -1 0 -1 0 1]
[ 0 0 1 0 0 -1 -2 2 -2 2 1 0 -1 1 0 -1 1 0 -1 1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + 2*x*y-1*z + z + x*y-2*z2 + x*y-1 + x-1*y + 2*x*y-2*z + 4*y-1*z + x*y-3*z2 + z-1 + 2*x-1*y*z-1 + 5*y-1 + 5*x-1 + 4*y-2*z + 4*x-1*z-1 + 2*x-2*y*z-1 + 6*x-1*y-1 + x-2*y*z-2 + 4*x-2*z-1 + x-3*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 107 2 Lattice Minkowski decompositions of facet 107
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3986
Image of polytope 3986 PALP id: 3986
grdb id: 568804
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 -1 1 0 1 0 -2 -2 -1 -2 -1 0 -2 -1 0 -1 -1 0 -1 0]
[ 0 0 1 1 0 1 -1 -2 1 -2 1 0 0 0 -1 -1 -1 -2 0 0 -1 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y + y-1*z + x-1*z + 2*z-1 + x-1*y*z-1 + 3*y-1 + 4*x-1 + 2*x-1*y-1*z + 2*y-1*z-1 + 4*x-1*z-1 + 6*x-1*y-1 + x-1*y-2*z + x-1*z-2 + 6*x-1*y-1*z-1 + 3*x-1*y-2 + 2*x-1*y-1*z-2 + 3*x-1*y-2*z-1 + x-1*y-2*z-2
31 rank 3, number 3 x + y + z + x-1*y + y-1*z + x-1*z + 2*z-1 + x-1*y*z-1 + 3*y-1 + 5*x-1 + 2*x-1*y-1*z + 2*y-1*z-1 + 5*x-1*z-1 + 7*x-1*y-1 + x-1*y-2*z + x-1*z-2 + 7*x-1*y-1*z-1 + 3*x-1*y-2 + 2*x-1*y-1*z-2 + 3*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 225 1 Lattice Minkowski decompositions of facet 225
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 3987
Image of polytope 3987 PALP id: 3987
grdb id: 568869
Integer points: [ 1 0 0 1 -1 1 -1 1 -2 -2 -2 -2 -1 -1 -1 0 0 0 -1 -1 0 0]
[ 0 1 0 -1 1 -1 1 -2 1 -2 -1 0 -2 -1 0 -2 -1 0 -1 0 -1 0]
[ 0 0 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*y-1 + x-1*y + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 3*y-1 + 3*x-1 + x*y-2*z-1 + 5*y-1*z-1 + 5*x-1*z-1 + x-2*y*z-1 + 2*x-1*y-1 + 3*y-2*z-1 + 7*x-1*y-1*z-1 + 3*x-2*z-1 + 3*x-1*y-2*z-1 + 3*x-2*y-1*z-1 + x-2*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 174 1 Lattice Minkowski decompositions of facet 174
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Polytope 3988
Image of polytope 3988 PALP id: 3988
grdb id: 569725
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 1 -1 1 -2 0 -2 -1 -2 -1 0 -1 0 1 0 -1 0 -1 0]
[ 0 0 1 -1 0 2 -2 2 -2 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + y*z-1 + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + 2*z-1 + 2*x-1*y*z-1 + 2*y-1 + 6*x-1 + 5*x-1*y-1*z + x-1*y-2*z2 + x-1*y*z-2 + 5*x-1*z-1 + 6*x-1*y-1 + 2*x-1*y-2*z + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
62 rank 2, number 9 x + y + z + y*z-1 + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + 2*z-1 + 2*x-1*y*z-1 + 2*y-1 + 5*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + x-1*y*z-2 + 4*x-1*z-1 + 5*x-1*y-1 + 2*x-1*y-2*z + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 11 4 Lattice Minkowski decompositions of facet 11
Image of facet 224 1 Lattice Minkowski decompositions of facet 224
Polytope 3989
Image of polytope 3989 PALP id: 3989
grdb id: 568994
Integer points: [ 1 0 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 1 0 -2 1 0 -3 -1 0 1 -2 -1 0 -2 -1 -1 0 -1 0]
[ 0 0 1 -1 0 1 1 -2 -2 1 1 0 -1 1 0 -1 0 -1 1 0 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + y*z-1 + x-1*y + 2*y-1*z + x-1*z + 2*z-1 + 2*x-1*y*z-1 + 3*y-1 + 5*x-1 + y-2*z + 3*x-1*y-1*z + x-1*y*z-2 + 5*x-1*z-1 + 7*x-1*y-1 + 3*x-1*y-2*z + x-1*z-2 + 3*x-1*y-1*z-1 + 3*x-1*y-2 + x-1*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 174 1 Lattice Minkowski decompositions of facet 174
Polytope 3990
Image of polytope 3990 PALP id: 3990
grdb id: 25067
Integer points: [ 1 0 0 2 1 -1 -2 2 1 -3 -1 0 1 0 -1 -2 1 0 -1 -2 0 -1]
[ 0 1 0 -1 -1 1 1 -1 -1 1 -1 0 0 -1 0 1 -1 0 1 0 -1 0]
[ 0 0 1 -1 0 0 2 -2 -2 2 0 -1 -1 -1 0 1 -1 0 1 1 0 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + 2*x-1*y*z + x-2*y*z2 + x2*y-1*z-1 + 2*x*z-1 + x*y-1 + x-1*y + 3*x-1*z + 2*x-2*y*z + x-3*y*z2 + x2*y-1*z-2 + 3*x*y-1*z-1 + 2*z-1 + 2*y-1 + 4*x-1 + 2*x-2*z + x*y-1*z-2 + 2*y-1*z-1 + x-1*y-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 3991
Image of polytope 3991 PALP id: 3991
grdb id: 24223
Integer points: [ 1 0 0 -1 1 -1 1 -2 -2 1 1 -1 0 -1 0 1 -1 0 1 0 1 0]
[ 0 1 0 1 0 1 -1 1 0 -1 -3 -1 -2 0 -1 -2 0 -1 -2 0 -1 0]
[ 0 0 1 1 -1 0 0 1 1 -2 -2 0 -1 1 0 -1 0 -1 -2 0 -1 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x-1*y*z + x*z-1 + x*y-1 + x-1*y + 2*x-1*z + x-2*y*z + 3*x*y-1*z-1 + 2*z-1 + 4*y-1 + 4*x-1 + x-2*z + x*y-1*z-2 + 2*x*y-2*z-1 + 5*y-1*z-1 + 3*x-1*y-1 + 2*x*y-2*z-2 + 3*y-2*z-1 + x*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3992
Image of polytope 3992 PALP id: 3992
grdb id: 23122
Integer points: [ 1 0 0 1 -1 0 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 -1 1 -1 0 -1 1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 0 1 0 0 1 1 -1 -1 1 -3 0 -1 -2 0 -1 -2 0 -1 -2 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x*y-1 + x-1*y + y-1*z + x-1*z + x*y-1*z-1 + 3*z-1 + x-1*y*z-1 + 4*y-1 + 4*x-1 + x-1*y-1*z + 5*y-1*z-1 + 5*x-1*z-1 + 4*x-1*y-1 + 2*y-1*z-2 + 2*x-1*z-2 + 6*x-1*y-1*z-1 + 4*x-1*y-1*z-2 + x-1*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 3 Lattice Minkowski decompositions of facet 3
Image of facet 107 2 Lattice Minkowski decompositions of facet 107
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 3993
Image of polytope 3993 PALP id: 3993
grdb id: 547415
Integer points: [ 1 1 0 -15 -12 -9 -6 -3 -11 -8 -5 -2 -7 -4 -1 -3 0 -7 -4 -1 -3 0 1]
[ 0 2 0 -10 -8 -6 -4 -2 -7 -5 -3 -1 -4 -2 0 -1 1 -5 -3 -1 -2 0 1]
[ 0 0 1 -4 -3 -2 -1 0 -3 -2 -1 0 -2 -1 0 -1 0 -2 -1 0 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 1 irreducible and admissible
Image of facet 73 1 none
Image of facet 263 1 none
Polytope 3994
Image of polytope 3994 PALP id: 3994
grdb id: 544753
Integer points: [ 1 0 0 0 -4 -1 0 -2 -1 0 -3 -2 -1 0 -3 -2 -1 0 -1 0 -2 -1 0]
[ 0 1 1 -3 1 1 0 1 0 -1 1 0 -1 -2 0 -1 -2 1 1 0 1 0 -1]
[ 0 0 2 -2 -2 1 1 0 0 0 -1 -1 -1 -1 -2 -2 -2 1 0 0 -1 -1 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 1 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 80 1 none
Image of facet 206 1 Lattice Minkowski decompositions of facet 206
Polytope 3995
Image of polytope 3995 PALP id: 3995
grdb id: 544745
Integer points: [ 1 1 1 -5 -1 0 -2 -1 0 1 -3 -2 -1 0 -4 -3 -2 0 1 -1 0 1 -2]
[ 0 2 0 -2 -2 -1 -2 -1 0 1 -2 -1 0 1 -2 -1 0 -1 0 -1 0 1 -1]
[ 0 0 2 -2 2 2 1 1 1 1 0 0 0 0 -1 -1 -1 1 1 0 0 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 3 Lattice Minkowski decompositions of facet 16
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 264 1 none
Polytope 3996
Image of polytope 3996 PALP id: 3996
grdb id: 544736
Integer points: [ 1 0 1 -5 1 0 -1 -2 -3 -4 1 0 -1 -2 -3 0 -1 1 0 -1 -2 1 0]
[ 0 1 0 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 -1 -1 -1 -1 0 0]
[ 0 0 2 -2 4 3 2 1 0 -1 3 2 1 0 -1 1 0 2 1 0 -1 1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Image of facet 265 1 none
Polytope 3997
Image of polytope 3997 PALP id: 3997
grdb id: 544752
Integer points: [ 1 0 1 -3 -7 -1 -3 -5 0 -2 -4 -6 -1 -3 -5 -2 -4 1 -1 -3 0 -2 -1]
[ 0 1 0 0 -4 -1 -2 -3 0 -1 -2 -3 0 -1 -2 0 -1 0 -1 -2 0 -1 0]
[ 0 0 2 -2 -6 0 -2 -4 1 -1 -3 -5 0 -2 -4 -1 -3 1 -1 -3 0 -2 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x*z2 + 2*x*z + x + y + 4*z + 6*x-1 + 3*x-1*z-1 + 4*x-1*y-1 + 4*x-1*y-1*z-1 + 4*x-2*z-1 + 12*x-2*y-1*z-1 + 4*x-2*y-1*z-2 + x-3*z-2 + 12*x-3*y-1*z-2 + 6*x-3*y-2*z-2 + 2*x-3*y-2*z-3 + 4*x-4*y-1*z-3 + 12*x-4*y-2*z-3 + 6*x-5*y-2*z-4 + 4*x-5*y-3*z-4 + 4*x-6*y-3*z-5 + x-7*y-4*z-6
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 1 irreducible and admissible
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Image of facet 13 1 irreducible and admissible
Image of facet 206 1 Lattice Minkowski decompositions of facet 206
Polytope 3998
Image of polytope 3998 PALP id: 3998
grdb id: 544751
Integer points: [ 1 0 1 -3 -7 -5 -3 -1 -6 -4 -2 0 -5 -3 -1 -4 -2 -3 -1 1 -2 0 -1]
[ 0 1 0 0 -4 -3 -2 -1 -3 -2 -1 0 -2 -1 0 -1 0 -2 -1 0 -1 0 0]
[ 0 0 2 -2 -2 -1 0 1 -2 -1 0 1 -2 -1 0 -2 -1 -1 0 1 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 2 Lattice Minkowski decompositions of facet 32
Image of facet 1 2 irreducible and admissible
Image of facet 266 1 none
Polytope 3999
Image of polytope 3999 PALP id: 3999
grdb id: 544760
Integer points: [ 1 1 0 -5 -9 -8 -7 -6 -6 -5 -4 -3 -2 -3 -2 -1 0 -4 -3 -2 -1 0 1]
[ 0 2 0 -2 -6 -5 -4 -3 -4 -3 -2 -1 0 -2 -1 0 1 -3 -2 -1 -1 0 1]
[ 0 0 1 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 0 -1 -1 -1 0 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 267 1 Lattice Minkowski decompositions of facet 267
Image of facet 14 1 none
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 4000
Image of polytope 4000 PALP id: 4000
grdb id: 544754
Integer points: [ 1 0 1 -3 -11 -8 -5 -2 -9 -6 -3 0 -7 -4 -1 -5 -2 -5 -2 1 -3 0 -1]
[ 0 1 0 0 -4 -3 -2 -1 -3 -2 -1 0 -2 -1 0 -1 0 -2 -1 0 -1 0 0]
[ 0 0 2 -2 -6 -4 -2 0 -5 -3 -1 1 -4 -2 0 -3 -1 -3 -1 1 -2 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 2 Lattice Minkowski decompositions of facet 32
Image of facet 1 2 irreducible and admissible
Image of facet 268 1 none
Polytope 4001
Image of polytope 4001 PALP id: 4001
grdb id: 544711
Integer points: [ 1 0 1 -3 -3 0 -1 -2 0 -1 -2 -3 -1 -2 -3 -2 -3 1 0 -1 0 -1 -1]
[ 0 1 0 0 -4 -1 -2 -3 0 -1 -2 -3 0 -1 -2 0 -1 0 -1 -2 0 -1 0]
[ 0 0 2 -2 -2 1 0 -1 1 0 -1 -2 0 -1 -2 -1 -2 1 0 -1 0 -1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 x*z2 + 2*x*z + x + y + 4*z + 4*y-1*z + 4*y-1 + 6*x-1 + 2*x-1*z-1 + 12*x-1*y-1 + 4*x-1*y-1*z-1 + 4*x-2*z-1 + 6*x-1*y-2 + 2*x-1*y-2*z-1 + 12*x-2*y-1*z-1 + x-3*z-2 + 12*x-2*y-2*z-1 + 4*x-3*y-1*z-2 + 4*x-2*y-3*z-1 + 6*x-3*y-2*z-2 + 4*x-3*y-3*z-2 + x-3*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 2 Lattice Minkowski decompositions of facet 32
Image of facet 1 2 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 206 1 Lattice Minkowski decompositions of facet 206
Polytope 4002
Image of polytope 4002 PALP id: 4002
grdb id: 522683
Integer points: [ 1 0 0 0 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0 0]
[ 0 1 1 -3 -1 3 0 1 2 -2 -1 0 1 2 -2 -1 0 0 1 2 -1 0 1]
[ 0 0 2 -2 -2 2 -1 0 1 -2 -1 0 1 2 -1 0 1 -1 0 1 -1 0 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
11 rank 2, number 6 y*z2 + 2*x-1*y2*z2 + x-2*y3*z2 + 2*y*z + 2*x-1*y2*z + x + y + 4*z + 8*x-1*y*z + 4*x-2*y2*z + 4*x-1*y + 6*y-1 + 12*x-1 + 6*x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + 4*y-2*z-1 + 8*x-1*y-1*z-1 + 4*x-2*z-1 + y-3*z-2 + 2*x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Image of facet 13 1 irreducible and admissible
Image of facet 214 1 Lattice Minkowski decompositions of facet 214
Polytope 4003
Image of polytope 4003 PALP id: 4003
grdb id: 522703
Integer points: [ 1 0 1 0 -1 -4 -3 -2 -1 -3 -2 -1 0 -2 -1 0 -2 -1 0 -1 0 1 0]
[ 0 1 0 1 -2 1 1 1 1 0 0 0 0 -1 -1 -1 1 1 1 0 0 0 -1]
[ 0 0 2 2 -2 -2 -1 0 1 -2 -1 0 1 -2 -1 0 -1 0 1 -1 0 1 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
11 rank 2, number 6 x*z2 + y*z2 + 2*x*z + 2*y*z + x + y + 4*z + 4*x-1*y*z + 4*x-1*y + 2*y-1 + 8*x-1 + 6*x-2*y + 2*y-1*z-1 + 4*x-1*z-1 + 2*x-2*y*z-1 + 4*x-1*y-1*z-1 + 8*x-2*z-1 + 4*x-3*y*z-1 + x-1*y-2*z-2 + 3*x-2*y-1*z-2 + 3*x-3*z-2 + x-4*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 213 1 Lattice Minkowski decompositions of facet 213
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 4004
Image of polytope 4004 PALP id: 4004
grdb id: 522681
Integer points: [ 1 1 1 -3 1 -3 0 -1 -2 0 -1 -2 1 0 -1 1 0 -1 1 0 -1 1 1]
[ 0 3 0 -4 1 -3 0 -1 -2 -1 -2 -3 2 1 0 1 0 -1 0 -1 -2 2 1]
[ 0 0 2 -2 2 -2 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 0 0]
Degree: 8
Hilbert function: 1 + 7 t + 25 t2 + 63 t3 + 129 t4 + 231 t5 + 377 t6 + 575 t7 + 833 t8 + 1159 t9 + 1561 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
5 rank 1, V8 x*y3 + 2*x*y2*z + x*y*z2 + 3*x*y2 + 4*x*y*z + x*z2 + 3*x*y + 2*x*z + x + 4*y + 4*z + 4*y-1*z + 4*y-1 + 2*x-1*z-1 + 6*x-1*y-1 + 4*x-1*y-1*z-1 + 6*x-1*y-2 + 2*x-1*y-2*z-1 + 4*x-2*y-2*z-1 + 4*x-2*y-3*z-1 + x-3*y-3*z-2 + x-3*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 2 Lattice Minkowski decompositions of facet 32
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Image of facet 134 1 Lattice Minkowski decompositions of facet 134
Polytope 4005
Image of polytope 4005 PALP id: 4005
grdb id: 522702
Integer points: [ 1 1 0 0 -1 -5 -2 -3 -4 -1 -2 -3 0 -1 -1 -2 -3 0 -1 1 0 -1 1]
[ 0 3 0 1 -1 -9 -3 -5 -7 -1 -3 -5 1 -1 -2 -4 -6 0 -2 2 -1 -3 1]
[ 0 0 1 1 1 -3 0 -1 -2 0 -1 -2 0 -1 0 -1 -2 0 -1 0 0 -1 0]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 148 2 none
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Polytope 4006
Image of polytope 4006 PALP id: 4006
grdb id: 522324
Integer points: [ 1 1 -1 1 -1 -3 0 -1 -2 1 0 -1 -2 0 0 -1 -2 1 0 -1 1 0 0]
[ 0 2 -2 0 2 0 0 0 0 1 1 1 1 2 -1 -1 -1 0 0 0 1 1 -1]
[ 0 0 0 2 -2 -2 1 0 -1 1 0 -1 -2 -1 1 0 -1 1 0 -1 0 -1 0]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x*y2 + 2*x*y*z + x*z2 + 2*x*y + 2*x*z + 2*y2*z-1 + x + 6*y + 4*z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 6*x-1*y*z-1 + 2*y-1 + 6*x-1 + 4*x-1*z-1 + 4*x-1*y-1 + 2*x-2*y*z-2 + 4*x-2*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 3 Lattice Minkowski decompositions of facet 16
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 4007
Image of polytope 4007 PALP id: 4007
grdb id: 522416
Integer points: [ 1 0 0 -1 -3 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0]
[ 0 1 0 -1 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0]
[ 0 0 1 2 -3 3 2 1 0 -1 -2 2 1 0 -1 -2 1 0 -1 1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 269 1 none
Image of facet 241 1 Lattice Minkowski decompositions of facet 241
Polytope 4008
Image of polytope 4008 PALP id: 4008
grdb id: 522622
Integer points: [ 1 1 1 -3 -3 3 -1 2 0 -2 1 -1 -3 2 0 -2 -1 1 -1 2 0 1 -1]
[ 0 2 0 0 -2 2 1 2 1 0 1 0 -1 1 0 -1 -1 1 0 1 0 0 -1]
[ 0 0 2 -2 0 2 -1 1 0 -1 1 0 -1 2 1 0 1 0 -1 1 0 1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
26 rank 2, number 8 x3*y2*z2 + 2*x2*y2*z + 2*x2*y*z2 + 2*x2*y*z + x*y2 + 4*x*y*z + x*z2 + 2*x*y + 2*x*z + x + 4*y + 4*z + 2*x-1*y*z-1 + 5*x-1 + 2*x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + 2*x-2*z-1 + 2*x-2*y-1 + x-3*z-2 + 2*x-3*y-1*z-1 + x-3*y-2
18 rank 1, V14 x3*y2*z2 + 2*x2*y2*z + 2*x2*y*z2 + 2*x2*y*z + x*y2 + 7*x*y*z + x*z2 + 2*x*y + 2*x*z + x + 6*y + 6*z + 2*x-1*y*z-1 + 8*x-1 + 2*x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + 4*x-2*z-1 + 4*x-2*y-1 + x-3*z-2 + 2*x-3*y-1*z-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 5 Lattice Minkowski decompositions of facet 16
Image of facet 270 1 Lattice Minkowski decompositions of facet 270
Polytope 4009
Image of polytope 4009 PALP id: 4009
grdb id: 522557
Integer points: [ 1 0 0 -1 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 2 -3 2 1 0 -1 -2 2 1 0 -1 -2 1 0 -1 1 0 -1 1 0]
[ 0 0 1 -2 1 -4 -3 -2 -1 0 -3 -2 -1 0 1 -1 0 1 -2 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 73 1 none
Image of facet 271 1 Lattice Minkowski decompositions of facet 271
Polytope 4010
Image of polytope 4010 PALP id: 4010
grdb id: 522634
Integer points: [ 1 0 1 -3 -3 1 -2 -1 0 -3 -2 -1 0 1 -2 -1 0 -1 0 1 -1 0 1]
[ 0 1 0 0 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0 0]
[ 0 0 2 -2 0 4 1 2 3 -1 0 1 2 3 -1 0 1 0 1 2 -1 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x*z2 + 2*x*y-1*z3 + x*y-2*z4 + 2*x*z + 2*x*y-1*z2 + x + y + 3*z + 6*y-1*z2 + 4*y-2*z3 + 4*y-1*z + 3*x-1 + 9*x-1*y-1*z + 6*x-1*y-2*z2 + 2*x-1*z-1 + 2*x-1*y-1 + 3*x-2*z-1 + 7*x-2*y-1 + 4*x-2*y-2*z + x-3*z-2 + 2*x-3*y-1*z-1 + x-3*y-2
101 ? x*z2 + 2*x*y-1*z3 + x*y-2*z4 + 2*x*z + 2*x*y-1*z2 + x + y + 6*z + 9*y-1*z2 + 4*y-2*z3 + 4*y-1*z + 6*x-1 + 12*x-1*y-1*z + 6*x-1*y-2*z2 + 2*x-1*z-1 + 2*x-1*y-1 + 4*x-2*z-1 + 8*x-2*y-1 + 4*x-2*y-2*z + x-3*z-2 + 2*x-3*y-1*z-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 272 1 Lattice Minkowski decompositions of facet 272
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 4011
Image of polytope 4011 PALP id: 4011
grdb id: 522645
Integer points: [ 1 1 -1 0 1 -3 -2 -1 0 -2 -1 0 1 -1 0 -2 -1 0 1 -1 0 1 0]
[ 0 2 -2 0 4 0 1 2 3 0 1 2 3 0 1 -1 0 1 2 -1 0 1 -1]
[ 0 0 0 1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 -1 0 0 0 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Image of facet 14 1 none
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Polytope 4012
Image of polytope 4012 PALP id: 4012
grdb id: 522675
Integer points: [ 1 1 0 -4 1 -1 0 1 0 -1 -2 0 -1 -2 -3 -1 -2 -3 1 0 1 0 -1]
[ 0 2 0 -4 4 2 3 3 2 1 0 1 0 -1 -2 -1 -2 -3 2 1 1 0 -1]
[ 0 0 1 1 -2 -2 -2 -1 -1 -1 -1 0 0 0 0 1 1 1 -1 -1 0 0 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 14 1 none
Image of facet 273 1 Lattice Minkowski decompositions of facet 273
Polytope 4013
Image of polytope 4013 PALP id: 4013
grdb id: 522639
Integer points: [ 1 0 0 -2 -1 -5 -2 -3 -4 -1 -2 -3 -4 0 -1 -2 -3 -1 0 -1 -2 0 -1]
[ 0 1 1 -1 0 -4 -1 -2 -3 0 -1 -2 -3 1 0 -1 -2 0 0 -1 -2 0 -1]
[ 0 0 2 -2 2 -2 1 0 -1 1 0 -1 -2 1 0 -1 -2 -1 1 0 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 3 irreducible and admissible
Image of facet 14 1 none
Image of facet 273 1 Lattice Minkowski decompositions of facet 273
Polytope 4014
Image of polytope 4014 PALP id: 4014
grdb id: 522631
Integer points: [ 1 0 1 -3 -5 -1 -2 -3 -4 0 -1 -2 -3 -4 0 -1 -2 0 -1 -2 1 0 -1]
[ 0 1 0 0 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0 0]
[ 0 0 2 -2 -2 2 1 0 -1 2 1 0 -1 -2 1 0 -1 1 0 -1 1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
75 ? x*z2 + 2*x*z + x + y + 4*z + 2*y-1*z2 + 2*y-1*z + 8*x-1 + 8*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 4*x-1*y-1 + 4*x-2*z-1 + 13*x-2*y-1 + 4*x-2*y-2*z + 2*x-2*y-1*z-1 + x-3*z-2 + 8*x-3*y-1*z-1 + 6*x-3*y-2 + 2*x-4*y-1*z-2 + 4*x-4*y-2*z-1 + x-5*y-2*z-2
13 rank 2, number 12 x*z2 + 2*x*z + x + y + 2*z + 2*y-1*z2 + 2*y-1*z + 3*x-1 + 6*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 4*x-1*y-1 + 2*x-2*z-1 + 8*x-2*y-1 + 4*x-2*y-2*z + 2*x-2*y-1*z-1 + x-3*z-2 + 6*x-3*y-1*z-1 + 6*x-3*y-2 + 2*x-4*y-1*z-2 + 4*x-4*y-2*z-1 + x-5*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 274 1 Lattice Minkowski decompositions of facet 274
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 4015
Image of polytope 4015 PALP id: 4015
grdb id: 522325
Integer points: [ 1 0 1 -3 -1 -5 0 -1 -2 0 -1 -2 -3 -4 -2 -3 -4 1 0 -1 0 -1 -2]
[ 0 1 0 0 -2 -2 0 0 0 -1 -1 -1 -1 -1 -2 -2 -2 0 0 0 -1 -1 -1]
[ 0 0 2 -2 0 -4 1 0 -1 1 0 -1 -2 -3 -1 -2 -3 1 0 -1 0 -1 -2]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x*z2 + 2*x*z + x + y + 4*z + 2*y-1*z + 2*y-1 + 6*x-1 + 2*x-1*z-1 + 8*x-1*y-1 + 4*x-1*y-1*z-1 + 4*x-2*z-1 + x-1*y-2 + 12*x-2*y-1*z-1 + 2*x-2*y-1*z-2 + x-3*z-2 + 4*x-2*y-2*z-1 + 8*x-3*y-1*z-2 + 6*x-3*y-2*z-2 + 2*x-4*y-1*z-3 + 4*x-4*y-2*z-3 + x-5*y-2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 1 irreducible and admissible
Image of facet 214 1 Lattice Minkowski decompositions of facet 214
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 13 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 4016
Image of polytope 4016 PALP id: 4016
grdb id: 522644
Integer points: [ 1 0 0 0 -2 -6 -1 -2 -3 -4 -5 0 -1 -2 -3 0 -1 -2 -3 -4 0 -1 -1]
[ 0 1 -1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 1]
[ 0 0 0 2 -2 -4 1 0 -1 -2 -3 1 0 -1 -2 1 0 -1 -2 -3 0 -1 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 y*z2 + 2*y*z + x + y + 2*z + 6*x-1*y*z + 8*x-1*y + 2*x-1*y*z-1 + y-1 + 6*x-1 + 15*x-2*y + 2*x-1*z-1 + 12*x-2*y*z-1 + x-2*y*z-2 + 6*x-2*z-1 + 20*x-3*y*z-1 + 8*x-3*y*z-2 + 2*x-3*z-2 + 15*x-4*y*z-2 + 2*x-4*y*z-3 + 6*x-5*y*z-3 + x-6*y*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 212 1 Lattice Minkowski decompositions of facet 212
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Polytope 4017
Image of polytope 4017 PALP id: 4017
grdb id: 522578
Integer points: [ 1 0 0 -1 -2 -7 -6 -5 -4 -3 -5 -4 -3 -2 -1 -3 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 0 1 -1 1 -4 -3 -2 -1 0 -3 -2 -1 0 1 -2 -1 0 -2 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 73 1 none
Image of facet 14 1 none
Image of facet 271 1 Lattice Minkowski decompositions of facet 271
Polytope 4018
Image of polytope 4018 PALP id: 4018
grdb id: 522577
Integer points: [ 1 0 0 0 -1 -6 -5 -4 -3 -2 -4 -3 -2 -1 -2 -1 0 -3 -2 -1 0 -1 0]
[ 0 1 0 -2 -2 3 2 1 0 -1 2 1 0 -1 1 0 -1 2 1 0 -1 1 0]
[ 0 0 1 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 227 1 Lattice Minkowski decompositions of facet 227
Image of facet 14 1 none
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Polytope 4019
Image of polytope 4019 PALP id: 4019
grdb id: 522576
Integer points: [ 1 0 0 -1 -2 -7 -6 -5 -4 -3 -5 -4 -3 -2 -1 -3 -2 -1 -3 -2 -1 -1 0]
[ 0 1 0 0 -1 -6 -5 -4 -3 -2 -4 -3 -2 -1 0 -2 -1 0 -3 -2 -1 -1 0]
[ 0 0 1 -1 2 2 2 2 2 2 1 1 1 1 1 0 0 0 1 1 1 0 0]
Degree: 32
Hilbert function: 1 + 19 t + 85 t2 + 231 t3 + 489 t4 + 891 t5 + 1469 t6 + 2255 t7 + 3281 t8 + 4579 t9 + 6181 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 14 1 none
Image of facet 254 1 Lattice Minkowski decompositions of facet 254
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Polytope 4020
Image of polytope 4020 PALP id: 4020
grdb id: 522103
Integer points: [ 1 0 1 -3 -3 1 0 -1 -2 1 0 -1 -2 -3 0 -1 -2 1 0 -1 1 0 -1]
[ 0 1 0 0 -2 -2 0 0 0 -1 -1 -1 -1 -1 -2 -2 -2 0 0 0 -1 -1 -1]
[ 0 0 2 -2 -2 2 1 0 -1 2 1 0 -1 -2 1 0 -1 1 0 -1 1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 x*z2 + 2*x*z + 2*x*y-1*z2 + x + y + 2*x*y-1*z + 4*z + x*y-2*z2 + 8*y-1*z + 4*y-1 + 6*x-1 + 4*y-2*z + 2*x-1*z-1 + 12*x-1*y-1 + 2*x-1*y-1*z-1 + 4*x-2*z-1 + 6*x-1*y-2 + 8*x-2*y-1*z-1 + x-3*z-2 + 4*x-2*y-2*z-1 + 2*x-3*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 13 1 irreducible and admissible
Image of facet 214 1 Lattice Minkowski decompositions of facet 214
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 4021
Image of polytope 4021 PALP id: 4021
grdb id: 439636
Integer points: [ 1 0 0 1 1 -2 -2 0 0 0 -1 -1 -1 -1 -2 -2 -2 1 0 0 -1 -1 -1]
[ 0 1 0 -1 -2 2 -2 -2 -1 0 -2 -1 0 1 -1 0 1 -1 -1 0 -1 0 1]
[ 0 0 1 -1 0 -1 3 1 0 -1 2 1 0 -1 2 1 0 0 1 0 2 1 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 80 1 none
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Polytope 4022
Image of polytope 4022 PALP id: 4022
grdb id: 439394
Integer points: [ 1 0 0 2 -1 0 -3 0 0 -1 -1 -1 -2 -2 1 1 0 0 -1 -1 -2 1 0]
[ 0 1 0 -1 2 -3 0 -1 -2 0 -1 -2 0 -1 -1 -2 0 -1 1 0 1 0 1]
[ 0 0 1 -1 -1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 -1 -1]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x + y + z + x2*y-1*z-1 + 3*x*z-1 + 3*y*z-1 + x-1*y2*z-1 + 3*x*y-1 + 3*x-1*y + 3*y-1*z + 3*x-1*z + 2*x*y-2 + 6*y-1 + 6*x-1 + 2*x-2*y + 3*y-2*z + 6*x-1*y-1*z + 3*x-2*z + y-3*z + 3*x-1*y-2*z + 3*x-2*y-1*z + x-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Polytope 4023
Image of polytope 4023 PALP id: 4023
grdb id: 439399
Integer points: [ 1 0 0 2 -3 3 0 -1 -2 1 0 -1 2 1 0 -1 -2 1 0 2 0 -1 1]
[ 0 1 0 -1 3 -3 -3 -1 1 -3 -1 1 -3 -1 -2 0 2 -2 0 -2 -1 1 -1]
[ 0 0 1 -1 1 -2 -2 -1 0 -2 -1 0 -2 -1 -1 0 1 -1 0 -1 0 1 0]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x + y + z + 3*x-1*y*z + 3*x-2*y2*z + x-3*y3*z + x2*y-1*z-1 + 3*x*y-1 + 3*x-1*y + 3*x2*y-2*z-1 + 4*x*y-1*z-1 + 3*y-1 + 6*x-1 + 3*x-2*y + x3*y-3*z-2 + 6*x*y-2*z-1 + 6*y-1*z-1 + 3*x2*y-3*z-2 + 3*y-2*z-1 + 3*x-1*y-1*z-1 + 3*x*y-3*z-2 + y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 52 2 Lattice Minkowski decompositions of facet 52
Image of facet 153 1 Lattice Minkowski decompositions of facet 153
Polytope 4024
Image of polytope 4024 PALP id: 4024
grdb id: 439601
Integer points: [ 1 0 0 -3 2 2 -4 1 0 -1 -2 -3 1 0 -1 -2 1 0 -1 -2 1 0 -1]
[ 0 1 0 2 -3 -4 2 -3 -2 -1 0 1 -2 -1 0 1 -2 -1 0 1 -1 0 1]
[ 0 0 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 -1 -1 -1 -1 0 0 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 8 2 none
Image of facet 58 1 Lattice Minkowski decompositions of facet 58
Image of facet 260 1 Lattice Minkowski decompositions of facet 260
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Polytope 4025
Image of polytope 4025 PALP id: 4025
grdb id: 439397
Integer points: [ 1 0 0 1 -2 1 -2 -2 -2 -1 -1 -1 -1 0 0 0 1 -1 -1 0 0 1 1]
[ 0 1 0 -2 2 -4 -1 0 1 -2 -1 0 1 -3 -2 -1 -3 0 1 -1 0 -2 -1]
[ 0 0 1 0 1 -2 -2 -1 0 -2 -1 0 1 -2 -1 0 -1 -1 0 -1 0 -1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 231 1 Lattice Minkowski decompositions of facet 231
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Polytope 4026
Image of polytope 4026 PALP id: 4026
grdb id: 439663
Integer points: [ 1 0 1 1 -3 -4 0 -1 -2 -3 0 -1 -2 1 0 -1 0 -1 -2 1 0 -1 1]
[ 0 1 -2 0 0 1 1 1 1 1 0 0 0 -1 -1 -1 1 1 1 0 0 0 -1]
[ 0 0 0 2 -2 -2 2 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x*z2 + y*z2 + 2*x*z + 2*y*z + x + y + 2*x*y-1*z + 5*z + 4*x-1*y*z + 2*x*y-1 + 4*x-1*y + x*y-2 + 4*y-1 + 8*x-1 + 6*x-2*y + 2*x-1*z-1 + 2*x-2*y*z-1 + 2*x-1*y-1*z-1 + 5*x-2*z-1 + 4*x-3*y*z-1 + x-3*z-2 + x-4*y*z-2
22 ? x*z2 + y*z2 + 2*x*z + 2*y*z + x + y + 2*x*y-1*z + 6*z + 4*x-1*y*z + 2*x*y-1 + 4*x-1*y + x*y-2 + 5*y-1 + 10*x-1 + 6*x-2*y + 2*x-1*z-1 + 2*x-2*y*z-1 + 2*x-1*y-1*z-1 + 6*x-2*z-1 + 4*x-3*y*z-1 + x-3*z-2 + x-4*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Image of facet 223 1 Lattice Minkowski decompositions of facet 223
Polytope 4027
Image of polytope 4027 PALP id: 4027
grdb id: 439692
Integer points: [ 1 0 0 -1 -2 0 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 0 -3 -5 -1 -2 -3 -4 0 -1 -2 0 -1 -2 -3 -4 0 -1 -1 -2]
[ 0 0 1 1 1 -2 -4 0 -1 -2 -3 0 -1 -2 1 0 -1 -2 -3 0 -1 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + x-1*y*z + 2*x-1*z + 3*y-1 + 4*x-1 + x-2*z + 2*y-1*z-1 + 8*x-1*y-1 + 3*y-2*z-1 + 5*x-1*y-1*z-1 + 5*x-2*y-1 + 12*x-1*y-2*z-1 + y-3*z-2 + 2*x-1*y-2*z-2 + 10*x-2*y-2*z-1 + 8*x-1*y-3*z-2 + 10*x-2*y-3*z-2 + 2*x-1*y-4*z-3 + 5*x-2*y-4*z-3 + x-2*y-5*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 216 1 Lattice Minkowski decompositions of facet 216
Image of facet 9 1 irreducible and admissible
Polytope 4028
Image of polytope 4028 PALP id: 4028
grdb id: 439696
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 1 -1 -1 1 1 1 1 1 1 0 0 0 0 0 -1 -1 1 1 0 0 0]
[ 0 0 3 -3 0 4 -1 0 1 2 3 -2 -1 0 1 2 -2 -1 1 2 -1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 2 none
Image of facet 9 2 irreducible and admissible
Image of facet 146 1 Lattice Minkowski decompositions of facet 146
Image of facet 216 1 Lattice Minkowski decompositions of facet 216
Polytope 4029
Image of polytope 4029 PALP id: 4029
grdb id: 439506
Integer points: [ 1 0 0 0 1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -1 1 -4 -3 -2 -1 0 -3 -2 -1 0 -2 -1 -2 -1 0 1 -1 0]
[ 0 0 1 -1 0 -2 3 2 1 0 -1 2 1 0 -1 1 0 2 1 0 -1 1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 218 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Polytope 4030
Image of polytope 4030 PALP id: 4030
grdb id: 437961
Integer points: [ 1 0 0 -1 2 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 1 1 1]
[ 0 1 0 -1 -1 2 -1 -1 -1 0 0 0 1 1 -1 -1 -1 0 0 1 -1 -1 0]
[ 0 0 1 2 -1 -1 -1 0 1 -1 0 1 -1 0 -1 0 1 -1 0 -1 -1 0 -1]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
49 rank 2, number 4 x + y + z + x2*y-1*z-1 + 3*x*z-1 + 3*y*z-1 + x-1*y2*z-1 + 3*x*y-1 + 3*x-1*y + 3*y-1*z + 3*x-1*z + x-1*y-1*z2 + 3*x*y-1*z-1 + 6*z-1 + 3*x-1*y*z-1 + 6*y-1 + 6*x-1 + 3*x-1*y-1*z + 3*y-1*z-1 + 3*x-1*z-1 + 3*x-1*y-1 + x-1*y-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 20 3 Lattice Minkowski decompositions of facet 20
Image of facet 52 3 Lattice Minkowski decompositions of facet 52
Polytope 4031
Image of polytope 4031 PALP id: 4031
grdb id: 438025
Integer points: [ 1 1 1 -1 -1 -1 -3 0 0 -1 -2 -2 1 0 1 0 -1 0 -1 -2 1 0 0]
[ 0 2 0 0 0 -2 -2 -1 0 -1 -2 -1 0 -1 1 0 -1 1 0 -1 1 0 1]
[ 0 0 2 0 -2 0 -2 1 1 0 -1 -1 1 0 1 0 -1 0 -1 -2 0 -1 -1]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x*y2 + 2*x*y*z + x*z2 + 2*x*y + 2*x*z + x + 2*y + 2*z + 2*y*z-1 + 2*y-1*z + 2*z-1 + 2*y-1 + x-1 + 4*x-1*z-1 + 4*x-1*y-1 + x-1*z-2 + 4*x-1*y-1*z-1 + x-1*y-2 + 2*x-2*y-1*z-1 + 2*x-2*y-1*z-2 + 2*x-2*y-2*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 4 Lattice Minkowski decompositions of facet 16
Image of facet 36 3 Lattice Minkowski decompositions of facet 36
Polytope 4032
Image of polytope 4032 PALP id: 4032
grdb id: 437950
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 2 -1 -1 -4 -3 -2 -3 -2 -1 0 -2 -1 0 1 0 1 -2 -1 -1 0]
[ 0 0 1 -1 -1 2 2 1 0 2 1 0 -1 2 1 0 -1 1 0 1 0 1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 243 1 Lattice Minkowski decompositions of facet 243
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 14 1 none
Polytope 4033
Image of polytope 4033 PALP id: 4033
grdb id: 438004
Integer points: [ 1 0 0 0 0 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 -1 -1 -1 -1 0 0 0 0]
[ 0 1 1 -1 -1 1 -3 0 -1 -2 1 0 -1 -2 0 1 0 -1 -2 1 0 -1 0]
[ 0 0 2 0 -2 0 -4 -1 -2 -3 1 0 -1 -2 1 0 -1 -2 -3 1 0 -1 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 y*z2 + 2*y*z + x + y + 2*z + 2*x-1*y*z + 2*x-1*y + 2*z-1 + y-1 + 6*x-1 + x-2*y + 2*y-1*z-1 + 6*x-1*z-1 + y-1*z-2 + 6*x-1*y-1*z-1 + 4*x-2*z-1 + 6*x-1*y-1*z-2 + 2*x-1*y-2*z-2 + 6*x-2*y-1*z-2 + 2*x-1*y-2*z-3 + 4*x-2*y-2*z-3 + x-2*y-3*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 3 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 127 2 Lattice Minkowski decompositions of facet 127
Polytope 4034
Image of polytope 4034 PALP id: 4034
grdb id: 439128
Integer points: [ 1 0 0 0 -1 -2 -5 -1 -3 -2 -1 -4 -3 -2 -1 -4 -3 -2 -1 0 -2 -1 0]
[ 0 1 0 -1 -2 2 2 1 2 1 0 2 1 0 -1 1 0 -1 1 0 1 0 -1]
[ 0 0 1 1 0 -1 -4 0 -2 -1 0 -3 -2 -1 0 -3 -2 -1 -1 0 -2 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + 2*x-1*y + y-1*z + 3*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 5*x-1 + 4*x-1*z-1 + 7*x-2*y*z-1 + 3*x-1*y-1 + 2*x-2*y*z-2 + 3*x-3*y2*z-2 + 9*x-2*z-1 + x-1*y-2 + 9*x-3*y*z-2 + 4*x-2*y-1*z-1 + 3*x-4*y2*z-3 + 6*x-3*z-2 + 4*x-4*y*z-3 + x-5*y2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 256 1 Lattice Minkowski decompositions of facet 256
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 4035
Image of polytope 4035 PALP id: 4035
grdb id: 438634
Integer points: [ 1 0 -1 0 -2 0 -5 -4 -3 -2 -1 -4 -3 -2 -1 -3 -2 -1 -2 -1 0 -1 0]
[ 0 1 1 0 0 -1 -6 -5 -4 -3 -2 -4 -3 -2 -1 -2 -1 0 -3 -2 -1 -1 0]
[ 0 0 0 1 -1 1 -4 -3 -2 -1 0 -3 -2 -1 0 -2 -1 0 -2 -1 0 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 258 1 none
Image of facet 73 1 none
Polytope 4036
Image of polytope 4036 PALP id: 4036
grdb id: 438626
Integer points: [ 1 0 0 0 0 -1 -6 -2 -3 -4 -5 -1 -2 -3 -4 0 -1 -2 -1 -2 -3 0 -1]
[ 0 1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 0 1 -1 1 1 -4 0 -1 -2 -3 0 -1 -2 -3 0 -1 -2 0 -1 -2 0 -1]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + y-1*z + 2*y-1 + 4*x-1 + x-1*y-1*z + y-1*z-1 + 3*x-1*z-1 + 6*x-1*y-1 + 5*x-1*y-1*z-1 + 5*x-2*z-1 + 5*x-2*y-1 + 12*x-2*y-1*z-1 + 3*x-2*y-1*z-2 + 2*x-3*z-2 + 10*x-3*y-1*z-1 + 10*x-3*y-1*z-2 + 10*x-4*y-1*z-2 + 3*x-4*y-1*z-3 + 5*x-5*y-1*z-3 + x-6*y-1*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 227 1 Lattice Minkowski decompositions of facet 227
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Polytope 4037
Image of polytope 4037 PALP id: 4037
grdb id: 438635
Integer points: [ 1 0 0 0 0 -1 -6 -5 -4 -3 -2 -4 -3 -2 -1 -2 -1 0 -3 -2 -1 -1 0]
[ 0 1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 0 1 -1 1 2 2 2 2 2 2 1 1 1 1 0 0 0 1 1 1 0 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 227 1 Lattice Minkowski decompositions of facet 227
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 14 1 none
Polytope 4038
Image of polytope 4038 PALP id: 4038
grdb id: 438633
Integer points: [ 1 0 0 -1 -1 -2 -7 -3 -4 -5 -6 -2 -3 -4 -5 -1 -2 -3 -1 -2 -3 0 -1]
[ 0 1 0 0 0 -1 -6 -2 -3 -4 -5 -1 -2 -3 -4 0 -1 -2 -1 -2 -3 0 -1]
[ 0 0 1 -1 1 1 -4 0 -1 -2 -3 0 -1 -2 -3 0 -1 -2 0 -1 -2 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 258 1 none
Image of facet 14 1 none
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Polytope 4039
Image of polytope 4039 PALP id: 4039
grdb id: 438565
Integer points: [ 1 0 0 0 -3 -2 -7 -3 -4 -5 -6 -1 -2 -3 -4 -5 -1 -2 -1 -2 -3 0 -1]
[ 0 1 0 -1 0 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
[ 0 0 1 1 -2 1 -4 0 -1 -2 -3 1 0 -1 -2 -3 0 -1 0 -1 -2 0 -1]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
46 ? x + y + z + y-1*z + 4*x-1 + 2*x-1*y-1*z + 2*x-1*z-1 + 4*x-1*y-1 + 4*x-2*z-1 + 8*x-2*y-1 + x-2*y-2*z + 5*x-2*y-1*z-1 + x-3*z-2 + 12*x-3*y-1*z-1 + 5*x-3*y-2 + 2*x-3*y-1*z-2 + 8*x-4*y-1*z-2 + 10*x-4*y-2*z-1 + 2*x-5*y-1*z-3 + 10*x-5*y-2*z-2 + 5*x-6*y-2*z-3 + x-7*y-2*z-4
67 ? x + y + z + y-1*z + 5*x-1 + 2*x-1*y-1*z + 2*x-1*z-1 + 4*x-1*y-1 + 5*x-2*z-1 + 9*x-2*y-1 + x-2*y-2*z + 5*x-2*y-1*z-1 + x-3*z-2 + 14*x-3*y-1*z-1 + 5*x-3*y-2 + 2*x-3*y-1*z-2 + 9*x-4*y-1*z-2 + 10*x-4*y-2*z-1 + 2*x-5*y-1*z-3 + 10*x-5*y-2*z-2 + 5*x-6*y-2*z-3 + x-7*y-2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 257 1 Lattice Minkowski decompositions of facet 257
Polytope 4040
Image of polytope 4040 PALP id: 4040
grdb id: 275527
Integer points: [ 1 0 0 1 0 0 -2 -2 0 0 1 -1 -1 -1 -1 0 0 0 -2 -2 -1 -1 -1]
[ 0 1 0 -2 1 -2 3 0 -1 0 -1 -1 0 1 2 -1 0 1 1 2 0 1 2]
[ 0 0 1 2 -2 1 -4 -1 0 -1 1 0 -1 -2 -3 1 0 -1 -2 -3 0 -1 -2]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
11 rank 2, number 6 x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*y*z-1 + 2*y-1*z + y*z-2 + 2*x-1*y2*z-2 + 3*z-1 + 4*x-1*y*z-1 + 3*y-1 + 2*x-1 + y-2*z + 2*x-1*y2*z-3 + 6*x-1*y*z-2 + 6*x-1*z-1 + 2*x-1*y-1 + x-2*y3*z-4 + 3*x-2*y2*z-3 + 3*x-2*y*z-2 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Polytope 4041
Image of polytope 4041 PALP id: 4041
grdb id: 275510
Integer points: [ 1 0 0 -3 2 1 -2 4 0 2 -1 1 3 0 2 -1 1 3 -2 0 2 -1 1]
[ 0 1 0 3 -1 -2 1 -5 -1 -3 0 -2 -4 -1 -3 1 -1 -3 2 0 -2 1 -1]
[ 0 0 1 1 -1 0 0 -3 -1 -2 0 -1 -2 0 -1 0 -1 -2 1 0 -1 1 0]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x + y + z + 3*x-1*y*z + 3*x-2*y2*z + x-3*y3*z + x2*y-1*z-1 + 3*x*y-1 + 3*x-1*y + 4*x2*y-2*z-1 + 4*x*y-1*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + 2*x3*y-3*z-2 + 3*x2*y-3*z-1 + 6*x*y-2*z-1 + 3*y-1*z-1 + 3*x3*y-4*z-2 + 3*x2*y-3*z-2 + x4*y-5*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 82 2 Lattice Minkowski decompositions of facet 82
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 4042
Image of polytope 4042 PALP id: 4042
grdb id: 274128
Integer points: [ 1 0 1 -2 1 -1 0 -2 0 -1 0 1 -2 -1 0 -1 0 1 -1 0 1 -1 0]
[ 0 1 -2 1 0 -2 1 -1 -2 -1 -1 -1 0 0 0 1 -1 -1 0 0 0 1 1]
[ 0 0 0 0 2 -2 2 -2 -1 -1 0 1 -1 0 1 1 -1 0 -1 0 1 0 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
11 rank 2, number 6 x*z2 + y*z2 + 2*x*z + 2*y*z + x + y + 2*x*y-1*z + 4*z + 2*x-1*y*z + 2*x*y-1 + 2*x-1*y + x*y-2 + 5*y-1 + 5*x-1 + x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + 2*y-2*z-1 + 4*x-1*y-1*z-1 + 2*x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
7 rank 1, V12 x*z2 + y*z2 + 2*x*z + 2*y*z + x + y + 2*x*y-1*z + 5*z + 2*x-1*y*z + 2*x*y-1 + 2*x-1*y + x*y-2 + 6*y-1 + 6*x-1 + x-2*y + 2*y-1*z-1 + 2*x-1*z-1 + 2*y-2*z-1 + 5*x-1*y-1*z-1 + 2*x-2*z-1 + x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 4 Lattice Minkowski decompositions of facet 16
Image of facet 224 1 Lattice Minkowski decompositions of facet 224
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 4043
Image of polytope 4043 PALP id: 4043
grdb id: 274167
Integer points: [ 1 0 1 -1 1 -2 0 -2 0 -1 -2 0 -1 0 -1 1 0 -1 1 0 -1 1 0]
[ 0 1 0 0 -2 1 1 1 -1 0 1 -1 0 0 1 -1 0 1 -1 0 1 0 1]
[ 0 0 2 -2 0 -2 2 0 -1 -1 -1 0 0 -1 -1 0 0 0 1 1 1 1 1]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x*z2 + y*z2 + 2*x*z + 2*y*z + x + y + 2*x*y-1*z + 4*z + 2*x-1*y*z + 2*x*y-1 + 4*x-1*y + 2*z-1 + 2*x-1*y*z-1 + x*y-2 + 3*y-1 + 3*x-1 + x-2*y + 2*y-1*z-1 + 4*x-1*z-1 + 2*x-2*y*z-1 + x-1*z-2 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 4044
Image of polytope 4044 PALP id: 4044
grdb id: 275383
Integer points: [ 1 0 0 0 0 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 -1 0 -2 2 3 -2 2 1 0 -1 1 0 -1 -2 2 1 0 -1 1 0 -1]
[ 0 0 0 1 1 -2 -2 3 -1 0 1 2 -1 0 1 2 -1 0 1 2 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + 2*y*z-1 + 2*x-1*y2*z-1 + 6*x-1*y + 2*y-1*z + 6*x-1*z + 2*x-1*y-1*z2 + x-1*y2*z-2 + x-2*y3*z-2 + 4*x-1*y*z-1 + 5*x-2*y2*z-1 + y-1 + 7*x-1 + 10*x-2*y + y-2*z + 6*x-1*y-1*z + 10*x-2*z + 2*x-1*y-2*z2 + 5*x-2*y-1*z2 + x-2*y-2*z3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 181 1 Lattice Minkowski decompositions of facet 181
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 4045
Image of polytope 4045 PALP id: 4045
grdb id: 274849
Integer points: [ 1 0 0 1 0 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0 0]
[ 0 1 0 -1 -2 2 -2 2 -1 0 1 -2 -1 0 1 -1 0 -1 0 1 -1 0 1]
[ 0 0 1 0 1 -2 1 -3 0 -1 -2 1 0 -1 -2 0 -1 1 0 -1 1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*y*z-1 + x*y-1 + 2*y-1*z + x-1*y2*z-2 + 3*z-1 + 4*x-1*y*z-1 + 4*y-1 + 5*x-1 + y-2*z + 2*x-1*y-1*z + 3*x-1*y*z-2 + 8*x-1*z-1 + 7*x-1*y-1 + 2*x-1*y-2*z + x-2*y2*z-3 + 4*x-2*y*z-2 + 6*x-2*z-1 + 4*x-2*y-1 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 4046
Image of polytope 4046 PALP id: 4046
grdb id: 274786
Integer points: [ 1 0 1 0 0 -1 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 -1 2 3 -1 2 1 0 2 1 0 -1 1 0 -1 1 0 -1 0 -1]
[ 0 0 0 1 1 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 14 1 none
Polytope 4047
Image of polytope 4047 PALP id: 4047
grdb id: 274838
Integer points: [ 1 0 0 -1 -1 -1 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 2 -3 2 -4 1 0 -1 -2 -3 0 -1 -2 1 0 -1 -2 1 0 -1]
[ 0 0 1 -2 -2 2 -3 3 -2 -1 0 1 2 -1 0 1 -1 0 1 2 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 8 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 200 1 Lattice Minkowski decompositions of facet 200
Image of facet 13 1 irreducible and admissible
Image of facet 173 1 Lattice Minkowski decompositions of facet 173
Polytope 4048
Image of polytope 4048 PALP id: 4048
grdb id: 273916
Integer points: [ 1 0 0 0 1 -1 -1 -4 -2 -3 -1 -2 -3 0 -1 -2 0 -1 -2 0 -1 1 0]
[ 0 1 0 -1 -2 0 0 3 1 2 0 1 2 -1 0 1 -1 1 2 0 1 -1 0]
[ 0 0 1 1 0 1 -2 -2 0 -1 0 -1 -2 0 -1 -2 -1 0 -1 0 -1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*x*y-1 + 3*x-1*y + y-1*z + x-1*z + 2*z-1 + 4*x-1*y*z-1 + 2*x-2*y2*z-1 + x*y-2 + 3*y-1 + 5*x-1 + 3*x-2*y + 2*y-1*z-1 + 6*x-1*z-1 + 7*x-2*y*z-1 + 3*x-3*y2*z-1 + x-1*z-2 + 3*x-2*y*z-2 + 3*x-3*y2*z-2 + x-4*y3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 220 1 Lattice Minkowski decompositions of facet 220
Polytope 4049
Image of polytope 4049 PALP id: 4049
grdb id: 272798
Integer points: [ 1 0 0 1 1 1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 0 1 -1 -1 -2 2 -2 -1 0 1 -2 -1 0 1 -2 -1 0 -1 0 1 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x*z-1 + 2*x-1*z + x*y-1*z-1 + 3*z-1 + 3*y-1 + 4*x-1 + 3*x-1*y-1*z + x-2*y-1*z2 + x*y-1*z-2 + 6*y-1*z-1 + 2*x-1*z-1 + 9*x-1*y-1 + 4*x-2*y-1*z + 3*y-1*z-2 + 9*x-1*y-1*z-1 + 6*x-2*y-1 + 3*x-1*y-1*z-2 + 4*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Polytope 4050
Image of polytope 4050 PALP id: 4050
grdb id: 273088
Integer points: [ 1 0 0 0 -1 -2 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 -2 2 2 -2 -1 0 1 -2 -1 0 1 -1 0 1 -1 0 1 -1 0]
[ 0 0 1 1 0 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + 2*x-1*y + y-1*z + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 6*x-1 + 4*x-1*z-1 + 6*x-2*y*z-1 + 5*x-1*y-1 + x-3*y2*z-2 + 2*x-1*y-1*z-1 + 11*x-2*z-1 + x-1*y-2 + 4*x-3*y*z-2 + 8*x-2*y-1*z-1 + 6*x-3*z-2 + 2*x-2*y-2*z-1 + 4*x-3*y-1*z-2 + x-3*y-2*z-2
52 rank 2, number 52 x + y + z + 2*x-1*y + y-1*z + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 5*x-1 + 4*x-1*z-1 + 5*x-2*y*z-1 + 4*x-1*y-1 + x-3*y2*z-2 + 2*x-1*y-1*z-1 + 9*x-2*z-1 + x-1*y-2 + 4*x-3*y*z-2 + 7*x-2*y-1*z-1 + 6*x-3*z-2 + 2*x-2*y-2*z-1 + 4*x-3*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 259 1 Lattice Minkowski decompositions of facet 259
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 4051
Image of polytope 4051 PALP id: 4051
grdb id: 272794
Integer points: [ 1 0 0 -1 0 -2 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -1 1 0 -4 -3 -2 -1 -3 -2 -1 0 -2 -1 0 -2 -1 0 -1 0]
[ 0 0 1 0 1 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Image of facet 262 1 Lattice Minkowski decompositions of facet 262
Polytope 4052
Image of polytope 4052 PALP id: 4052
grdb id: 272829
Integer points: [ 1 0 0 1 -1 1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 1 0 0 1 -1 0 -4 -3 -2 -1 -3 -2 -1 0 -2 -1 0 -2 -1 0 -1 0]
[ 0 0 1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*z-1 + x-1*y + x*y-1*z-1 + 3*z-1 + 3*y-1 + 3*x-1 + 6*y-1*z-1 + 3*x-1*z-1 + 4*x-1*y-1 + 3*y-2*z-1 + 9*x-1*y-1*z-1 + x-2*z-1 + 2*x-1*y-2 + 9*x-1*y-2*z-1 + 4*x-2*y-1*z-1 + 3*x-1*y-3*z-1 + 6*x-2*y-2*z-1 + 4*x-2*y-3*z-1 + x-2*y-4*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Polytope 4053
Image of polytope 4053 PALP id: 4053
grdb id: 271678
Integer points: [ 1 0 0 0 -1 -2 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 2 -2 -2 3 2 1 0 -1 2 1 0 -1 1 0 -1 1 0 -1 0]
[ 0 0 0 1 -1 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y2*z-1 + 3*x-1*y + 4*x-1*y*z-1 + 3*x-2*y2*z-1 + y-1 + 5*x-1 + x-3*y3*z-2 + 5*x-1*z-1 + 10*x-2*y*z-1 + 2*x-1*y-1 + 5*x-3*y2*z-2 + 2*x-1*y-1*z-1 + 12*x-2*z-1 + 10*x-3*y*z-2 + 6*x-2*y-1*z-1 + 10*x-3*z-2 + x-2*y-2*z-1 + 5*x-3*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 227 1 Lattice Minkowski decompositions of facet 227
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 4054
Image of polytope 4054 PALP id: 4054
grdb id: 272813
Integer points: [ 1 0 0 -1 0 -2 -1 -5 -4 -3 -2 -4 -3 -2 -1 -3 -2 -1 -2 -1 0 -1 0]
[ 0 1 0 1 -1 1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 0 1 0 1 -1 0 -4 -3 -2 -1 -3 -2 -1 0 -2 -1 0 -2 -1 0 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y + y-1*z + 2*y-1 + 4*x-1 + 3*x-1*z-1 + x-2*y*z-1 + 5*x-1*y-1 + 4*x-1*y-1*z-1 + 6*x-2*z-1 + x-1*y-2 + 10*x-2*y-1*z-1 + 2*x-2*y-1*z-2 + 3*x-3*z-2 + 4*x-2*y-2*z-1 + 9*x-3*y-1*z-2 + 6*x-3*y-2*z-2 + 3*x-4*y-1*z-3 + 4*x-4*y-2*z-3 + x-5*y-2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 262 1 Lattice Minkowski decompositions of facet 262
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 4055
Image of polytope 4055 PALP id: 4055
grdb id: 86711
Integer points: [ 1 0 0 2 1 -1 -1 -2 -2 0 -1 0 -1 -2 -1 -2 1 0 1 0 -1 0 -1]
[ 0 1 0 -1 -1 2 -1 2 -1 -1 -1 0 0 0 1 1 -1 -1 0 0 0 1 1]
[ 0 0 1 -1 -1 -1 2 -1 2 0 1 -1 0 1 -1 0 0 1 -1 0 1 -1 0]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x + y + z + x2*y-1*z-1 + 3*x*z-1 + 3*y*z-1 + x-1*y2*z-1 + 3*x*y-1 + 3*x-1*y + 3*y-1*z + 3*x-1*z + x-1*y-1*z2 + x*y-1*z-1 + 3*z-1 + 3*x-1*y*z-1 + x-2*y2*z-1 + 3*y-1 + 6*x-1 + 3*x-2*y + 3*x-1*y-1*z + 3*x-2*z + x-2*y-1*z2
49 rank 2, number 4 x + y + z + x2*y-1*z-1 + 3*x*z-1 + 3*y*z-1 + x-1*y2*z-1 + 3*x*y-1 + 4*x-1*y + 3*y-1*z + 4*x-1*z + x-1*y-1*z2 + x*y-1*z-1 + 3*z-1 + 3*x-1*y*z-1 + x-2*y2*z-1 + 3*y-1 + 6*x-1 + 3*x-2*y + 3*x-1*y-1*z + 3*x-2*z + x-2*y-1*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 100 1 Lattice Minkowski decompositions of facet 100
Image of facet 60 2 Lattice Minkowski decompositions of facet 60
Polytope 4056
Image of polytope 4056 PALP id: 4056
grdb id: 86778
Integer points: [ 1 0 0 1 -1 1 -1 1 -3 -2 -1 0 -2 -1 0 -2 -1 0 1 -1 0 1 0]
[ 0 1 0 -1 1 -2 1 -3 1 0 -1 -2 1 0 -1 1 0 -1 -2 1 0 -1 0]
[ 0 0 1 -1 1 0 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + x*y-2 + 4*y-1 + 5*x-1 + 2*x-2*y + 2*x*y-2*z-1 + 6*y-1*z-1 + 6*x-1*z-1 + 2*x-2*y*z-1 + x*y-3*z-1 + 4*y-2*z-1 + 6*x-1*y-1*z-1 + 4*x-2*z-1 + x-3*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 4057
Image of polytope 4057 PALP id: 4057
grdb id: 87167
Integer points: [ 1 0 0 -1 0 -2 2 2 -3 1 0 -1 -2 1 0 -1 1 0 -1 -2 1 0 -1]
[ 0 1 0 0 -1 2 -2 -3 2 -2 -1 0 1 -1 0 1 -2 -1 0 1 -1 0 1]
[ 0 0 1 1 1 -1 -1 -1 -1 0 0 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + 3*x*y-1 + 2*x-1*y + y-1*z + x-1*z + x2*y-2*z-1 + 4*x*y-1*z-1 + 6*z-1 + 4*x-1*y*z-1 + x-2*y2*z-1 + 2*x*y-2 + 6*y-1 + 6*x-1 + 2*x-2*y + x2*y-3*z-1 + 5*x*y-2*z-1 + 10*y-1*z-1 + 10*x-1*z-1 + 5*x-2*y*z-1 + x-3*y2*z-1
22 ? x + y + z + 3*x*y-1 + 3*x-1*y + y-1*z + x-1*z + x2*y-2*z-1 + 4*x*y-1*z-1 + 6*z-1 + 4*x-1*y*z-1 + x-2*y2*z-1 + 2*x*y-2 + 6*y-1 + 6*x-1 + 2*x-2*y + x2*y-3*z-1 + 5*x*y-2*z-1 + 10*y-1*z-1 + 10*x-1*z-1 + 5*x-2*y*z-1 + x-3*y2*z-1
7 rank 1, V12 x + y + z + 2*x*y-1 + 3*x-1*y + y-1*z + x-1*z + x2*y-2*z-1 + 4*x*y-1*z-1 + 6*z-1 + 4*x-1*y*z-1 + x-2*y2*z-1 + 2*x*y-2 + 6*y-1 + 6*x-1 + 2*x-2*y + x2*y-3*z-1 + 5*x*y-2*z-1 + 10*y-1*z-1 + 10*x-1*z-1 + 5*x-2*y*z-1 + x-3*y2*z-1
11 rank 2, number 6 x + y + z + 2*x*y-1 + 2*x-1*y + y-1*z + x-1*z + x2*y-2*z-1 + 4*x*y-1*z-1 + 6*z-1 + 4*x-1*y*z-1 + x-2*y2*z-1 + 2*x*y-2 + 6*y-1 + 6*x-1 + 2*x-2*y + x2*y-3*z-1 + 5*x*y-2*z-1 + 10*y-1*z-1 + 10*x-1*z-1 + 5*x-2*y*z-1 + x-3*y2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 23 2 Lattice Minkowski decompositions of facet 23
Image of facet 157 1 Lattice Minkowski decompositions of facet 157
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Polytope 4058
Image of polytope 4058 PALP id: 4058
grdb id: 86668
Integer points: [ 1 0 0 0 -2 1 1 -3 0 -1 0 1 -2 -1 0 -2 -1 0 1 -1 0 1 -1]
[ 0 1 0 -1 2 -2 -2 2 -1 0 -1 -2 1 0 -1 1 0 0 -1 1 0 -1 1]
[ 0 0 1 1 1 0 -2 1 -2 -1 -1 -1 0 0 0 1 1 -1 -1 0 0 0 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + 2*x-1*y*z + x-2*y2*z + 2*x*y-1 + 3*x-1*y + y-1*z + 3*x-1*z + 3*x-2*y*z + x-3*y2*z + 2*x*y-1*z-1 + 2*z-1 + x*y-2 + 5*y-1 + 7*x-1 + 3*x-2*y + 2*x*y-2*z-1 + 5*y-1*z-1 + 3*x-1*z-1 + x*y-2*z-2 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 174 1 Lattice Minkowski decompositions of facet 174
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 4059
Image of polytope 4059 PALP id: 4059
grdb id: 86880
Integer points: [ 1 0 0 2 -2 -1 -3 2 0 -2 -1 -1 0 -2 -1 0 1 -1 0 1 0 1 1]
[ 0 1 0 -1 1 1 1 -2 -2 0 -1 0 -1 1 0 -1 -2 1 0 -1 0 -1 0]
[ 0 0 1 -2 2 0 2 -3 -1 1 0 1 0 1 0 -1 -2 1 0 -1 -1 -2 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + 2*x-1*y*z + x-2*y*z2 + 2*x*z-1 + x-1*y + 3*x-1*z + 2*x-2*y*z + x-3*y*z2 + x2*y-1*z-2 + 3*x*y-1*z-1 + 3*z-1 + 2*y-1 + 6*x-1 + 3*x-2*z + 3*x*y-1*z-2 + 6*y-1*z-1 + 3*x-1*y-1 + x2*y-2*z-3 + 2*x*y-2*z-2 + y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 4060
Image of polytope 4060 PALP id: 4060
grdb id: 87169
Integer points: [ 1 0 0 -1 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 2 0 2 -3 1 -4 0 -1 -2 -3 1 0 -1 -2 1 -1 -2 1 0 -1]
[ 0 0 1 1 -1 2 -2 2 -3 1 0 -1 -2 1 0 -1 -2 0 0 -1 1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
51 rank 2, number 7 x-1*y2*z2 + 2*y*z + x-1*y2*z + x-1*y*z2 + x + y + z + 5*x-1*y*z + 2*x-1*y + 5*x-1*z + 3*y-1 + 9*x-1 + 3*y-1*z-1 + x-1*z-1 + 10*x-1*y-1 + 3*y-2*z-1 + 7*x-1*y-1*z-1 + 10*x-1*y-2*z-1 + y-3*z-2 + 2*x-1*y-2*z-2 + 5*x-1*y-3*z-2 + x-1*y-4*z-3
18 rank 1, V14 x-1*y2*z2 + 2*y*z + x-1*y2*z + x-1*y*z2 + x + y + z + 5*x-1*y*z + 2*x-1*y + 5*x-1*z + 3*y-1 + 9*x-1 + 2*y-1*z-1 + x-1*z-1 + 10*x-1*y-1 + 3*y-2*z-1 + 7*x-1*y-1*z-1 + 10*x-1*y-2*z-1 + y-3*z-2 + 2*x-1*y-2*z-2 + 5*x-1*y-3*z-2 + x-1*y-4*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 146 1 Lattice Minkowski decompositions of facet 146
Image of facet 9 1 irreducible and admissible
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 201 1 Lattice Minkowski decompositions of facet 201
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 4061
Image of polytope 4061 PALP id: 4061
grdb id: 82704
Integer points: [ 1 0 0 0 -1 -2 1 1 -2 -1 0 -2 -1 0 1 -1 0 -1 0 1 -1 0 1]
[ 0 1 0 1 1 0 0 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0 0]
[ 0 0 1 -1 0 1 -2 -2 1 0 -1 1 0 -1 -2 0 -1 1 0 -1 1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*x*z-1 + y*z-1 + x-1*y + 2*x-1*z + x*z-2 + 2*x*y-1*z-1 + 4*z-1 + 4*y-1 + 4*x-1 + 2*x-1*y-1*z + x-2*z + 2*x*y-1*z-2 + 6*y-1*z-1 + 6*x-1*y-1 + 2*x-2*y-1*z + x*y-2*z-2 + 3*y-2*z-1 + 3*x-1*y-2 + x-2*y-2*z
51 rank 2, number 7 x + y + z + 2*x*z-1 + y*z-1 + x-1*y + 2*x-1*z + x*z-2 + 2*x*y-1*z-1 + 5*z-1 + 4*y-1 + 5*x-1 + 2*x-1*y-1*z + x-2*z + 2*x*y-1*z-2 + 7*y-1*z-1 + 7*x-1*y-1 + 2*x-2*y-1*z + x*y-2*z-2 + 3*y-2*z-1 + 3*x-1*y-2 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 225 1 Lattice Minkowski decompositions of facet 225
Polytope 4062
Image of polytope 4062 PALP id: 4062
grdb id: 82771
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 -1 1 1 0 -2 -2 1 0 0 0 -1 -1 -1 -1 -2 -2 0 0 -1 -1]
[ 0 0 1 1 1 -1 -2 1 -2 0 1 0 -1 1 0 -1 -2 0 -1 0 -1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y*z + 2*x-1*y + y-1*z + 3*x-1*z + 2*z-1 + x-1*y*z-1 + 3*y-1 + 7*x-1 + 3*x-1*y-1*z + 2*y-1*z-1 + 5*x-1*z-1 + 8*x-1*y-1 + x-1*y-2*z + x-1*z-2 + 7*x-1*y-1*z-1 + 3*x-1*y-2 + 2*x-1*y-1*z-2 + 3*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 231 1 Lattice Minkowski decompositions of facet 231
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 4063
Image of polytope 4063 PALP id: 4063
grdb id: 83456
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 1 0 -1 -2 0 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
[ 0 0 1 -1 1 2 2 -2 -2 -1 0 1 -2 -1 0 1 -1 0 -1 0 1 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + y*z-1 + 2*y-1*z + x-1*z + x-1*y-1*z2 + 2*z-1 + 4*y-1 + 3*x-1 + 5*x-1*y-1*z + x-1*y-2*z2 + 2*y-1*z-1 + 3*x-1*z-1 + 9*x-1*y-1 + 4*x-1*y-2*z + x-1*z-2 + 7*x-1*y-1*z-1 + 6*x-1*y-2 + 2*x-1*y-1*z-2 + 4*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 198 1 Lattice Minkowski decompositions of facet 198
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 4064
Image of polytope 4064 PALP id: 4064
grdb id: 85219
Integer points: [ 1 0 0 -1 1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 0 0 -1 1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
[ 0 0 1 1 -1 1 0 1 -3 0 -1 -2 1 0 -1 -2 0 -1 0 -1 -2 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x*z-1 + x-1*y + y-1*z + x-1*z + 3*z-1 + 4*y-1 + 4*x-1 + 2*x-1*y-1*z + 5*y-1*z-1 + 3*x-1*z-1 + 7*x-1*y-1 + x-1*y-2*z + 2*y-1*z-2 + 8*x-1*y-1*z-1 + 4*x-1*y-2 + 3*x-1*y-1*z-2 + 6*x-1*y-2*z-1 + 4*x-1*y-2*z-2 + x-1*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 4065
Image of polytope 4065 PALP id: 4065
grdb id: 85225
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 -2 1 1 0 -3 0 -1 -2 1 0 -1 -2 1 0 -1 -1 0 -1 0]
[ 0 0 1 -1 1 1 -2 -2 1 1 1 1 0 0 0 0 -1 -1 -1 1 0 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x-1*y*z + y*z-1 + 3*x-1*y + 2*y-1*z + 4*x-1*z + 2*z-1 + 3*x-1*y*z-1 + 3*y-1 + 9*x-1 + y-2*z + 6*x-1*y-1*z + x-1*y*z-2 + 6*x-1*z-1 + 9*x-1*y-1 + 4*x-1*y-2*z + x-1*z-2 + 3*x-1*y-1*z-1 + 3*x-1*y-2 + x-1*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Polytope 4066
Image of polytope 4066 PALP id: 4066
grdb id: 85150
Integer points: [ 1 0 0 1 1 -1 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 0 0]
[ 0 1 0 -1 -1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 0 1 1 0 1 -2 1 -3 0 -1 -2 1 0 -1 -2 1 0 -1 0 -1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + x*y-1*z + z + x*y-1 + 3*y-1*z + x-1*z + 2*z-1 + 6*y-1 + 4*x-1 + 3*x-1*y-1*z + 3*y-1*z-1 + 4*x-1*z-1 + 9*x-1*y-1 + x-2*y-1*z + x-1*z-2 + 9*x-1*y-1*z-1 + 4*x-2*y-1 + 3*x-1*y-1*z-2 + 6*x-2*y-1*z-1 + 4*x-2*y-1*z-2 + x-2*y-1*z-3
62 rank 2, number 9 x + y + x*y-1*z + z + x*y-1 + 3*y-1*z + x-1*z + 2*z-1 + 6*y-1 + 3*x-1 + 3*x-1*y-1*z + 3*y-1*z-1 + 3*x-1*z-1 + 9*x-1*y-1 + x-2*y-1*z + x-1*z-2 + 9*x-1*y-1*z-1 + 4*x-2*y-1 + 3*x-1*y-1*z-2 + 6*x-2*y-1*z-1 + 4*x-2*y-1*z-2 + x-2*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Image of facet 93 1 Lattice Minkowski decompositions of facet 93
Polytope 4067
Image of polytope 4067 PALP id: 4067
grdb id: 86200
Integer points: [ 1 0 0 0 0 -1 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 -1 -1 -1 0 0]
[ 0 1 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 0 1 1 -1 -2 2 2 -3 1 0 -1 -2 1 0 -1 -2 0 1 0 -1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + y-1*z + 2*x-1*z + x-1*y-1*z2 + 2*z-1 + 2*y-1 + 5*x-1 + 5*x-1*y-1*z + x-2*y-1*z2 + y-1*z-1 + 4*x-1*z-1 + 9*x-1*y-1 + 5*x-2*y-1*z + x-1*z-2 + 7*x-1*y-1*z-1 + 10*x-2*y-1 + 2*x-1*y-1*z-2 + 10*x-2*y-1*z-1 + 5*x-2*y-1*z-2 + x-2*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 201 1 Lattice Minkowski decompositions of facet 201
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 4068
Image of polytope 4068 PALP id: 4068
grdb id: 86228
Integer points: [ 1 0 0 1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 1 0 -1 1 -1 1 -1 -1 -1 -1 -1 -1 0 0 0 0 -1 -1 -1 -1 0 0]
[ 0 0 1 0 0 -1 -1 2 -3 1 0 -1 -2 1 0 -1 -2 1 0 -1 -2 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x*y-1 + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + x*y-1*z-1 + 3*z-1 + x-1*y*z-1 + 6*y-1 + 6*x-1 + 5*x-1*y-1*z + 6*y-1*z-1 + 6*x-1*z-1 + 10*x-1*y-1 + 2*y-1*z-2 + 2*x-1*z-2 + 10*x-1*y-1*z-1 + 5*x-1*y-1*z-2 + x-1*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 129 2 Lattice Minkowski decompositions of facet 129
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 4069
Image of polytope 4069 PALP id: 4069
grdb id: 83883
Integer points: [ 1 0 0 1 1 -2 1 -2 1 -1 0 -2 -1 0 1 -1 0 -1 0 1 -1 0 1]
[ 0 1 0 0 -1 2 -1 0 -3 1 0 1 0 -1 -2 -1 -2 1 0 -1 0 -1 -2]
[ 0 0 1 -1 0 1 -2 1 -2 0 -1 1 0 -1 -2 0 -1 1 0 -1 1 0 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + 2*x-1*y*z + x-2*y2*z + x*z-1 + x*y-1 + 3*x-1*y + 2*x-1*z + 2*x-2*y*z + 3*x*y-1*z-1 + 3*z-1 + 4*y-1 + 6*x-1 + x-2*z + x*y-1*z-2 + 2*x*y-2*z-1 + 6*y-1*z-1 + 3*x-1*y-1 + 2*x*y-2*z-2 + 3*y-2*z-1 + x*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Polytope 4070
Image of polytope 4070 PALP id: 4070
grdb id: 86235
Integer points: [ 1 0 0 0 -1 -1 0 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 1 1 -2 1 -4 -3 -2 -1 0 -2 -1 0 -3 -2 -1 0 -1 0 -1]
[ 0 0 1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y + z-1 + x-1*y*z-1 + 2*y-1 + 4*x-1 + 2*y-1*z-1 + 5*x-1*z-1 + x-2*y*z-1 + 5*x-1*y-1 + y-2*z-1 + 9*x-1*y-1*z-1 + 5*x-2*z-1 + 2*x-1*y-2 + 7*x-1*y-2*z-1 + 10*x-2*y-1*z-1 + 2*x-1*y-3*z-1 + 10*x-2*y-2*z-1 + 5*x-2*y-3*z-1 + x-2*y-4*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 201 1 Lattice Minkowski decompositions of facet 201
Polytope 4071
Image of polytope 4071 PALP id: 4071
grdb id: 86196
Integer points: [ 1 0 0 0 0 -1 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 -1 2 -2 -2 3 -1 0 1 2 -1 0 1 2 -1 0 1 -1 0 1]
[ 0 0 1 -1 0 2 -2 -3 2 -2 -1 0 1 -2 -1 0 1 -1 0 1 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 x-1*y2*z2 + x-2*y3*z2 + 2*y*z + 2*x-1*y2*z + x + y + z + 5*x-1*y*z + 5*x-2*y2*z + 6*x-1*y + z-1 + y-1 + 8*x-1 + 10*x-2*y + 2*y-1*z-1 + 6*x-1*z-1 + 5*x-1*y-1*z-1 + 10*x-2*z-1 + 2*x-1*y-1*z-2 + x-1*y-2*z-2 + 5*x-2*y-1*z-2 + x-2*y-2*z-3
20 rank 1, V16 x-1*y2*z2 + x-2*y3*z2 + 2*y*z + 2*x-1*y2*z + x + y + z + 4*x-1*y*z + 5*x-2*y2*z + 6*x-1*y + z-1 + y-1 + 6*x-1 + 10*x-2*y + 2*y-1*z-1 + 6*x-1*z-1 + 4*x-1*y-1*z-1 + 10*x-2*z-1 + 2*x-1*y-1*z-2 + x-1*y-2*z-2 + 5*x-2*y-1*z-2 + x-2*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 186 1 Lattice Minkowski decompositions of facet 186
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Polytope 4072
Image of polytope 4072 PALP id: 4072
grdb id: 82865
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 0 1 1 -1 -1 -4 -2 -3 0 -1 -2 -3 0 -1 -2 0 -1 -2 0 -1]
[ 0 0 1 -1 0 -1 -1 2 2 0 1 -1 0 1 2 0 1 2 1 0 1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y + 3*y-1*z + 2*x-1*z + x-1*y-1*z2 + z-1 + x-1*y*z-1 + 3*y-1 + 5*x-1 + 2*y-2*z + 7*x-1*y-1*z + 3*x-1*y-2*z2 + 2*x-1*z-1 + 7*x-1*y-1 + 8*x-1*y-2*z + 3*x-1*y-3*z2 + x-1*y-1*z-1 + 3*x-1*y-2 + 3*x-1*y-3*z + x-1*y-4*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 231 1 Lattice Minkowski decompositions of facet 231
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 4073
Image of polytope 4073 PALP id: 4073
grdb id: 566718
Integer points: [ 1 0 1 0 1 1 0 0 -2 -2 0 0 1 1 -1 -1 -1 0 0 0 1 -1 -1]
[ 0 1 0 1 -1 -1 -1 -1 1 1 -1 -1 -1 -1 0 0 0 0 0 0 0 1 1]
[ 0 0 2 1 -1 2 1 -2 -1 -2 -1 0 0 1 -2 -1 0 -1 0 1 1 -1 0]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x*z2 + 2*x*z + y*z + x*y-1*z2 + x + y + 3*x*y-1*z + 3*z + 3*x*y-1 + 2*x-1*y + y-1*z + x*y-1*z-1 + 3*z-1 + 2*x-1*y*z-1 + 3*y-1 + 2*x-1 + 3*y-1*z-1 + 4*x-1*z-1 + x-2*y*z-1 + y-1*z-2 + 2*x-1*z-2 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 4074
Image of polytope 4074 PALP id: 4074
grdb id: 566716
Integer points: [ 1 0 0 -2 2 0 2 0 -3 -1 -2 -1 -1 -2 -1 0 1 -1 0 1 0 1 1]
[ 0 1 0 2 -2 0 -3 -1 2 0 1 0 1 1 0 -1 -2 1 0 -1 -1 -2 -1]
[ 0 0 1 1 -1 -1 -1 1 1 -1 1 1 1 0 0 0 0 0 0 0 -1 -1 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
22 ? x + y + z + 2*x-1*y*z + x-2*y2*z + 3*x*y-1 + 3*x-1*y + y-1*z + 3*x-1*z + 3*x-2*y*z + x-3*y2*z + x2*y-2*z-1 + 2*x*y-1*z-1 + z-1 + 2*x*y-2 + 6*y-1 + 6*x-1 + 2*x-2*y + x2*y-3*z-1 + 3*x*y-2*z-1 + 3*y-1*z-1 + x-1*z-1
11 rank 2, number 6 x + y + z + 2*x-1*y*z + x-2*y2*z + 2*x*y-1 + 2*x-1*y + y-1*z + 3*x-1*z + 3*x-2*y*z + x-3*y2*z + x2*y-2*z-1 + 2*x*y-1*z-1 + z-1 + 2*x*y-2 + 6*y-1 + 6*x-1 + 2*x-2*y + x2*y-3*z-1 + 3*x*y-2*z-1 + 3*y-1*z-1 + x-1*z-1
7 rank 1, V12 x + y + z + 2*x-1*y*z + x-2*y2*z + 3*x*y-1 + 2*x-1*y + y-1*z + 3*x-1*z + 3*x-2*y*z + x-3*y2*z + x2*y-2*z-1 + 2*x*y-1*z-1 + z-1 + 2*x*y-2 + 6*y-1 + 6*x-1 + 2*x-2*y + x2*y-3*z-1 + 3*x*y-2*z-1 + 3*y-1*z-1 + x-1*z-1
7 rank 1, V12 x + y + z + 2*x-1*y*z + x-2*y2*z + 2*x*y-1 + 3*x-1*y + y-1*z + 3*x-1*z + 3*x-2*y*z + x-3*y2*z + x2*y-2*z-1 + 2*x*y-1*z-1 + z-1 + 2*x*y-2 + 6*y-1 + 6*x-1 + 2*x-2*y + x2*y-3*z-1 + 3*x*y-2*z-1 + 3*y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Image of facet 23 2 Lattice Minkowski decompositions of facet 23
Polytope 4075
Image of polytope 4075 PALP id: 4075
grdb id: 566695
Integer points: [ 1 0 0 -1 0 -1 -2 2 -2 2 -1 -2 -1 0 1 -1 0 1 -1 0 1 0 1]
[ 0 1 0 1 -1 1 1 -2 1 -3 0 1 0 -1 -2 1 0 -1 0 -1 -2 0 -1]
[ 0 0 1 1 1 -1 1 -1 -1 -1 1 0 0 0 0 0 0 0 -1 -1 -1 -1 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
22 ? x + y + z + x-1*y*z + 3*x*y-1 + 3*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + x2*y-2*z-1 + 3*x*y-1*z-1 + 3*z-1 + x-1*y*z-1 + 2*x*y-2 + 6*y-1 + 6*x-1 + 2*x-2*y + x2*y-3*z-1 + 4*x*y-2*z-1 + 6*y-1*z-1 + 4*x-1*z-1 + x-2*y*z-1
7 rank 1, V12 x + y + z + x-1*y*z + 3*x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + x2*y-2*z-1 + 3*x*y-1*z-1 + 3*z-1 + x-1*y*z-1 + 2*x*y-2 + 6*y-1 + 6*x-1 + 2*x-2*y + x2*y-3*z-1 + 4*x*y-2*z-1 + 6*y-1*z-1 + 4*x-1*z-1 + x-2*y*z-1
11 rank 2, number 6 x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + x2*y-2*z-1 + 3*x*y-1*z-1 + 3*z-1 + x-1*y*z-1 + 2*x*y-2 + 6*y-1 + 6*x-1 + 2*x-2*y + x2*y-3*z-1 + 4*x*y-2*z-1 + 6*y-1*z-1 + 4*x-1*z-1 + x-2*y*z-1
7 rank 1, V12 x + y + z + x-1*y*z + 2*x*y-1 + 3*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + x2*y-2*z-1 + 3*x*y-1*z-1 + 3*z-1 + x-1*y*z-1 + 2*x*y-2 + 6*y-1 + 6*x-1 + 2*x-2*y + x2*y-3*z-1 + 4*x*y-2*z-1 + 6*y-1*z-1 + 4*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 23 2 Lattice Minkowski decompositions of facet 23
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 4076
Image of polytope 4076 PALP id: 4076
grdb id: 564955
Integer points: [ 1 0 0 1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 0 1 1 -1 1 -2 -2 -2 -2 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 0 1 -1 -1 0 2 -1 2 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x*z-1 + y*z-1 + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + 3*z-1 + x-1*y*z-1 + 4*y-1 + 5*x-1 + 5*x-1*y-1*z + x-1*y-2*z2 + 2*y-1*z-1 + 3*x-1*z-1 + 7*x-1*y-1 + 3*x-1*y-2*z + 3*x-1*y-1*z-1 + 3*x-1*y-2 + x-1*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 174 1 Lattice Minkowski decompositions of facet 174
Polytope 4077
Image of polytope 4077 PALP id: 4077
grdb id: 565284
Integer points: [ 1 0 0 1 -1 1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 -1 1 -1 -1 1 -1 -1 1 0 0 0 0 -1 -1 -1 0 0 -1 -1 -1]
[ 0 0 1 0 1 -1 1 -1 1 -3 0 1 0 -1 -2 0 -1 -2 0 -1 0 -1 -2]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x-1*y*z + x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x*y-1*z-1 + 3*z-1 + x-1*y*z-1 + 4*y-1 + 6*x-1 + x-1*y-1*z + 5*y-1*z-1 + 6*x-1*z-1 + 4*x-1*y-1 + 2*y-1*z-2 + 2*x-1*z-2 + 6*x-1*y-1*z-1 + 4*x-1*y-1*z-2 + x-1*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 4078
Image of polytope 4078 PALP id: 4078
grdb id: 565273
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 0 -2 2 2 1 -1 -3 0 -1 -2 1 0 -1 -2 1 0 -1 1 0 -1]
[ 0 0 1 -1 1 -1 -2 -2 2 2 -1 0 1 -1 0 1 2 0 1 0 -1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + x-1*y2*z-2 + z-1 + 5*x-1*y*z-1 + 2*y-1 + 9*x-1 + y-2*z + 7*x-1*y-1*z + 2*x-1*y-2*z2 + x-1*y*z-2 + 4*x-1*z-1 + 6*x-1*y-1 + 4*x-1*y-2*z + x-1*y-3*z2
51 rank 2, number 7 x + y + z + 2*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 3*y-1*z + 3*x-1*z + x-1*y-1*z2 + x-1*y2*z-2 + z-1 + 5*x-1*y*z-1 + 2*y-1 + 9*x-1 + y-2*z + 7*x-1*y-1*z + 2*x-1*y-2*z2 + x-1*y*z-2 + 4*x-1*z-1 + 6*x-1*y-1 + 4*x-1*y-2*z + x-1*y-3*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 198 1 Lattice Minkowski decompositions of facet 198
Image of facet 23 1 Lattice Minkowski decompositions of facet 23
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 4079
Image of polytope 4079 PALP id: 4079
grdb id: 21153
Integer points: [ 1 0 0 -1 1 0 0 1 -2 1 -2 -1 -2 -1 0 -1 0 1 -1 0 -1 0 1]
[ 0 1 0 1 0 -1 1 -2 1 -2 1 0 1 0 -1 1 0 -1 0 -1 1 0 -1]
[ 0 0 1 1 -1 1 -1 0 1 -1 -1 1 0 0 0 0 0 0 -1 -1 -1 -1 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + x-1*y*z + x*z-1 + y*z-1 + 2*x*y-1 + 3*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + 2*x*y-1*z-1 + 4*z-1 + 2*x-1*y*z-1 + x*y-2 + 4*y-1 + 5*x-1 + 2*x-2*y + x*y-2*z-1 + 3*y-1*z-1 + 3*x-1*z-1 + x-2*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 4080
Image of polytope 4080 PALP id: 4080
grdb id: 547408
Integer points: [ 1 0 0 -21 -18 -15 -12 -9 -6 -3 -14 -11 -8 -5 -2 -7 -4 -1 -10 -7 -4 -1 -3 0]
[ 0 1 0 -14 -12 -10 -8 -6 -4 -2 -9 -7 -5 -3 -1 -4 -2 0 -7 -5 -3 -1 -2 0]
[ 0 0 1 -6 -5 -4 -3 -2 -1 0 -4 -3 -2 -1 0 -2 -1 0 -3 -2 -1 0 -1 0]
Degree: 42
Hilbert function: 1 + 24 t + 110 t2 + 301 t3 + 639 t4 + 1166 t5 + 1924 t6 + 2955 t7 + 4301 t8 + 6004 t9 + 8106 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 275 1 none
Image of facet 276 1 none
Image of facet 14 1 none
Polytope 4081
Image of polytope 4081 PALP id: 4081
grdb id: 544693
Integer points: [ 1 0 0 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 -1 -1 -1 0 0]
[ 0 1 1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 0 1 -1 -1 -1 0 0]
[ 0 0 2 -3 2 1 0 -1 -2 2 1 0 -1 -2 2 1 0 -1 1 1 0 -1 1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 277 1 Lattice Minkowski decompositions of facet 277
Image of facet 14 1 none
Image of facet 73 1 none
Polytope 4082
Image of polytope 4082 PALP id: 4082
grdb id: 544680
Integer points: [ 1 0 0 -3 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -6 -5 -4 -3 -2 -1 -4 -3 -2 -1 0 -2 -1 0 -3 -2 -1 0 -1 0]
[ 0 0 1 -2 4 3 2 1 0 -1 3 2 1 0 -1 2 1 0 2 1 0 -1 1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 14 1 none
Image of facet 278 1 none
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Polytope 4083
Image of polytope 4083 PALP id: 4083
grdb id: 544683
Integer points: [ 1 0 0 0 -6 -5 -4 -3 -2 -1 -4 -3 -2 -1 0 -2 -1 0 -3 -2 -1 0 -1 0]
[ 0 1 0 -3 3 2 1 0 -1 -2 2 1 0 -1 -2 1 0 -1 2 1 0 -1 1 0]
[ 0 0 1 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 241 1 Lattice Minkowski decompositions of facet 241
Image of facet 14 1 none
Image of facet 279 1 none
Polytope 4084
Image of polytope 4084 PALP id: 4084
grdb id: 544685
Integer points: [ 1 0 0 0 -6 -1 -2 -3 -4 -5 0 -1 -2 -3 -4 0 -1 -2 0 -1 -2 -3 0 -1]
[ 0 1 0 -3 3 -2 -1 0 1 2 -2 -1 0 1 2 -1 0 1 -1 0 1 2 0 1]
[ 0 0 1 -2 4 -1 0 1 2 3 -1 0 1 2 3 0 1 2 -1 0 1 2 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + 3*x-1*y*z + 3*x-2*y*z2 + 2*x-3*y2*z2 + 3*x-4*y2*z3 + x-6*y3*z4 + 6*x-1*z + 6*x-2*y*z + 12*x-3*y*z2 + 6*x-5*y2*z3 + 3*y-1 + 6*x-1 + 18*x-2*z + 15*x-4*y*z2 + 2*y-1*z-1 + 12*x-1*y-1 + 20*x-3*z + 3*y-2*z-1 + 15*x-2*y-1 + 6*x-1*y-2*z-1 + y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 241 1 Lattice Minkowski decompositions of facet 241
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Polytope 4085
Image of polytope 4085 PALP id: 4085
grdb id: 544682
Integer points: [ 1 0 0 -3 -9 -4 -5 -6 -7 -8 -2 -3 -4 -5 -6 -1 -2 -3 -1 -2 -3 -4 0 -1]
[ 0 1 0 -2 -8 -3 -4 -5 -6 -7 -1 -2 -3 -4 -5 0 -1 -2 -1 -2 -3 -4 0 -1]
[ 0 0 1 0 -6 -1 -2 -3 -4 -5 0 -1 -2 -3 -4 0 -1 -2 0 -1 -2 -3 0 -1]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 171 1 Lattice Minkowski decompositions of facet 171
Image of facet 14 1 none
Image of facet 241 1 Lattice Minkowski decompositions of facet 241
Polytope 4086
Image of polytope 4086 PALP id: 4086
grdb id: 544679
Integer points: [ 1 0 0 -3 -9 -8 -7 -6 -5 -4 -6 -5 -4 -3 -2 -3 -2 -1 -4 -3 -2 -1 -1 0]
[ 0 1 0 0 -6 -5 -4 -3 -2 -1 -4 -3 -2 -1 0 -2 -1 0 -3 -2 -1 0 -1 0]
[ 0 0 1 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0]
Degree: 30
Hilbert function: 1 + 18 t + 80 t2 + 217 t3 + 459 t4 + 836 t5 + 1378 t6 + 2115 t7 + 3077 t8 + 4294 t9 + 5796 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 14 1 none
Image of facet 280 1 none
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Polytope 4087
Image of polytope 4087 PALP id: 4087
grdb id: 544697
Integer points: [ 1 0 0 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 0 -1 -1 0 0 0]
[ 0 1 1 -2 -2 -2 -1 -1 -1 -1 0 0 0 0 0 1 1 1 1 -1 -1 0 0 0]
[ 0 0 5 -4 -6 -5 -1 -2 -3 -4 2 1 0 -1 -2 4 3 2 1 -2 -3 1 0 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 43 1 irreducible and admissible
Image of facet 277 1 Lattice Minkowski decompositions of facet 277
Image of facet 14 2 none
Polytope 4088
Image of polytope 4088 PALP id: 4088
grdb id: 544673
Integer points: [ 1 0 1 -1 -11 -9 -7 -5 -3 -8 -6 -4 -2 -5 -3 -1 -2 0 -5 -3 -1 -2 0 1]
[ 0 1 0 1 -4 -3 -2 -1 0 -3 -2 -1 0 -2 -1 0 -1 0 -2 -1 0 -1 0 0]
[ 0 0 2 -1 -6 -5 -4 -3 -2 -4 -3 -2 -1 -2 -1 0 0 1 -3 -2 -1 -1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 73 1 none
Image of facet 281 1 none
Polytope 4089
Image of polytope 4089 PALP id: 4089
grdb id: 544681
Integer points: [ 1 0 0 -3 -15 -5 -7 -9 -11 -13 -2 -4 -6 -8 -10 -1 -3 -5 -1 -3 -5 -7 0 -2]
[ 0 1 0 -2 -8 -3 -4 -5 -6 -7 -1 -2 -3 -4 -5 0 -1 -2 -1 -2 -3 -4 0 -1]
[ 0 0 1 0 -6 -1 -2 -3 -4 -5 0 -1 -2 -3 -4 0 -1 -2 0 -1 -2 -3 0 -1]
Degree: 36
Hilbert function: 1 + 21 t + 95 t2 + 259 t3 + 549 t4 + 1001 t5 + 1651 t6 + 2535 t7 + 3689 t8 + 5149 t9 + 6951 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 282 1 none
Image of facet 14 1 none
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Polytope 4090
Image of polytope 4090 PALP id: 4090
grdb id: 544648
Integer points: [ 1 0 0 -3 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 0 -6 -5 -4 -3 -2 -1 -4 -3 -2 -1 0 -2 -1 0 -3 -2 -1 0 -1 0]
[ 0 0 1 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 241 1 Lattice Minkowski decompositions of facet 241
Image of facet 9 1 irreducible and admissible
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Image of facet 14 1 none
Polytope 4091
Image of polytope 4091 PALP id: 4091
grdb id: 522075
Integer points: [ 1 0 0 -2 2 -2 -1 0 1 -2 -1 0 1 -2 -1 0 -2 -1 -1 0 1 -1 0 -1]
[ 0 1 0 2 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 1 1 -1 -1 -1 0 0 1]
[ 0 0 1 -1 -1 3 2 1 0 2 1 0 -1 1 0 -1 0 -1 2 1 0 1 0 0]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 206 1 Lattice Minkowski decompositions of facet 206
Image of facet 80 2 none
Polytope 4092
Image of polytope 4092 PALP id: 4092
grdb id: 522086
Integer points: [ 1 0 0 0 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 -1 -1 -1 -1 0 0]
[ 0 1 0 -3 1 -5 -4 -3 -2 -1 0 -4 -3 -2 -1 0 -2 -1 -2 -1 0 1 -1 0]
[ 0 0 1 -2 2 -4 -3 -2 -1 0 1 -3 -2 -1 0 1 -1 0 -2 -1 0 1 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 9 1 irreducible and admissible
Image of facet 283 1 none
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Polytope 4093
Image of polytope 4093 PALP id: 4093
grdb id: 522085
Integer points: [ 1 1 0 0 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0 0 1]
[ 0 2 0 1 -2 -6 -3 -4 -5 -1 -2 -3 -4 0 -1 -2 0 -1 -2 -3 1 0 -1 1]
[ 0 0 1 1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0 0 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 2 none
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 4094
Image of polytope 4094 PALP id: 4094
grdb id: 522058
Integer points: [ 1 0 0 -3 3 0 -1 -2 1 0 -1 -2 2 1 0 -1 2 1 0 -1 1 0 2 1]
[ 0 1 0 3 -6 -3 -1 1 -4 -2 0 2 -5 -3 -1 1 -4 -2 -1 1 -2 0 -3 -1]
[ 0 0 1 1 -2 -2 -1 0 -2 -1 0 1 -2 -1 0 1 -1 0 -1 0 -1 0 -1 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 14 2 none
Image of facet 243 1 Lattice Minkowski decompositions of facet 243
Polytope 4095
Image of polytope 4095 PALP id: 4095
grdb id: 521906
Integer points: [ 1 0 0 -1 -1 -5 -4 -3 -2 -4 -3 -2 -1 -3 -2 -1 -2 -1 -2 -1 0 -1 0 0]
[ 0 1 0 2 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 1 1 -1 -1 -1 0 0 1]
[ 0 0 1 -2 2 -2 -1 0 1 -2 -1 0 1 -2 -1 0 -2 -1 -1 0 1 -1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 3*x-1*y*z-1 + 5*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + 4*x-1*z-1 + 4*x-1*y-1 + 4*x-2*y*z-2 + 10*x-2*z-1 + 10*x-2*y-1 + 4*x-2*y-2*z + 2*x-2*y-1*z-1 + 6*x-3*z-2 + 11*x-3*y-1*z-1 + 6*x-3*y-2 + 4*x-4*y-1*z-2 + 4*x-4*y-2*z-1 + x-5*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 284 1 Lattice Minkowski decompositions of facet 284
Image of facet 32 2 Lattice Minkowski decompositions of facet 32
Polytope 4096
Image of polytope 4096 PALP id: 4096
grdb id: 521907
Integer points: [ 1 0 0 -1 -1 -5 -4 -3 -2 -4 -3 -2 -1 -3 -2 -1 -2 -1 -2 -1 0 -1 0 0]
[ 0 1 0 2 -2 -6 -4 -2 0 -5 -3 -1 1 -4 -2 0 -3 -1 -3 -1 1 -2 0 -1]
[ 0 0 1 -2 2 2 1 0 -1 2 1 0 -1 2 1 0 2 1 1 0 -1 1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 285 1 none
Image of facet 32 2 Lattice Minkowski decompositions of facet 32
Polytope 4097
Image of polytope 4097 PALP id: 4097
grdb id: 521909
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 1 0 2 -2 -6 1 0 -1 0 -1 -2 -3 -2 -3 -4 -4 -5 1 0 -1 -1 -2 -3]
[ 0 0 1 -2 2 2 -1 0 1 -1 0 1 2 0 1 2 1 2 -1 0 1 0 1 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*y*z-1 + 3*y-1*z + x-1*y2*z-2 + 4*x-1*y*z-1 + 4*y-1 + 6*x-1 + 4*y-2*z + 4*x-1*y-1*z + x-1*y-2*z2 + 4*x-1*z-1 + 12*x-1*y-1 + 2*y-3*z + 12*x-1*y-2*z + 4*x-1*y-3*z2 + 6*x-1*y-2 + 12*x-1*y-3*z + 6*x-1*y-4*z2 + 4*x-1*y-4*z + 4*x-1*y-5*z2 + x-1*y-6*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Image of facet 206 1 Lattice Minkowski decompositions of facet 206
Polytope 4098
Image of polytope 4098 PALP id: 4098
grdb id: 522021
Integer points: [ 1 0 0 -1 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 2 -2 -6 -3 -4 -5 0 -1 -2 -3 -4 1 0 -1 -2 -1 -2 -3 1 0 -1]
[ 0 0 1 -2 0 4 1 2 3 -1 0 1 2 3 -1 0 1 2 0 1 2 -1 0 1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 286 1 Lattice Minkowski decompositions of facet 286
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 14 1 none
Polytope 4099
Image of polytope 4099 PALP id: 4099
grdb id: 521842
Integer points: [ 1 0 0 -3 -1 -7 -6 -5 -4 -3 -2 -5 -4 -3 -2 -1 -2 -1 -3 -2 -1 0 -1 0]
[ 0 1 0 0 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 -1 -1 -1 -1 0 0]
[ 0 0 1 -2 2 -4 -3 -2 -1 0 1 -3 -2 -1 0 1 -1 0 -2 -1 0 1 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 287 1 none
Polytope 4100
Image of polytope 4100 PALP id: 4100
grdb id: 521707
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 1 0 2 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 1 1 -1 -1 -1 0 0 1]
[ 0 0 1 -2 2 -2 -1 0 1 -2 -1 0 1 -2 -1 0 -2 -1 -1 0 1 -1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
51 rank 2, number 7 x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 4*z-1 + 4*x-1*y*z-1 + 4*y-1 + 6*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + 4*x-1*y*z-2 + 2*y-1*z-1 + 12*x-1*z-1 + 12*x-1*y-1 + 4*x-1*y-2*z + 6*x-1*z-2 + 12*x-1*y-1*z-1 + 6*x-1*y-2 + 4*x-1*y-1*z-2 + 4*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 32 2 Lattice Minkowski decompositions of facet 32
Image of facet 206 1 Lattice Minkowski decompositions of facet 206
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Polytope 4101
Image of polytope 4101 PALP id: 4101
grdb id: 437078
Integer points: [ 1 0 0 0 1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 -1 0 0 0 0]
[ 0 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 1]
[ 0 0 2 -2 -1 -2 2 -1 0 1 -2 -1 0 1 -1 0 -1 0 1 2 -1 0 1 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 y*z2 + 2*y*z + x + y + 3*z + 2*x-1*z2 + 6*x-1*z + x*y-1*z-1 + 2*z-1 + 3*y-1 + 6*x-1 + 3*x-1*y-1*z + x-2*y-1*z2 + 4*y-1*z-1 + 2*x-1*z-1 + 8*x-1*y-1 + 4*x-2*y-1*z + y-1*z-2 + 7*x-1*y-1*z-1 + 6*x-2*y-1 + 2*x-1*y-1*z-2 + 4*x-2*y-1*z-1 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 4102
Image of polytope 4102 PALP id: 4102
grdb id: 437058
Integer points: [ 1 0 0 -1 -1 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 -1 -1 -1 0 0 0]
[ 0 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 1 -1 -1 -1 0 0 0]
[ 0 0 2 1 -3 2 -4 1 0 -1 -2 -3 2 1 0 -1 -2 1 0 -1 -2 1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 2 none
Image of facet 1 1 irreducible and admissible
Image of facet 212 1 Lattice Minkowski decompositions of facet 212
Image of facet 13 1 irreducible and admissible
Image of facet 173 1 Lattice Minkowski decompositions of facet 173
Polytope 4103
Image of polytope 4103 PALP id: 4103
grdb id: 436976
Integer points: [ 1 0 1 -3 1 0 -5 -1 -2 -3 -4 0 -1 -2 -3 1 0 -1 -1 -2 1 0 -1 1]
[ 0 1 0 1 -2 1 1 1 1 1 1 0 0 0 0 -1 -1 -1 1 1 0 0 0 -1]
[ 0 0 2 -3 2 1 -4 0 -1 -2 -3 1 0 -1 -2 2 1 0 -1 -2 1 0 -1 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x*z2 + 2*x*z + y*z + 2*x*y-1*z2 + x + y + 2*x*y-1*z + 6*z + x*y-2*z2 + 5*x-1*y + 5*y-1*z + 3*x-1*y*z-1 + 12*x-1 + 3*x-1*z-1 + 10*x-2*y*z-1 + 3*x-1*y-1 + 3*x-2*y*z-2 + 10*x-2*z-1 + 10*x-3*y*z-2 + x-3*y*z-3 + 3*x-3*z-2 + 5*x-4*y*z-3 + x-5*y*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 146 1 Lattice Minkowski decompositions of facet 146
Image of facet 227 1 Lattice Minkowski decompositions of facet 227
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 4104
Image of polytope 4104 PALP id: 4104
grdb id: 437024
Integer points: [ 1 0 1 1 -4 1 -6 0 -1 -2 -3 -4 -5 0 -1 -2 -3 0 -1 -2 -3 1 0 -1]
[ 0 1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 -1 -1 -1 -1 0 0 0]
[ 0 0 2 2 -3 3 -4 2 1 0 -1 -2 -3 1 0 -1 -2 1 0 -1 -2 1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 288 1 Lattice Minkowski decompositions of facet 288
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 195 1 Lattice Minkowski decompositions of facet 195
Image of facet 8 1 none
Image of facet 43 1 irreducible and admissible
Polytope 4105
Image of polytope 4105 PALP id: 4105
grdb id: 436663
Integer points: [ 1 0 0 0 -2 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 0 -1 -1 -1 0 0]
[ 0 1 0 -2 2 2 -2 -1 0 1 -2 -1 0 1 -2 -1 0 1 -1 -1 0 1 -1 0]
[ 0 0 1 1 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 0 1 -1 -1 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 273 1 Lattice Minkowski decompositions of facet 273
Image of facet 14 1 none
Polytope 4106
Image of polytope 4106 PALP id: 4106
grdb id: 436363
Integer points: [ 1 0 1 0 -2 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 2 2 -3 -2 -1 0 1 -2 -1 0 1 -1 0 1 -2 -1 0 1 -1 0]
[ 0 0 0 1 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 227 1 Lattice Minkowski decompositions of facet 227
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Polytope 4107
Image of polytope 4107 PALP id: 4107
grdb id: 436417
Integer points: [ 1 0 0 -1 -1 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -2 2 -2 3 2 1 0 -1 2 1 0 -1 -2 1 0 -1 1 0 -1 0 -1]
[ 0 0 1 0 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
52 rank 2, number 52 x + y + z + x-1*y2*z-1 + 3*x-1*y + 4*x-1*y*z-1 + 3*x-2*y2*z-1 + 2*y-1 + 5*x-1 + x-3*y3*z-2 + 5*x-1*z-1 + 10*x-2*y*z-1 + 3*x-1*y-1 + 5*x-3*y2*z-2 + 2*x-1*y-1*z-1 + 13*x-2*z-1 + x-1*y-2 + 10*x-3*y*z-2 + 8*x-2*y-1*z-1 + 10*x-3*z-2 + 2*x-2*y-2*z-1 + 5*x-3*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 254 1 Lattice Minkowski decompositions of facet 254
Polytope 4108
Image of polytope 4108 PALP id: 4108
grdb id: 436835
Integer points: [ 1 0 0 0 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 -1 -1 -1 0 0 0]
[ 0 1 0 -3 2 -3 2 -2 -1 0 1 -3 -2 -1 0 1 -2 -1 -1 0 1 -1 0 1]
[ 0 0 1 -2 2 -2 3 -1 0 1 2 -2 -1 0 1 2 -1 0 -1 0 1 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x-1*y2*z2 + x-2*y2*z3 + 2*y*z + 2*x-1*y*z2 + x + y + z + 4*x-1*y*z + 5*x-2*y*z2 + 8*x-1*z + 3*y-1 + 5*x-1 + 10*x-2*z + 2*y-1*z-1 + 12*x-1*y-1 + 3*y-2*z-1 + 2*x-1*y-1*z-1 + 10*x-2*y-1 + 8*x-1*y-2*z-1 + y-3*z-2 + 5*x-2*y-2*z-1 + 2*x-1*y-3*z-2 + x-2*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 216 1 Lattice Minkowski decompositions of facet 216
Image of facet 9 1 irreducible and admissible
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 4109
Image of polytope 4109 PALP id: 4109
grdb id: 436777
Integer points: [ 1 0 0 -1 -1 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -2 2 -2 2 -1 0 1 -2 -1 0 1 2 -1 0 1 -1 0 1 -1 0 1]
[ 0 0 1 2 -2 0 -4 -1 -2 -3 1 0 -1 -2 -3 1 0 -1 0 -1 -2 1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
151 ? x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 6*x-1*y*z-1 + 8*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*y*z-2 + 4*x-1*z-1 + 2*x-1*y-1 + 2*x-2*y2*z-3 + 9*x-2*y*z-2 + 13*x-2*z-1 + 8*x-2*y-1 + 2*x-2*y-2*z + x-3*y2*z-4 + 4*x-3*y*z-3 + 6*x-3*z-2 + 4*x-3*y-1*z-1 + x-3*y-2
10 rank 1, V18 x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 4*x-1*y*z-1 + 5*x-1 + 3*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*y*z-2 + 4*x-1*z-1 + 2*x-1*y-1 + 2*x-2*y2*z-3 + 7*x-2*y*z-2 + 10*x-2*z-1 + 7*x-2*y-1 + 2*x-2*y-2*z + x-3*y2*z-4 + 4*x-3*y*z-3 + 6*x-3*z-2 + 4*x-3*y-1*z-1 + x-3*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 289 1 Lattice Minkowski decompositions of facet 289
Polytope 4110
Image of polytope 4110 PALP id: 4110
grdb id: 435745
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 1 0 2 -2 0 -4 -1 -2 -3 1 0 -1 -2 -3 1 0 -1 0 -1 -2 1 0 -1]
[ 0 0 1 -2 2 -2 2 -1 0 1 -2 -1 0 1 2 -1 0 1 -1 0 1 -1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 2*z-1 + 4*x-1*y*z-1 + 4*y-1 + 6*x-1 + 2*y-2*z + 4*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*y*z-2 + 8*x-1*z-1 + 12*x-1*y-1 + 8*x-1*y-2*z + 2*x-1*y-3*z2 + x-1*z-2 + 4*x-1*y-1*z-1 + 6*x-1*y-2 + 4*x-1*y-3*z + x-1*y-4*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 214 1 Lattice Minkowski decompositions of facet 214
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 4111
Image of polytope 4111 PALP id: 4111
grdb id: 436667
Integer points: [ 1 0 0 0 0 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 -2 2 -4 -3 -2 -1 0 1 -2 -1 0 1 -3 -2 -1 0 1 -1 0 -1]
[ 0 0 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 -1 -1 -1 -1 -1 0 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + 2*x-1*y + z-1 + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 6*x-1 + 2*y-1*z-1 + 8*x-1*z-1 + 6*x-2*y*z-1 + 6*x-1*y-1 + y-2*z-1 + 12*x-1*y-1*z-1 + 15*x-2*z-1 + 2*x-1*y-2 + 8*x-1*y-2*z-1 + 20*x-2*y-1*z-1 + 2*x-1*y-3*z-1 + 15*x-2*y-2*z-1 + 6*x-2*y-3*z-1 + x-2*y-4*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 212 1 Lattice Minkowski decompositions of facet 212
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 4112
Image of polytope 4112 PALP id: 4112
grdb id: 436374
Integer points: [ 1 0 0 1 1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 1 0 -1 -2 0 -5 -4 -3 -2 -1 -4 -3 -2 -1 0 -3 -2 -1 -2 -1 0 -1 0]
[ 0 0 1 0 -1 1 -4 -3 -2 -1 0 -3 -2 -1 0 1 -2 -1 0 -2 -1 0 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 73 1 none
Image of facet 271 1 Lattice Minkowski decompositions of facet 271
Polytope 4113
Image of polytope 4113 PALP id: 4113
grdb id: 436698
Integer points: [ 1 0 0 0 -2 -1 -5 -1 -3 -2 -1 0 -4 -3 -2 -1 -4 -3 -2 -1 0 -2 -1 0]
[ 0 1 0 -2 2 -2 2 1 2 1 0 -1 2 1 0 -1 1 0 -1 1 0 1 0 -1]
[ 0 0 1 1 -1 0 -4 0 -2 -1 0 1 -3 -2 -1 0 -3 -2 -1 -1 0 -2 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + 2*x-1*y + 2*y-1*z + 3*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 7*x-1 + y-2*z + 4*x-1*z-1 + 8*x-2*y*z-1 + 6*x-1*y-1 + 2*x-2*y*z-2 + 3*x-3*y2*z-2 + 12*x-2*z-1 + x-1*y-2 + 10*x-3*y*z-2 + 4*x-2*y-1*z-1 + 3*x-4*y2*z-3 + 6*x-3*z-2 + 4*x-4*y*z-3 + x-5*y2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 3 irreducible and admissible
Image of facet 273 1 Lattice Minkowski decompositions of facet 273
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 4114
Image of polytope 4114 PALP id: 4114
grdb id: 436364
Integer points: [ 1 0 -1 0 -1 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 1 0 0 -1 -6 -5 -4 -3 -2 -4 -3 -2 -1 0 -2 -1 0 -3 -2 -1 -1 0]
[ 0 0 0 1 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Image of facet 254 1 Lattice Minkowski decompositions of facet 254
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Polytope 4115
Image of polytope 4115 PALP id: 4115
grdb id: 436368
Integer points: [ 1 0 0 0 -1 -2 -7 -3 -4 -5 -6 -1 -2 -3 -4 -5 -1 -2 -3 -1 -2 -3 0 -1]
[ 0 1 0 -1 1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 0 1 1 -1 1 -4 0 -1 -2 -3 1 0 -1 -2 -3 0 -1 -2 0 -1 -2 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 14 1 none
Image of facet 271 1 Lattice Minkowski decompositions of facet 271
Polytope 4116
Image of polytope 4116 PALP id: 4116
grdb id: 269333
Integer points: [ 1 0 0 -2 2 0 0 -4 -1 -2 -3 1 0 -1 -2 1 0 -1 -2 -3 1 0 -1 -1]
[ 0 1 0 2 -2 0 -2 2 -1 0 1 -2 -1 0 1 -1 -1 0 1 2 -1 0 1 1]
[ 0 0 1 1 -1 -1 1 1 1 1 1 0 0 0 0 -1 1 1 1 1 0 0 0 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
11 rank 2, number 6 x + y + z + 2*x-1*y*z + x-2*y2*z + 2*x*y-1 + 2*x-1*y + 2*y-1*z + 6*x-1*z + 6*x-2*y*z + 2*x-3*y2*z + x2*y-2*z-1 + 2*x*y-1*z-1 + z-1 + 2*x*y-2 + 6*y-1 + 6*x-1 + 2*x-2*y + y-2*z + 4*x-1*y-1*z + 6*x-2*z + 4*x-3*y*z + x-4*y2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Image of facet 127 2 Lattice Minkowski decompositions of facet 127
Polytope 4117
Image of polytope 4117 PALP id: 4117
grdb id: 269340
Integer points: [ 1 1 0 0 -1 -1 -1 -1 -1 -1 0 0 -1 -1 -1 -1 0 0 0 1 -1 -1 0 0]
[ 0 2 0 2 -1 1 -4 -2 0 -1 1 0 0 -1 -2 -3 1 0 -1 1 -2 -3 -1 -2]
[ 0 0 1 1 1 1 -2 -2 0 -1 0 -1 1 0 -1 -2 1 0 -1 0 0 -1 0 -1]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x*y2 + y2*z + 2*x*y + 2*y*z + x + 3*y + z + x-1*y*z + 2*x-1*z + 2*z-1 + 3*y-1 + 3*x-1 + x-1*y-1*z + 4*y-1*z-1 + 6*x-1*y-1 + 2*y-2*z-1 + 3*x-1*y-1*z-1 + 3*x-1*y-2 + 6*x-1*y-2*z-1 + x-1*y-2*z-2 + 3*x-1*y-3*z-1 + 2*x-1*y-3*z-2 + x-1*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 4118
Image of polytope 4118 PALP id: 4118
grdb id: 268997
Integer points: [ 1 0 0 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 1 0 -1 2 -1 2 -1 -1 -1 -1 0 0 0 0 1 1 1 -1 -1 -1 0 0 1]
[ 0 0 1 0 -1 2 -2 -2 -1 0 1 -2 -1 0 1 -2 -1 0 -1 0 1 -1 0 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + 2*y*z-1 + x-1*y2*z-1 + x*y-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + x-1*y2*z-2 + 4*z-1 + 6*x-1*y*z-1 + 4*y-1 + 9*x-1 + 4*x-1*y-1*z + 3*x-1*y*z-2 + 2*y-1*z-1 + 9*x-1*z-1 + 6*x-1*y-1 + 3*x-1*z-2 + 4*x-1*y-1*z-1 + x-1*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Polytope 4119
Image of polytope 4119 PALP id: 4119
grdb id: 269275
Integer points: [ 1 0 0 0 0 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 -2 2 3 -2 2 1 0 -1 1 0 -1 -2 -1 2 1 0 -1 1 0 -1]
[ 0 0 1 -1 1 -2 -2 3 -1 0 1 2 -1 0 1 2 0 -1 0 1 2 -1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*y*z-1 + 2*x-1*y2*z-1 + 6*x-1*y + 2*y-1*z + 6*x-1*z + 2*x-1*y-1*z2 + x-1*y2*z-2 + x-2*y3*z-2 + z-1 + 5*x-1*y*z-1 + 5*x-2*y2*z-1 + 2*y-1 + 9*x-1 + 10*x-2*y + y-2*z + 7*x-1*y-1*z + 10*x-2*z + 2*x-1*y-2*z2 + 5*x-2*y-1*z2 + x-2*y-2*z3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Image of facet 201 1 Lattice Minkowski decompositions of facet 201
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 4120
Image of polytope 4120 PALP id: 4120
grdb id: 268442
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 1 -1 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 0 1 0 -2 2 2 -3 1 0 -1 -2 1 0 -1 -2 1 0 -1 1 0 -1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + 2*z-1 + 5*y-1 + 5*x-1 + 6*x-1*y-1*z + x-1*y-2*z2 + 4*y-1*z-1 + 3*x-1*z-1 + 12*x-1*y-1 + 5*x-1*y-2*z + y-1*z-2 + 10*x-1*y-1*z-1 + 10*x-1*y-2 + 3*x-1*y-1*z-2 + 10*x-1*y-2*z-1 + 5*x-1*y-2*z-2 + x-1*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 227 1 Lattice Minkowski decompositions of facet 227
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 4121
Image of polytope 4121 PALP id: 4121
grdb id: 268912
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 1 1 -2 1 1 0 -3 0 -1 -2 1 0 -1 -2 1 0 -1 0 -1 1 0 -1 0]
[ 0 0 2 -1 -1 2 -2 -2 1 0 -1 1 0 -1 -2 0 -1 -2 1 0 1 0 -1 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 y*z2 + 2*y*z + x-1*y*z2 + x + y + 3*z + 3*x-1*y*z + 3*x-1*y + 4*x-1*z + 2*z-1 + x-1*y*z-1 + 3*y-1 + 9*x-1 + 3*y-1*z-1 + 6*x-1*z-1 + 6*x-1*y-1 + x-1*z-2 + y-2*z-1 + 9*x-1*y-1*z-1 + 3*x-1*y-1*z-2 + 4*x-1*y-2*z-1 + 3*x-1*y-2*z-2 + x-1*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Image of facet 1 1 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 9 1 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 4122
Image of polytope 4122 PALP id: 4122
grdb id: 268454
Integer points: [ 1 0 0 1 -1 1 1 -4 -3 -2 -1 0 -3 -2 -1 0 -2 -1 0 -2 -1 0 -1 0]
[ 0 1 0 -1 1 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 0 1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x*y-1 + x*y-1*z-1 + 2*z-1 + x-1*y*z-1 + 4*y-1 + 3*x-1 + x*y-2*z-1 + 6*y-1*z-1 + 5*x-1*z-1 + 5*x-1*y-1 + 5*y-2*z-1 + 12*x-1*y-1*z-1 + 3*x-2*z-1 + 2*x-2*y-1 + 10*x-1*y-2*z-1 + 10*x-2*y-1*z-1 + 10*x-2*y-2*z-1 + 3*x-3*y-1*z-1 + 5*x-3*y-2*z-1 + x-4*y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 227 1 Lattice Minkowski decompositions of facet 227
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 4123
Image of polytope 4123 PALP id: 4123
grdb id: 268019
Integer points: [ 1 0 0 -2 2 0 -2 2 -1 -2 -1 0 1 -1 0 1 -1 0 1 -1 0 1 2 1]
[ 0 1 0 2 -2 0 0 -4 1 1 0 -1 -2 -1 -2 -3 1 0 -1 0 -1 -2 -3 -1]
[ 0 0 1 1 -1 -1 1 -3 0 1 0 -1 -2 0 -1 -2 1 0 -1 1 0 -1 -2 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + 2*x-1*y*z + x-2*y2*z + 2*x*y-1 + 2*x-1*y + 2*x-1*z + 2*x-2*y*z + x2*y-2*z-1 + 3*x*y-1*z-1 + z-1 + 6*y-1 + 6*x-1 + x-2*z + 6*x*y-2*z-1 + 6*y-1*z-1 + 4*x-1*y-1 + 2*x2*y-3*z-2 + 2*x*y-2*z-2 + 6*y-2*z-1 + 4*x*y-3*z-2 + x2*y-4*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 127 2 Lattice Minkowski decompositions of facet 127
Polytope 4124
Image of polytope 4124 PALP id: 4124
grdb id: 268995
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 1 1 0 -1 -4 -3 -2 -1 -3 -2 -1 0 -2 -1 0 0 -2 -1 0 -1 0]
[ 0 0 1 0 -1 -2 2 2 1 0 -1 2 1 0 -1 2 1 0 1 1 0 -1 1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + x-1*y + 3*y-1*z + 2*x-1*z + x-1*y-1*z2 + 2*z-1 + x-1*y*z-1 + 4*y-1 + 5*x-1 + 2*y-2*z + 7*x-1*y-1*z + 3*x-1*y-2*z2 + 3*x-1*z-1 + 9*x-1*y-1 + 9*x-1*y-2*z + 3*x-1*y-3*z2 + x-1*z-2 + 4*x-1*y-1*z-1 + 6*x-1*y-2 + 4*x-1*y-3*z + x-1*y-4*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 256 1 Lattice Minkowski decompositions of facet 256
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 4125
Image of polytope 4125 PALP id: 4125
grdb id: 268804
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 2 2 -2 -1 -4 0 1 -2 -1 0 1 -3 -2 -1 0 -3 -1 0 1 -2 -1]
[ 0 0 1 -1 -2 0 2 2 1 0 2 1 0 -1 2 1 0 -1 1 1 0 -1 1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 3*y-1*z + 3*x-1*z + x-1*y-1*z2 + x-1*y2*z-2 + 4*x-1*y*z-1 + 2*y-1 + 8*x-1 + 2*y-2*z + 8*x-1*y-1*z + 3*x-1*y-2*z2 + 2*x-1*z-1 + 6*x-1*y-1 + 7*x-1*y-2*z + 3*x-1*y-3*z2 + x-1*y-2 + 2*x-1*y-3*z + x-1*y-4*z2
51 rank 2, number 7 x + y + z + 2*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 3*y-1*z + 3*x-1*z + x-1*y-1*z2 + x-1*y2*z-2 + 5*x-1*y*z-1 + 2*y-1 + 10*x-1 + 2*y-2*z + 9*x-1*y-1*z + 3*x-1*y-2*z2 + 2*x-1*z-1 + 7*x-1*y-1 + 8*x-1*y-2*z + 3*x-1*y-3*z2 + x-1*y-2 + 2*x-1*y-3*z + x-1*y-4*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 255 1 Lattice Minkowski decompositions of facet 255
Polytope 4126
Image of polytope 4126 PALP id: 4126
grdb id: 269009
Integer points: [ 1 0 0 0 -1 1 0 -4 -3 -2 -1 -3 -2 -1 0 -2 -1 0 -2 -1 0 -1 0 1]
[ 0 1 0 1 2 -2 -2 2 1 0 -1 2 1 0 -1 2 1 0 1 0 -1 1 0 -1]
[ 0 0 1 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + y*z-1 + x-1*y2*z-1 + 2*x*y-1 + 3*x-1*y + 3*z-1 + 6*x-1*y*z-1 + 3*x-2*y2*z-1 + x*y-2 + 3*y-1 + 4*x-1 + 2*x-2*y + 3*y-1*z-1 + 9*x-1*z-1 + 9*x-2*y*z-1 + 3*x-3*y2*z-1 + y-2*z-1 + 4*x-1*y-1*z-1 + 6*x-2*z-1 + 4*x-3*y*z-1 + x-4*y2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Polytope 4127
Image of polytope 4127 PALP id: 4127
grdb id: 268453
Integer points: [ 1 0 1 0 0 0 -1 -6 -2 -3 -4 -5 -1 -2 -3 -4 0 -1 -2 -1 -2 -3 0 -1]
[ 0 1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 0 0 1 -1 1 1 -4 0 -1 -2 -3 0 -1 -2 -3 0 -1 -2 0 -1 -2 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 258 1 none
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Polytope 4128
Image of polytope 4128 PALP id: 4128
grdb id: 266401
Integer points: [ 1 0 0 -1 -1 -1 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 1 -2 1 -4 -3 -2 -1 0 -3 -2 -1 0 1 -1 0 -2 -1 0 -1 0]
[ 0 0 1 0 -1 0 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 -1 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x + y + z + x-1*y + x-1*y*z-1 + 2*y-1 + 4*x-1 + 4*x-1*z-1 + 2*x-2*y*z-1 + 4*x-1*y-1 + 5*x-1*y-1*z-1 + 8*x-2*z-1 + x-1*y-2 + x-3*y*z-2 + 2*x-1*y-2*z-1 + 12*x-2*y-1*z-1 + 5*x-3*z-2 + 8*x-2*y-2*z-1 + 10*x-3*y-1*z-2 + 2*x-2*y-3*z-1 + 10*x-3*y-2*z-2 + 5*x-3*y-3*z-2 + x-3*y-4*z-2
146 ? x + y + z + x-1*y + x-1*y*z-1 + 2*y-1 + 5*x-1 + 4*x-1*z-1 + 2*x-2*y*z-1 + 5*x-1*y-1 + 5*x-1*y-1*z-1 + 9*x-2*z-1 + x-1*y-2 + x-3*y*z-2 + 2*x-1*y-2*z-1 + 14*x-2*y-1*z-1 + 5*x-3*z-2 + 9*x-2*y-2*z-1 + 10*x-3*y-1*z-2 + 2*x-2*y-3*z-1 + 10*x-3*y-2*z-2 + 5*x-3*y-3*z-2 + x-3*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 257 1 Lattice Minkowski decompositions of facet 257
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 4129
Image of polytope 4129 PALP id: 4129
grdb id: 267792
Integer points: [ 1 0 0 0 -1 0 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 1 -2 1 -4 -3 -2 -1 0 -2 -1 0 -3 -2 -1 0 1 -1 0 -1 0]
[ 0 0 1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 -1 0 0 -1 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + y*z-1 + x-1*y + 3*z-1 + 2*x-1*y*z-1 + 2*y-1 + 4*x-1 + 3*y-1*z-1 + 8*x-1*z-1 + x-2*y*z-1 + 5*x-1*y-1 + y-2*z-1 + 12*x-1*y-1*z-1 + 5*x-2*z-1 + 2*x-1*y-2 + 8*x-1*y-2*z-1 + 10*x-2*y-1*z-1 + 2*x-1*y-3*z-1 + 10*x-2*y-2*z-1 + 5*x-2*y-3*z-1 + x-2*y-4*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 216 1 Lattice Minkowski decompositions of facet 216
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 4130
Image of polytope 4130 PALP id: 4130
grdb id: 78248
Integer points: [ 1 0 0 -1 2 -2 0 2 -2 0 -1 1 0 -1 1 0 -1 1 0 -1 -2 1 0 -1]
[ 0 1 0 2 -1 0 -2 -2 2 -1 0 -1 0 1 0 1 -1 -2 -1 0 1 -1 0 1]
[ 0 0 1 -1 -1 1 1 -1 -1 1 1 0 0 0 -1 -1 1 0 0 0 0 -1 -1 -1]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x + y + z + x2*y-1*z-1 + 3*x*z-1 + 3*y*z-1 + x-1*y2*z-1 + 3*x*y-1 + 3*x-1*y + 2*y-1*z + 2*x-1*z + x2*y-2*z-1 + 4*x*y-1*z-1 + 6*z-1 + 4*x-1*y*z-1 + x-2*y2*z-1 + 2*x*y-2 + 6*y-1 + 6*x-1 + 2*x-2*y + y-2*z + 2*x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 4131
Image of polytope 4131 PALP id: 4131
grdb id: 78175
Integer points: [ 1 0 0 2 -2 2 0 1 -2 0 -1 0 -1 -2 -1 -2 1 1 0 -1 0 -1 -1 1]
[ 0 1 0 -1 2 -1 -1 -1 -1 0 1 -1 0 1 -1 0 0 -1 0 1 -1 0 -1 -1]
[ 0 0 1 -1 1 -2 1 -2 1 -1 0 -1 0 1 0 1 -1 -1 0 1 0 1 1 0]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x + y + z + 2*x-1*y*z + x-2*y2*z + x2*y-1*z-1 + 2*x*z-1 + 2*x*y-1 + 3*x-1*y + y-1*z + 4*x-1*z + 3*x-2*y*z + x2*y-1*z-2 + 4*x*y-1*z-1 + 3*z-1 + 5*y-1 + 6*x-1 + 2*x-1*y-1*z + 3*x-2*z + x*y-1*z-2 + 3*y-1*z-1 + 3*x-1*y-1 + x-2*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Polytope 4132
Image of polytope 4132 PALP id: 4132
grdb id: 78482
Integer points: [ 1 0 0 0 0 -1 1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0 1]
[ 0 1 0 1 -1 1 -2 1 1 1 1 1 0 0 0 0 -1 -1 1 1 1 0 0 -1]
[ 0 0 1 -1 1 1 0 1 -3 0 -1 -2 1 0 -1 -2 0 -1 0 -1 -2 0 -1 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + x-1*y*z + y*z-1 + 2*x*y-1 + 4*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + 4*z-1 + 5*x-1*y*z-1 + x*y-2 + 4*y-1 + 7*x-1 + 4*x-2*y + 2*x-1*y*z-2 + 3*y-1*z-1 + 8*x-1*z-1 + 6*x-2*y*z-1 + 3*x-1*z-2 + 4*x-2*y*z-2 + x-2*y*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Polytope 4133
Image of polytope 4133 PALP id: 4133
grdb id: 78269
Integer points: [ 1 0 0 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 1 0 -1 2 2 -1 1 -3 0 -1 -2 1 0 -1 -2 1 0 0 -1 -2 1 0 -1]
[ 0 0 1 0 -1 -2 2 -2 2 -1 0 1 -1 0 1 2 0 1 -1 0 1 -1 0 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + 2*y*z-1 + x-1*y2*z-1 + x*y-1 + 3*x-1*y + 3*y-1*z + 3*x-1*z + x-1*y-1*z2 + x-1*y2*z-2 + 2*z-1 + 5*x-1*y*z-1 + 4*y-1 + 9*x-1 + 2*y-2*z + 7*x-1*y-1*z + 2*x-1*y-2*z2 + x-1*y*z-2 + 4*x-1*z-1 + 6*x-1*y-1 + 4*x-1*y-2*z + x-1*y-3*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 198 1 Lattice Minkowski decompositions of facet 198
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 4134
Image of polytope 4134 PALP id: 4134
grdb id: 78330
Integer points: [ 1 0 0 1 -1 -2 -2 1 1 0 1 0 1 0 -1 1 0 -1 1 0 -1 1 0 -1]
[ 0 1 0 -2 2 3 2 -2 -4 0 -1 1 -3 -1 1 -2 0 2 -1 -2 0 -3 -1 1]
[ 0 0 1 2 -2 -2 -1 0 2 -1 0 -1 1 0 -1 1 0 -1 1 1 0 2 1 0]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*y*z-1 + 2*x-1*y2*z-1 + 2*x*y-1 + 2*x-1*y + 4*x*y-2*z + 4*y-1*z + 2*x*y-3*z2 + x-1*y2*z-2 + x-2*y3*z-2 + 2*z-1 + 4*x-1*y*z-1 + x-2*y2*z-1 + x*y-2 + 5*y-1 + 3*x-1 + 2*x*y-3*z + 3*y-2*z + x*y-4*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 36 1 Lattice Minkowski decompositions of facet 36
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 108 1 Lattice Minkowski decompositions of facet 108
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 4135
Image of polytope 4135 PALP id: 4135
grdb id: 77741
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 -1 2 -2 2 -2 0 -1 1 0 -1 -2 1 0 -1 1 0 0 -1 1 0 -1]
[ 0 0 1 2 -1 2 -2 0 -2 -1 -2 -1 0 1 -1 0 1 0 1 -1 0 -1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + x-1*y2*z-2 + 2*z-1 + 5*x-1*y*z-1 + 2*y-1 + 8*x-1 + 5*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*y*z-2 + 6*x-1*z-1 + 6*x-1*y-1 + 2*x-1*y-2*z + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
51 rank 2, number 7 x + y + z + 2*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + x-1*y2*z-2 + 2*z-1 + 6*x-1*y*z-1 + 2*y-1 + 10*x-1 + 6*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*y*z-2 + 7*x-1*z-1 + 7*x-1*y-1 + 2*x-1*y-2*z + x-1*z-2 + 2*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 16 3 Lattice Minkowski decompositions of facet 16
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 261 1 Lattice Minkowski decompositions of facet 261
Polytope 4136
Image of polytope 4136 PALP id: 4136
grdb id: 76930
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 1 1 0 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 0 1 0 -1 -2 2 2 -2 -1 0 1 -2 -1 0 1 -1 0 1 -1 0 1 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + 2*z-1 + x-1*y*z-1 + 4*y-1 + 6*x-1 + 6*x-1*y-1*z + x-1*y-2*z2 + 2*y-1*z-1 + 5*x-1*z-1 + 11*x-1*y-1 + 4*x-1*y-2*z + x-1*z-2 + 8*x-1*y-1*z-1 + 6*x-1*y-2 + 2*x-1*y-1*z-2 + 4*x-1*y-2*z-1 + x-1*y-2*z-2
62 rank 2, number 9 x + y + z + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + 2*z-1 + x-1*y*z-1 + 4*y-1 + 5*x-1 + 5*x-1*y-1*z + x-1*y-2*z2 + 2*y-1*z-1 + 4*x-1*z-1 + 9*x-1*y-1 + 4*x-1*y-2*z + x-1*z-2 + 7*x-1*y-1*z-1 + 6*x-1*y-2 + 2*x-1*y-1*z-2 + 4*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 259 1 Lattice Minkowski decompositions of facet 259
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 4137
Image of polytope 4137 PALP id: 4137
grdb id: 76994
Integer points: [ 1 0 0 0 1 1 -2 1 -3 -1 0 1 -2 -1 0 1 -2 -1 0 -1 0 1 -1 0]
[ 0 1 0 -1 -1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 0 1 1 0 -2 1 -3 1 1 0 -1 1 0 -1 -2 0 -1 -2 1 0 -1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*x*z-1 + x*y-1 + y-1*z + 2*x-1*z + x*z-2 + 3*x*y-1*z-1 + 3*z-1 + 6*y-1 + 3*x-1 + 3*x-1*y-1*z + x-2*z + 3*x*y-1*z-2 + 9*y-1*z-1 + 9*x-1*y-1 + 3*x-2*y-1*z + x*y-1*z-3 + 4*y-1*z-2 + 6*x-1*y-1*z-1 + 4*x-2*y-1 + x-3*y-1*z
51 rank 2, number 7 x + y + z + 2*x*z-1 + x*y-1 + y-1*z + 2*x-1*z + x*z-2 + 3*x*y-1*z-1 + 4*z-1 + 6*y-1 + 4*x-1 + 3*x-1*y-1*z + x-2*z + 3*x*y-1*z-2 + 9*y-1*z-1 + 9*x-1*y-1 + 3*x-2*y-1*z + x*y-1*z-3 + 4*y-1*z-2 + 6*x-1*y-1*z-1 + 4*x-2*y-1 + x-3*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Image of facet 93 1 Lattice Minkowski decompositions of facet 93
Polytope 4138
Image of polytope 4138 PALP id: 4138
grdb id: 77044
Integer points: [ 1 0 0 0 1 1 -1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 1 0 1 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 0 1 -1 1 0 1 1 -3 0 -1 -2 1 0 -1 -2 1 0 -1 0 -1 -2 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + x*y-1*z + z + y*z-1 + x*y-1 + 3*y-1*z + x-1*z + 3*z-1 + 6*y-1 + 4*x-1 + 3*x-1*y-1*z + 3*y-1*z-1 + 5*x-1*z-1 + 9*x-1*y-1 + x-2*y-1*z + 2*x-1*z-2 + 9*x-1*y-1*z-1 + 4*x-2*y-1 + 3*x-1*y-1*z-2 + 6*x-2*y-1*z-1 + 4*x-2*y-1*z-2 + x-2*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Polytope 4139
Image of polytope 4139 PALP id: 4139
grdb id: 75065
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 1 1 -1 -2 -2 1 0 1 0 -1 1 0 -1 -2 0 -1 1 0 -1 0 -1]
[ 0 0 1 0 -2 2 2 0 -3 1 -1 0 1 -2 -1 0 1 -2 -1 -1 0 1 -1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*y*z-1 + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + y*z-2 + 3*z-1 + 3*x-1*y*z-1 + 2*y-1 + 7*x-1 + 5*x-1*y-1*z + x-1*y-2*z2 + 3*x-1*y*z-2 + 8*x-1*z-1 + 7*x-1*y-1 + 2*x-1*y-2*z + x-1*y*z-3 + 3*x-1*z-2 + 3*x-1*y-1*z-1 + x-1*y-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 231 1 Lattice Minkowski decompositions of facet 231
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 4140
Image of polytope 4140 PALP id: 4140
grdb id: 77945
Integer points: [ 1 0 0 0 0 0 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 0 1 -1 1 -1 2 2 -3 1 0 -1 -2 1 0 -1 -2 0 1 0 -1 -2 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + y*z-1 + y-1*z + 2*x-1*z + x-1*y-1*z2 + 2*z-1 + 2*y-1 + 6*x-1 + 5*x-1*y-1*z + x-2*y-1*z2 + y-1*z-1 + 6*x-1*z-1 + 9*x-1*y-1 + 5*x-2*y-1*z + 2*x-1*z-2 + 7*x-1*y-1*z-1 + 10*x-2*y-1 + 2*x-1*y-1*z-2 + 10*x-2*y-1*z-1 + 5*x-2*y-1*z-2 + x-2*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Image of facet 201 1 Lattice Minkowski decompositions of facet 201
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 4141
Image of polytope 4141 PALP id: 4141
grdb id: 77057
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 1 0 1 -1 0 -4 -2 -1 0 -3 -2 -1 0 -3 -2 -1 -1 0 -2 -1 0]
[ 0 0 1 0 1 -1 1 -2 -2 0 0 0 -1 -1 -1 -1 -2 -2 -2 0 0 -1 -1 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y + x-1*z + 2*z-1 + x-1*y*z-1 + 3*y-1 + 4*x-1 + x-1*y-1*z + 4*y-1*z-1 + 5*x-1*z-1 + 6*x-1*y-1 + x-1*z-2 + 2*y-2*z-1 + 10*x-1*y-1*z-1 + 3*x-1*y-2 + 4*x-1*y-1*z-2 + 9*x-1*y-2*z-1 + 6*x-1*y-2*z-2 + 3*x-1*y-3*z-1 + 4*x-1*y-3*z-2 + x-1*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 262 1 Lattice Minkowski decompositions of facet 262
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 4142
Image of polytope 4142 PALP id: 4142
grdb id: 560035
Integer points: [ 1 1 0 0 -1 -1 1 1 -1 -1 -1 0 -1 0 -1 0 1 -1 0 0 -1 0 1 0]
[ 0 2 0 2 -1 1 -1 1 -3 -1 0 1 0 1 -1 0 1 -2 -1 0 -2 -1 0 -2]
[ 0 0 1 1 1 1 -1 -1 -1 -1 1 1 0 0 0 0 0 0 0 -1 -1 -1 -1 -1]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x*y2 + y2*z + 2*x*y + 2*y*z + x*y*z-1 + x + 3*y + z + x-1*y*z + 2*x*z-1 + 2*x-1*z + x*y-1*z-1 + 2*z-1 + 3*y-1 + 2*x-1 + x-1*y-1*z + 4*y-1*z-1 + 4*x-1*y-1 + 2*y-2*z-1 + x-1*y-1*z-1 + 2*x-1*y-2 + 2*x-1*y-2*z-1 + x-1*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 36 2 Lattice Minkowski decompositions of facet 36
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Image of facet 15 3 Lattice Minkowski decompositions of facet 15
Polytope 4143
Image of polytope 4143 PALP id: 4143
grdb id: 558361
Integer points: [ 1 0 0 -1 1 -2 0 1 -2 1 -1 -1 -1 0 0 0 1 1 -1 0 0 1 1 1]
[ 0 1 0 1 0 1 -1 -2 1 -2 0 0 0 -1 -1 -1 -2 -2 1 0 0 -1 -1 -1]
[ 0 0 1 1 -1 1 1 0 0 -3 -1 0 1 -2 -1 0 -2 -1 0 -1 0 -2 -1 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + x-1*y*z + x*z-1 + 2*x*y-1 + 2*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + 4*x*y-1*z-1 + 4*z-1 + x*y-2 + 5*y-1 + 5*x-1 + x-2*y + 2*x*y-1*z-2 + 3*x*y-2*z-1 + 7*y-1*z-1 + 3*x-1*z-1 + 3*x*y-2*z-2 + 3*y-1*z-2 + x*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 174 1 Lattice Minkowski decompositions of facet 174
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Polytope 4144
Image of polytope 4144 PALP id: 4144
grdb id: 558688
Integer points: [ 1 0 0 1 -1 1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 1 0 0 1 -1 1 -1 1 -3 0 -1 -2 1 0 -1 -2 0 0 -1 -2 1 0 -1]
[ 0 0 1 -1 0 0 -2 2 -2 2 -1 0 1 -1 0 1 2 1 -1 0 1 -1 0 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + x*z-1 + 2*y*z-1 + x*y-1 + x-1*y + 3*y-1*z + 2*x-1*z + x-1*y-1*z2 + y*z-2 + 4*z-1 + 2*x-1*y*z-1 + 5*y-1 + 6*x-1 + 2*y-2*z + 6*x-1*y-1*z + 2*x-1*y-2*z2 + x-1*y*z-2 + 4*x-1*z-1 + 6*x-1*y-1 + 4*x-1*y-2*z + x-1*y-3*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 4145
Image of polytope 4145 PALP id: 4145
grdb id: 555757
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 -1 1 0 1 -2 -2 -1 -2 -1 0 -2 -1 0 1 -1 0 -1 0 -1 0]
[ 0 0 1 -1 1 0 1 -2 1 -2 1 0 0 0 -1 -1 -1 -1 -2 -2 0 0 -1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + y*z-1 + x-1*y + y-1*z + x-1*z + 3*z-1 + 2*x-1*y*z-1 + 3*y-1 + 5*x-1 + 2*x-1*y-1*z + x-1*y*z-2 + 2*y-1*z-1 + 7*x-1*z-1 + 7*x-1*y-1 + x-1*y-2*z + 3*x-1*z-2 + 8*x-1*y-1*z-1 + 3*x-1*y-2 + 3*x-1*y-1*z-2 + 3*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Image of facet 231 1 Lattice Minkowski decompositions of facet 231
Polytope 4146
Image of polytope 4146 PALP id: 4146
grdb id: 544614
Integer points: [ 1 0 1 -2 -7 -6 -5 -4 -3 -5 -4 -3 -2 -1 -3 -2 -1 -1 0 -3 -2 -1 -1 0 1]
[ 0 1 0 1 -4 -3 -2 -1 0 -3 -2 -1 0 1 -2 -1 0 -1 0 -2 -1 0 -1 0 0]
[ 0 0 2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 1 1 -1 -1 -1 0 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 2 irreducible and admissible
Image of facet 290 1 none
Image of facet 73 1 none
Polytope 4147
Image of polytope 4147 PALP id: 4147
grdb id: 544607
Integer points: [ 1 0 0 -1 -15 -13 -11 -9 -7 -5 -3 -10 -8 -6 -4 -2 -5 -3 -1 -7 -5 -3 -1 -2 0]
[ 0 1 0 -1 -8 -7 -6 -5 -4 -3 -2 -5 -4 -3 -2 -1 -2 -1 0 -4 -3 -2 -1 -1 0]
[ 0 0 1 1 -6 -5 -4 -3 -2 -1 0 -4 -3 -2 -1 0 -2 -1 0 -3 -2 -1 0 -1 0]
Degree: 34
Hilbert function: 1 + 20 t + 90 t2 + 245 t3 + 519 t4 + 946 t5 + 1560 t6 + 2395 t7 + 3485 t8 + 4864 t9 + 6566 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 275 1 none
Image of facet 291 1 none
Image of facet 14 1 none
Polytope 4148
Image of polytope 4148 PALP id: 4148
grdb id: 521504
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0]
[ 0 1 1 0 0 -4 -1 -2 -3 0 -1 -2 -3 0 -1 -2 0 -1 0 -1 -2 1 0 -1 0]
[ 0 0 2 -2 2 -2 1 0 -1 1 0 -1 -2 0 -1 -2 -1 -2 1 0 -1 1 0 -1 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 y*z2 + 2*y*z + x + y + 3*z + x-1*z2 + 4*x-1*z + 2*z-1 + 4*y-1 + 6*x-1 + 4*x-1*y-1*z + 4*y-1*z-1 + 4*x-1*z-1 + 12*x-1*y-1 + x-1*z-2 + 2*y-2*z-1 + 12*x-1*y-1*z-1 + 6*x-1*y-2 + 4*x-1*y-1*z-2 + 12*x-1*y-2*z-1 + 6*x-1*y-2*z-2 + 4*x-1*y-3*z-1 + 4*x-1*y-3*z-2 + x-1*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 2 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 76 1 Lattice Minkowski decompositions of facet 76
Image of facet 206 1 Lattice Minkowski decompositions of facet 206
Polytope 4149
Image of polytope 4149 PALP id: 4149
grdb id: 521466
Integer points: [ 1 0 0 1 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 0 1 -1 2 -4 1 0 -1 -2 -3 1 0 -1 -2 -3 0 -1 -2 1 0 -1 -2 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + 2*x-1*z + x*y-1*z-1 + 3*z-1 + 3*y-1 + 6*x-1 + 3*x-1*y-1*z + x-2*y-1*z2 + 6*y-1*z-1 + 6*x-1*z-1 + 12*x-1*y-1 + 6*x-2*y-1*z + 3*y-1*z-2 + 2*x-1*z-2 + 18*x-1*y-1*z-1 + 15*x-2*y-1 + 12*x-1*y-1*z-2 + 20*x-2*y-1*z-1 + 3*x-1*y-1*z-3 + 15*x-2*y-1*z-2 + 6*x-2*y-1*z-3 + x-2*y-1*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 241 1 Lattice Minkowski decompositions of facet 241
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Polytope 4150
Image of polytope 4150 PALP id: 4150
grdb id: 521543
Integer points: [ 1 0 0 -2 0 -5 -1 -3 -2 -1 0 -4 -3 -2 -1 0 -4 -3 -2 -1 -1 0 -2 -1 0]
[ 0 1 0 2 -3 2 1 2 1 0 -1 2 1 0 -1 -2 1 0 -1 -2 1 0 1 0 -1]
[ 0 0 1 -1 1 -4 0 -2 -1 0 1 -3 -2 -1 0 1 -3 -2 -1 0 -1 0 -2 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 277 1 Lattice Minkowski decompositions of facet 277
Image of facet 9 1 irreducible and admissible
Image of facet 73 1 none
Polytope 4151
Image of polytope 4151 PALP id: 4151
grdb id: 521506
Integer points: [ 1 0 0 -1 -1 -5 -2 -1 0 -3 -2 -1 -4 -3 -2 -1 -4 -3 -2 0 -1 0 -2 -1 0]
[ 0 1 1 0 0 -4 -1 0 1 -2 -1 0 -3 -2 -1 0 -3 -2 -1 0 -1 0 -2 -1 0]
[ 0 0 2 -2 2 -2 1 1 1 0 0 0 -1 -1 -1 -1 -2 -2 -2 1 0 0 -1 -1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 y*z2 + 2*y*z + x + y + 2*z + x-1*z2 + 6*x-1*z + 2*z-1 + 8*x-1 + 4*x-1*z-1 + 4*x-1*y-1 + 4*x-2*y-1*z + x-1*z-2 + 4*x-1*y-1*z-1 + 13*x-2*y-1 + 12*x-2*y-1*z-1 + 4*x-2*y-1*z-2 + 2*x-2*y-2*z-1 + 6*x-3*y-2 + 12*x-3*y-2*z-1 + 6*x-3*y-2*z-2 + 4*x-4*y-3*z-1 + 4*x-4*y-3*z-2 + x-5*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 2 Lattice Minkowski decompositions of facet 32
Image of facet 1 3 irreducible and admissible
Image of facet 292 1 Lattice Minkowski decompositions of facet 292
Polytope 4152
Image of polytope 4152 PALP id: 4152
grdb id: 521572
Integer points: [ 1 0 1 -2 -1 -5 -2 -3 -4 0 -1 -2 -3 -4 0 -1 -2 -3 -1 0 -1 -2 1 0 -1]
[ 0 1 0 1 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 0 1 -1 -1 -1 0 0 0]
[ 0 0 2 -2 2 -2 1 0 -1 2 1 0 -1 -2 1 0 -1 -2 -1 1 0 -1 1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 293 1 Lattice Minkowski decompositions of facet 293
Image of facet 14 1 none
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Polytope 4153
Image of polytope 4153 PALP id: 4153
grdb id: 521465
Integer points: [ 1 0 0 -1 -3 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 0 -6 -5 -4 -3 -2 -1 -4 -3 -2 -1 0 -2 -1 0 -3 -2 -1 0 -1 0]
[ 0 0 1 -1 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 241 1 Lattice Minkowski decompositions of facet 241
Image of facet 171 1 Lattice Minkowski decompositions of facet 171
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 14 1 none
Polytope 4154
Image of polytope 4154 PALP id: 4154
grdb id: 521439
Integer points: [ 1 0 1 -4 -5 1 0 -1 -2 -3 -4 1 0 -1 -2 -3 0 -1 -2 1 0 -1 -2 1 0]
[ 0 1 0 -1 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0]
[ 0 0 2 -2 -2 4 3 2 1 0 -1 3 2 1 0 -1 1 0 -1 2 1 0 -1 1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
17 rank 1, V22 x*z2 + 2*x*y-1*z3 + x*y-2*z4 + 2*x*z + 2*x*y-1*z2 + x + y + 5*z + 10*y-1*z2 + 6*y-2*z3 + 6*y-1*z + 6*x-1 + 19*x-1*y-1*z + 15*x-1*y-2*z2 + 6*x-1*y-1 + 2*x-2*z-1 + 17*x-2*y-1 + 20*x-2*y-2*z + 2*x-2*y-1*z-1 + 7*x-3*y-1*z-1 + 15*x-3*y-2 + x-4*y-1*z-2 + 6*x-4*y-2*z-1 + x-5*y-2*z-2
59 rank 2, number 16 x*z2 + 2*x*y-1*z3 + x*y-2*z4 + 2*x*z + 2*x*y-1*z2 + x + y + 4*z + 9*y-1*z2 + 6*y-2*z3 + 6*y-1*z + 5*x-1 + 16*x-1*y-1*z + 15*x-1*y-2*z2 + 6*x-1*y-1 + 2*x-2*z-1 + 14*x-2*y-1 + 20*x-2*y-2*z + 2*x-2*y-1*z-1 + 6*x-3*y-1*z-1 + 15*x-3*y-2 + x-4*y-1*z-2 + 6*x-4*y-2*z-1 + x-5*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 3 irreducible and admissible
Image of facet 294 1 Lattice Minkowski decompositions of facet 294
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Polytope 4155
Image of polytope 4155 PALP id: 4155
grdb id: 521539
Integer points: [ 1 0 0 1 -1 -6 -5 -4 -3 -2 -4 -3 -2 -1 0 -2 -1 0 -3 -2 -1 0 -1 0 1]
[ 0 1 0 -2 -2 3 2 1 0 -1 2 1 0 -1 -2 1 0 -1 2 1 0 -1 1 0 -1]
[ 0 0 1 0 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 254 1 Lattice Minkowski decompositions of facet 254
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Image of facet 14 1 none
Polytope 4156
Image of polytope 4156 PALP id: 4156
grdb id: 521469
Integer points: [ 1 0 0 -1 -1 -7 -6 -5 -4 -3 -2 -5 -4 -3 -2 -1 -3 -2 -1 -3 -2 -1 0 -1 0]
[ 0 1 0 1 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0]
[ 0 0 1 -1 2 -4 -3 -2 -1 0 1 -3 -2 -1 0 1 -2 -1 0 -2 -1 0 1 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Image of facet 14 1 none
Image of facet 295 1 none
Polytope 4157
Image of polytope 4157 PALP id: 4157
grdb id: 521468
Integer points: [ 1 0 0 -1 -3 -9 -8 -7 -6 -5 -4 -6 -5 -4 -3 -2 -3 -2 -1 -4 -3 -2 -1 -1 0]
[ 0 1 0 1 0 -6 -5 -4 -3 -2 -1 -4 -3 -2 -1 0 -2 -1 0 -3 -2 -1 0 -1 0]
[ 0 0 1 -1 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Image of facet 14 1 none
Image of facet 296 1 Lattice Minkowski decompositions of facet 296
Polytope 4158
Image of polytope 4158 PALP id: 4158
grdb id: 435216
Integer points: [ 1 0 0 0 0 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 -2 -2 3 2 1 0 -1 2 1 0 -1 -2 0 -1 2 1 0 -1 1 0 -1]
[ 0 0 1 -2 1 3 -2 -1 0 1 2 -2 -1 0 1 2 -1 0 -1 0 1 2 -1 0 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
11 rank 2, number 6 x + y + z + 2*y*z-1 + 2*x-1*y2*z-1 + 6*x-1*y + 2*y-1*z + 6*x-1*z + 2*x-1*y-1*z2 + y*z-2 + 2*x-1*y2*z-2 + x-2*y3*z-2 + 3*z-1 + 8*x-1*y*z-1 + 5*x-2*y2*z-1 + 3*y-1 + 12*x-1 + 10*x-2*y + y-2*z + 8*x-1*y-1*z + 10*x-2*z + 2*x-1*y-2*z2 + 5*x-2*y-1*z2 + x-2*y-2*z3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 216 1 Lattice Minkowski decompositions of facet 216
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Polytope 4159
Image of polytope 4159 PALP id: 4159
grdb id: 434956
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 0 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0 0]
[ 0 1 1 0 0 -2 -2 0 0 0 1 -1 -1 -1 -1 -1 0 0 0 -2 -2 -2 -1 -1 -1]
[ 0 0 2 2 -2 -4 0 1 0 -1 1 1 0 -1 -2 -3 1 0 -1 -1 -2 -3 0 -1 -2]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
11 rank 2, number 6 y*z2 + 2*y*z + x + y + 2*z + x-1*z2 + 4*x-1*z + 2*z-1 + 2*y-1 + 6*x-1 + 2*x-1*y-1*z + 4*y-1*z-1 + 4*x-1*z-1 + 8*x-1*y-1 + 2*y-1*z-2 + x-1*z-2 + 12*x-1*y-1*z-1 + x-1*y-2 + 8*x-1*y-1*z-2 + 4*x-1*y-2*z-1 + 2*x-1*y-1*z-3 + 6*x-1*y-2*z-2 + 4*x-1*y-2*z-3 + x-1*y-2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Image of facet 214 1 Lattice Minkowski decompositions of facet 214
Polytope 4160
Image of polytope 4160 PALP id: 4160
grdb id: 435180
Integer points: [ 1 0 0 0 1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 -1 0 0 0 1 0]
[ 0 1 1 -1 0 1 -3 0 -1 -2 1 0 -1 -2 0 -1 1 0 -1 -2 1 0 -1 0 0]
[ 0 0 2 -2 2 0 -4 -1 -2 -3 1 0 -1 -2 1 0 0 -1 -2 -3 1 0 -1 1 -1]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x*z2 + y*z2 + 2*x*z + 2*y*z + x + y + 4*z + 2*x-1*y*z + 2*x-1*y + 2*z-1 + 3*y-1 + 7*x-1 + x-2*y + 4*y-1*z-1 + 6*x-1*z-1 + y-1*z-2 + 8*x-1*y-1*z-1 + 4*x-2*z-1 + 6*x-1*y-1*z-2 + 3*x-1*y-2*z-2 + 6*x-2*y-1*z-2 + 2*x-1*y-2*z-3 + 4*x-2*y-2*z-3 + x-2*y-3*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 167 1 Lattice Minkowski decompositions of facet 167
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 4161
Image of polytope 4161 PALP id: 4161
grdb id: 435142
Integer points: [ 1 0 0 -1 -1 -2 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -3 2 -4 3 2 1 0 -1 -2 -3 1 0 -1 -2 2 1 0 -1 -2 1 0 -1]
[ 0 0 1 2 -3 3 -4 -3 -2 -1 0 1 2 -2 -1 0 1 -2 -1 0 1 2 -1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 8 2 none
Image of facet 43 1 irreducible and admissible
Image of facet 215 1 Lattice Minkowski decompositions of facet 215
Image of facet 288 1 Lattice Minkowski decompositions of facet 288
Polytope 4162
Image of polytope 4162 PALP id: 4162
grdb id: 435181
Integer points: [ 1 0 0 1 -2 0 -6 -1 -2 -3 -4 -5 0 -1 -2 -3 0 -1 -2 -3 -4 1 0 -1 -1]
[ 0 1 -1 0 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0 1]
[ 0 0 0 2 -2 2 -4 1 0 -1 -2 -3 1 0 -1 -2 1 0 -1 -2 -3 1 0 -1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x*z2 + y*z2 + 2*x*z + 2*y*z + x + y + 4*z + 6*x-1*y*z + 8*x-1*y + 2*x-1*y*z-1 + y-1 + 7*x-1 + 15*x-2*y + 2*x-1*z-1 + 12*x-2*y*z-1 + x-2*y*z-2 + 6*x-2*z-1 + 20*x-3*y*z-1 + 8*x-3*y*z-2 + 2*x-3*z-2 + 15*x-4*y*z-2 + 2*x-4*y*z-3 + 6*x-5*y*z-3 + x-6*y*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 171 1 Lattice Minkowski decompositions of facet 171
Image of facet 212 1 Lattice Minkowski decompositions of facet 212
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 4163
Image of polytope 4163 PALP id: 4163
grdb id: 434689
Integer points: [ 1 0 0 -2 1 -4 1 0 -1 -2 -3 1 0 -1 -2 -3 0 -1 1 0 -1 -2 1 0 -1]
[ 0 1 0 1 -2 1 -4 -3 -2 -1 0 -3 -2 -1 0 1 -1 0 -2 -1 0 1 -1 0 1]
[ 0 0 1 0 0 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 -1 -1 -1 -1 0 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + 2*x*y-1 + 2*x-1*y + x*y-2 + 4*y-1 + 4*x-1 + x-2*y + 2*x*y-2*z-1 + 6*y-1*z-1 + 6*x-1*z-1 + 2*x-2*y*z-1 + 2*x*y-3*z-1 + 8*y-2*z-1 + 12*x-1*y-1*z-1 + 8*x-2*z-1 + 2*x-3*y*z-1 + x*y-4*z-2 + 5*y-3*z-2 + 10*x-1*y-2*z-2 + 10*x-2*y-1*z-2 + 5*x-3*z-2 + x-4*y*z-2
40 rank 2, number 10 x + y + z + 2*x*y-1 + 2*x-1*y + x*y-2 + 5*y-1 + 5*x-1 + x-2*y + 2*x*y-2*z-1 + 6*y-1*z-1 + 6*x-1*z-1 + 2*x-2*y*z-1 + 2*x*y-3*z-1 + 9*y-2*z-1 + 14*x-1*y-1*z-1 + 9*x-2*z-1 + 2*x-3*y*z-1 + x*y-4*z-2 + 5*y-3*z-2 + 10*x-1*y-2*z-2 + 10*x-2*y-1*z-2 + 5*x-3*z-2 + x-4*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 257 1 Lattice Minkowski decompositions of facet 257
Polytope 4164
Image of polytope 4164 PALP id: 4164
grdb id: 434819
Integer points: [ 1 0 0 -1 -1 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -1 -1 -1 0 -1 -1 -1 0 0 0]
[ 0 1 1 0 0 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 1 -1 -1 -1 0 0 0]
[ 0 0 2 2 -2 0 -4 -3 -2 -1 -3 -2 -1 0 1 -1 0 1 1 -2 -1 0 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 y*z2 + 2*y*z + x + y + 2*z + x-1*z2 + 6*x-1*z + 2*z-1 + 10*x-1 + 6*x-1*z-1 + 2*x-1*y-1 + 2*x-2*y-1*z + x-1*z-2 + 4*x-1*y-1*z-1 + 9*x-2*y-1 + 2*x-1*y-1*z-2 + 14*x-2*y-1*z-1 + 9*x-2*y-1*z-2 + x-3*y-2 + 2*x-2*y-1*z-3 + 4*x-3*y-2*z-1 + 6*x-3*y-2*z-2 + 4*x-3*y-2*z-3 + x-3*y-2*z-4
20 rank 1, V16 y*z2 + 2*y*z + x + y + 2*z + x-1*z2 + 5*x-1*z + 2*z-1 + 8*x-1 + 5*x-1*z-1 + 2*x-1*y-1 + 2*x-2*y-1*z + x-1*z-2 + 4*x-1*y-1*z-1 + 8*x-2*y-1 + 2*x-1*y-1*z-2 + 12*x-2*y-1*z-1 + 8*x-2*y-1*z-2 + x-3*y-2 + 2*x-2*y-1*z-3 + 4*x-3*y-2*z-1 + 6*x-3*y-2*z-2 + 4*x-3*y-2*z-3 + x-3*y-2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 3 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 297 1 Lattice Minkowski decompositions of facet 297
Polytope 4165
Image of polytope 4165 PALP id: 4165
grdb id: 434943
Integer points: [ 1 0 0 0 0 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 -1 -1 -1 -1 0 0 0]
[ 0 1 0 1 -2 1 -4 0 -1 -2 -3 1 0 -1 -2 -3 0 -1 1 0 -1 -2 1 0 -1]
[ 0 0 1 -2 1 -2 3 -1 0 1 2 -2 -1 0 1 2 -1 0 -1 0 1 2 -1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*y*z-1 + 2*y-1*z + y*z-2 + 3*z-1 + 2*x-1*y*z-1 + 3*y-1 + 6*x-1 + y-2*z + 6*x-1*y-1*z + 2*x-1*y-2*z2 + 2*x-1*y*z-2 + 8*x-1*z-1 + 12*x-1*y-1 + 8*x-1*y-2*z + 2*x-1*y-3*z2 + x-2*y*z-2 + 5*x-2*z-1 + 10*x-2*y-1 + 10*x-2*y-2*z + 5*x-2*y-3*z2 + x-2*y-4*z3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Image of facet 216 1 Lattice Minkowski decompositions of facet 216
Image of facet 9 1 irreducible and admissible
Polytope 4166
Image of polytope 4166 PALP id: 4166
grdb id: 264812
Integer points: [ 1 0 1 -2 1 0 1 -2 1 0 1 0 1 0 -1 1 0 -1 1 0 -1 0 -1 0 -1]
[ 0 1 0 3 -3 -2 -1 2 -2 -1 -1 0 -2 -1 0 -1 0 1 0 1 2 0 1 1 2]
[ 0 0 2 2 -3 -3 1 1 -2 -2 -1 -1 -1 -1 -1 0 0 0 1 1 1 1 1 2 2]
Degree: 8
Hilbert function: 1 + 7 t + 25 t2 + 63 t3 + 129 t4 + 231 t5 + 377 t6 + 575 t7 + 833 t8 + 1159 t9 + 1561 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
5 rank 1, V8 x*z2 + 3*y*z2 + 3*x-1*y2*z2 + x-2*y3*z2 + 2*x*z + 4*y*z + 2*x-1*y2*z + x + y + x*y-1*z + 3*z + 3*x-1*y*z + x-2*y2*z + 4*x*y-1 + 4*x-1*y + 3*x*y-1*z-1 + 3*z-1 + 2*x*y-2*z-1 + 4*y-1*z-1 + 2*x-1*z-1 + 3*x*y-2*z-2 + 3*y-1*z-2 + x*y-3*z-3 + y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 35 4 Lattice Minkowski decompositions of facet 35
Image of facet 60 2 Lattice Minkowski decompositions of facet 60
Polytope 4167
Image of polytope 4167 PALP id: 4167
grdb id: 264850
Integer points: [ 1 0 0 -3 3 2 0 -4 -3 -2 -1 -2 -1 0 1 0 1 2 -2 -1 -1 0 1 1 2]
[ 0 1 0 3 -4 -3 -1 3 2 1 0 1 0 -1 -2 -1 -2 -3 2 1 1 0 -1 -1 -2]
[ 0 0 1 1 -2 -2 1 1 1 1 1 0 0 0 0 -1 -1 -1 1 1 0 0 0 -1 -1]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x + y + z + 3*x-1*y*z + 3*x-2*y2*z + x-3*y3*z + 3*x*y-1 + 3*x-1*y + y-1*z + 4*x-1*z + 6*x-2*y*z + 4*x-3*y2*z + x-4*y3*z + 2*x2*y-2*z-1 + 2*x*y-1*z-1 + 3*x*y-2 + 9*y-1 + 9*x-1 + 3*x-2*y + 3*x2*y-3*z-1 + 6*x*y-2*z-1 + 3*y-1*z-1 + x3*y-4*z-2 + x2*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 4168
Image of polytope 4168 PALP id: 4168
grdb id: 264855
Integer points: [ 1 0 0 -2 -2 2 -4 2 -3 -2 -1 0 1 -3 -2 -1 0 1 -1 -1 0 1 -1 0 1]
[ 0 1 0 2 1 -3 2 -4 1 0 -1 -2 -3 2 1 0 -1 -2 1 0 -1 -2 1 0 -1]
[ 0 0 1 -1 -2 2 -3 3 -2 -1 0 1 2 -2 -1 0 1 2 0 -1 0 1 -1 0 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
11 rank 2, number 6 x + y + 2*x*y-1*z + z + x2*y-3*z2 + 2*x*y-2*z2 + x2*y-4*z3 + 2*x-1*y + 4*x*y-2*z + 8*y-1*z + 6*x*y-3*z2 + 2*x-1*y*z-1 + x-2*y2*z-1 + 6*y-1 + 12*x-1 + 15*y-2*z + 4*x-1*z-1 + 8*x-2*y*z-1 + 20*x-1*y-1 + x-2*y*z-2 + 2*x-3*y2*z-2 + 15*x-2*z-1 + 6*x-3*y*z-2 + x-4*y2*z-3
22 ? x + y + 3*x*y-1*z + z + x2*y-3*z2 + 2*x*y-2*z2 + x2*y-4*z3 + 2*x-1*y + 4*x*y-2*z + 8*y-1*z + 6*x*y-3*z2 + 3*x-1*y*z-1 + x-2*y2*z-1 + 6*y-1 + 12*x-1 + 15*y-2*z + 4*x-1*z-1 + 8*x-2*y*z-1 + 20*x-1*y-1 + x-2*y*z-2 + 2*x-3*y2*z-2 + 15*x-2*z-1 + 6*x-3*y*z-2 + x-4*y2*z-3
7 rank 1, V12 x + y + 2*x*y-1*z + z + x2*y-3*z2 + 2*x*y-2*z2 + x2*y-4*z3 + 2*x-1*y + 4*x*y-2*z + 8*y-1*z + 6*x*y-3*z2 + 3*x-1*y*z-1 + x-2*y2*z-1 + 6*y-1 + 12*x-1 + 15*y-2*z + 4*x-1*z-1 + 8*x-2*y*z-1 + 20*x-1*y-1 + x-2*y*z-2 + 2*x-3*y2*z-2 + 15*x-2*z-1 + 6*x-3*y*z-2 + x-4*y2*z-3
7 rank 1, V12 x + y + 3*x*y-1*z + z + x2*y-3*z2 + 2*x*y-2*z2 + x2*y-4*z3 + 2*x-1*y + 4*x*y-2*z + 8*y-1*z + 6*x*y-3*z2 + 2*x-1*y*z-1 + x-2*y2*z-1 + 6*y-1 + 12*x-1 + 15*y-2*z + 4*x-1*z-1 + 8*x-2*y*z-1 + 20*x-1*y-1 + x-2*y*z-2 + 2*x-3*y2*z-2 + 15*x-2*z-1 + 6*x-3*y*z-2 + x-4*y2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 23 2 Lattice Minkowski decompositions of facet 23
Image of facet 212 1 Lattice Minkowski decompositions of facet 212
Image of facet 13 1 irreducible and admissible
Image of facet 173 1 Lattice Minkowski decompositions of facet 173
Polytope 4169
Image of polytope 4169 PALP id: 4169
grdb id: 263867
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 -2 1 1 -3 1 1 1 1 0 0 0 0 -1 -1 -1 -2 -2 1 0 0 -1 -1]
[ 0 0 1 1 -2 1 1 -3 0 -1 -2 1 0 -1 -2 1 0 -1 1 0 -1 0 -1 1 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + x-1*y*z + 2*y*z-1 + 4*x-1*y + 2*y-1*z + 4*x-1*z + y*z-2 + 4*z-1 + 6*x-1*y*z-1 + 4*y-1 + 12*x-1 + y-2*z + 6*x-1*y-1*z + 4*x-1*y*z-2 + 12*x-1*z-1 + 12*x-1*y-1 + 4*x-1*y-2*z + x-1*y*z-3 + 4*x-1*z-2 + 6*x-1*y-1*z-1 + 4*x-1*y-2 + x-1*y-3*z
11 rank 2, number 6 x + y + z + x-1*y*z + 2*y*z-1 + 4*x-1*y + 2*y-1*z + 4*x-1*z + y*z-2 + 3*z-1 + 6*x-1*y*z-1 + 3*y-1 + 12*x-1 + y-2*z + 6*x-1*y-1*z + 4*x-1*y*z-2 + 12*x-1*z-1 + 12*x-1*y-1 + 4*x-1*y-2*z + x-1*y*z-3 + 4*x-1*z-2 + 6*x-1*y-1*z-1 + 4*x-1*y-2 + x-1*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 93 1 Lattice Minkowski decompositions of facet 93
Image of facet 206 1 Lattice Minkowski decompositions of facet 206
Image of facet 59 2 Lattice Minkowski decompositions of facet 59
Polytope 4170
Image of polytope 4170 PALP id: 4170
grdb id: 264166
Integer points: [ 1 0 0 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 1 0 0 1 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0]
[ 0 0 1 -1 0 2 2 -3 1 0 -1 -2 1 0 -1 -2 1 0 -1 1 0 -1 -2 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x*z-1 + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + 3*z-1 + 6*y-1 + 5*x-1 + 6*x-1*y-1*z + x-1*y-2*z2 + 6*y-1*z-1 + 3*x-1*z-1 + 12*x-1*y-1 + 5*x-1*y-2*z + 2*y-1*z-2 + 10*x-1*y-1*z-1 + 10*x-1*y-2 + 3*x-1*y-1*z-2 + 10*x-1*y-2*z-1 + 5*x-1*y-2*z-2 + x-1*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Image of facet 227 1 Lattice Minkowski decompositions of facet 227
Polytope 4171
Image of polytope 4171 PALP id: 4171
grdb id: 264649
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 1 1 -1 0 -4 0 -2 -1 0 1 -3 -2 -1 0 -3 -2 -1 -1 0 -2 -1 0]
[ 0 0 1 1 -1 1 -2 -2 1 0 0 0 0 -1 -1 -1 -1 -2 -2 -2 0 0 -1 -1 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y*z + 2*x-1*y + 2*x-1*z + 2*z-1 + x-1*y*z-1 + 3*y-1 + 7*x-1 + x-1*y-1*z + 4*y-1*z-1 + 6*x-1*z-1 + 8*x-1*y-1 + x-1*z-2 + 2*y-2*z-1 + 12*x-1*y-1*z-1 + 3*x-1*y-2 + 4*x-1*y-1*z-2 + 10*x-1*y-2*z-1 + 6*x-1*y-2*z-2 + 3*x-1*y-3*z-1 + 4*x-1*y-3*z-2 + x-1*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 2 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 273 1 Lattice Minkowski decompositions of facet 273
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 4172
Image of polytope 4172 PALP id: 4172
grdb id: 264772
Integer points: [ 1 0 0 1 1 -2 1 -4 -3 -2 -1 0 -2 -1 0 -3 -2 -1 0 1 -1 0 1 -1 0]
[ 0 1 0 -1 -2 2 -3 2 1 0 -1 -2 1 0 -1 2 1 0 -1 -2 1 0 -1 1 0]
[ 0 0 1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 -1 0 0 0 -1 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*x*y-1 + 2*x-1*y + x*y-1*z-1 + 3*z-1 + 3*x-1*y*z-1 + x-2*y2*z-1 + x*y-2 + 4*y-1 + 5*x-1 + 2*x-2*y + 2*x*y-2*z-1 + 8*y-1*z-1 + 12*x-1*z-1 + 8*x-2*y*z-1 + 2*x-3*y2*z-1 + x*y-3*z-1 + 5*y-2*z-1 + 10*x-1*y-1*z-1 + 10*x-2*z-1 + 5*x-3*y*z-1 + x-4*y2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 216 1 Lattice Minkowski decompositions of facet 216
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 4173
Image of polytope 4173 PALP id: 4173
grdb id: 264169
Integer points: [ 1 0 1 0 -1 1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 1 -1 0 1 -2 0 -5 -1 -2 -3 -4 0 -1 -2 -3 -4 -1 -2 -3 0 -1 -2 0 -1]
[ 0 0 0 1 1 -1 1 -4 0 -1 -2 -3 1 0 -1 -2 -3 0 -1 -2 0 -1 -2 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y*z + x*y-1 + 2*x-1*z + 5*y-1 + 4*x-1 + x-2*z + x*y-2*z-1 + 3*y-1*z-1 + 9*x-1*y-1 + 7*y-2*z-1 + 5*x-1*y-1*z-1 + 5*x-2*y-1 + 15*x-1*y-2*z-1 + 3*y-3*z-2 + 2*x-1*y-2*z-2 + 10*x-2*y-2*z-1 + 11*x-1*y-3*z-2 + 10*x-2*y-3*z-2 + 3*x-1*y-4*z-3 + 5*x-2*y-4*z-3 + x-2*y-5*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 271 1 Lattice Minkowski decompositions of facet 271
Polytope 4174
Image of polytope 4174 PALP id: 4174
grdb id: 264553
Integer points: [ 1 0 0 0 -1 -1 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 -1 -1 -1 0 0 0]
[ 0 1 0 -2 2 -2 -4 2 1 0 -1 -2 -3 1 0 -1 -2 -3 -1 1 0 -1 1 0 -1]
[ 0 0 1 -1 2 -2 -3 3 2 1 0 -1 -2 2 1 0 -1 -2 0 1 0 -1 1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 x-1*y2*z2 + x-2*y2*z3 + 2*y*z + 2*x-1*y*z2 + x + y + z + 5*x-1*y*z + 6*x-2*y*z2 + 8*x-1*z + 2*y-1 + 8*x-1 + 15*x-2*z + 2*y-1*z-1 + 12*x-1*y-1 + y-2*z-1 + 5*x-1*y-1*z-1 + 20*x-2*y-1 + 8*x-1*y-2*z-1 + x-1*y-2*z-2 + 15*x-2*y-2*z-1 + 2*x-1*y-3*z-2 + 6*x-2*y-3*z-2 + x-2*y-4*z-3
20 rank 1, V16 x-1*y2*z2 + x-2*y2*z3 + 2*y*z + 2*x-1*y*z2 + x + y + z + 4*x-1*y*z + 6*x-2*y*z2 + 8*x-1*z + 2*y-1 + 6*x-1 + 15*x-2*z + 2*y-1*z-1 + 12*x-1*y-1 + y-2*z-1 + 4*x-1*y-1*z-1 + 20*x-2*y-1 + 8*x-1*y-2*z-1 + x-1*y-2*z-2 + 15*x-2*y-2*z-1 + 2*x-1*y-3*z-2 + 6*x-2*y-3*z-2 + x-2*y-4*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 3 irreducible and admissible
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Image of facet 212 1 Lattice Minkowski decompositions of facet 212
Image of facet 183 1 Lattice Minkowski decompositions of facet 183
Polytope 4175
Image of polytope 4175 PALP id: 4175
grdb id: 262796
Integer points: [ 1 0 0 -1 0 -1 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -1 1 1 -4 -3 -2 -1 0 -3 -2 -1 0 1 -2 -1 0 -2 -1 0 -1 0]
[ 0 0 1 0 1 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Image of facet 271 1 Lattice Minkowski decompositions of facet 271
Polytope 4176
Image of polytope 4176 PALP id: 4176
grdb id: 262193
Integer points: [ 1 0 0 0 -1 -1 -3 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0]
[ 0 1 -1 0 -2 2 3 -3 -2 -1 0 1 2 -2 -1 0 1 2 -1 0 1 -1 0 1 0]
[ 0 0 0 1 -1 -1 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
13 rank 2, number 12 x + y + z + x-1*y2*z-1 + 3*x-1*y + 4*x-1*y*z-1 + 3*x-2*y2*z-1 + y-1 + 6*x-1 + x-3*y3*z-2 + 6*x-1*z-1 + 12*x-2*y*z-1 + 3*x-1*y-1 + 6*x-3*y2*z-2 + 4*x-1*y-1*z-1 + 18*x-2*z-1 + 15*x-3*y*z-2 + x-1*y-2*z-1 + 12*x-2*y-1*z-1 + 20*x-3*z-2 + 3*x-2*y-2*z-1 + 15*x-3*y-1*z-2 + 6*x-3*y-2*z-2 + x-3*y-3*z-2
52 rank 2, number 52 x + y + z + x-1*y2*z-1 + 3*x-1*y + 5*x-1*y*z-1 + 3*x-2*y2*z-1 + y-1 + 6*x-1 + x-3*y3*z-2 + 8*x-1*z-1 + 12*x-2*y*z-1 + 3*x-1*y-1 + 6*x-3*y2*z-2 + 5*x-1*y-1*z-1 + 18*x-2*z-1 + 15*x-3*y*z-2 + x-1*y-2*z-1 + 12*x-2*y-1*z-1 + 20*x-3*z-2 + 3*x-2*y-2*z-1 + 15*x-3*y-1*z-2 + 6*x-3*y-2*z-2 + x-3*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 4 irreducible and admissible
Image of facet 241 1 Lattice Minkowski decompositions of facet 241
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 183 1 Lattice Minkowski decompositions of facet 183
Polytope 4177
Image of polytope 4177 PALP id: 4177
grdb id: 262832
Integer points: [ 1 0 0 0 -1 -1 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 2 -2 3 -2 2 1 0 -1 2 1 0 -1 -2 1 0 -1 1 0 -1 0 -1]
[ 0 0 1 1 -1 0 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y2*z-1 + 3*x-1*y + y-1*z + 4*x-1*y*z-1 + 3*x-2*y2*z-1 + 2*y-1 + 7*x-1 + x-3*y3*z-2 + 5*x-1*z-1 + 11*x-2*y*z-1 + 5*x-1*y-1 + 5*x-3*y2*z-2 + 2*x-1*y-1*z-1 + 15*x-2*z-1 + x-1*y-2 + 10*x-3*y*z-2 + 9*x-2*y-1*z-1 + 10*x-3*z-2 + 2*x-2*y-2*z-1 + 5*x-3*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 271 1 Lattice Minkowski decompositions of facet 271
Polytope 4178
Image of polytope 4178 PALP id: 4178
grdb id: 72123
Integer points: [ 1 0 0 -1 0 1 -2 1 -2 -1 -2 -1 0 -2 -1 0 1 -1 0 -1 0 1 -1 0 1]
[ 0 1 0 1 -1 -2 1 -2 1 0 1 0 -1 1 0 -1 -2 0 -1 1 0 -1 1 0 -1]
[ 0 0 1 1 1 0 1 -2 -2 1 0 0 0 -1 -1 -1 -1 -2 -2 0 0 0 -1 -1 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + x-1*y*z + 2*x*y-1 + 3*x-1*y + y-1*z + 2*x-1*z + x-2*y*z + 2*x*y-1*z-1 + 4*z-1 + 2*x-1*y*z-1 + x*y-2 + 5*y-1 + 7*x-1 + 3*x-2*y + 2*x*y-2*z-1 + 7*y-1*z-1 + 8*x-1*z-1 + 3*x-2*y*z-1 + x*y-2*z-2 + 3*y-1*z-2 + 3*x-1*z-2 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 231 1 Lattice Minkowski decompositions of facet 231
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Polytope 4179
Image of polytope 4179 PALP id: 4179
grdb id: 72493
Integer points: [ 1 0 0 -1 1 0 1 1 -3 -2 -1 0 -2 -1 0 1 -1 0 1 -2 -1 0 -1 0 1]
[ 0 1 0 1 0 1 -2 -3 1 0 -1 -2 1 0 -1 -2 1 0 -1 1 0 -1 1 0 -1]
[ 0 0 1 1 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + x-1*y*z + x*z-1 + y*z-1 + 2*x*y-1 + 3*x-1*y + 3*x*y-1*z-1 + 6*z-1 + 3*x-1*y*z-1 + x*y-2 + 4*y-1 + 5*x-1 + 2*x-2*y + 3*x*y-2*z-1 + 9*y-1*z-1 + 9*x-1*z-1 + 3*x-2*y*z-1 + x*y-3*z-1 + 4*y-2*z-1 + 6*x-1*y-1*z-1 + 4*x-2*z-1 + x-3*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Image of facet 1 1 irreducible and admissible
Image of facet 3 2 Lattice Minkowski decompositions of facet 3
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 4180
Image of polytope 4180 PALP id: 4180
grdb id: 72114
Integer points: [ 1 0 0 -1 1 1 0 0 -3 -2 -1 0 -1 0 1 0 1 -2 -1 -2 -1 0 -1 0 1]
[ 0 1 0 1 0 -2 -2 1 1 1 1 1 0 0 0 -1 -1 1 1 0 0 0 -1 -1 -1]
[ 0 0 1 1 -2 0 1 -2 1 1 0 -1 1 0 -1 1 0 0 -1 1 0 -1 1 0 -1]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x + y + z + x-1*y*z + 2*x*z-1 + 2*y*z-1 + 2*x*y-1 + 4*x-1*y + 2*y-1*z + 4*x-1*z + 2*x-2*y*z + x*z-2 + y*z-2 + 2*x*y-1*z-1 + 5*z-1 + 3*x-1*y*z-1 + x*y-2 + 5*y-1 + 7*x-1 + 3*x-2*y + y-2*z + 3*x-1*y-1*z + 3*x-2*z + x-3*y*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Image of facet 174 1 Lattice Minkowski decompositions of facet 174
Image of facet 15 2 Lattice Minkowski decompositions of facet 15
Polytope 4181
Image of polytope 4181 PALP id: 4181
grdb id: 72684
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 1 -2 -1 2 2 -3 0 1 -2 -1 0 1 2 -2 -1 0 1 -1 0 1 -1 0]
[ 0 0 1 -2 1 2 -1 -3 2 1 0 2 1 0 -1 -2 1 0 -1 -2 1 0 -1 0 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + 3*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + y*z-2 + 2*x-1*y2*z-2 + 3*z-1 + 8*x-1*y*z-1 + 3*y-1 + 12*x-1 + y-2*z + 8*x-1*y-1*z + 2*x-1*y-2*z2 + x-1*y2*z-3 + 5*x-1*y*z-2 + 10*x-1*z-1 + 10*x-1*y-1 + 5*x-1*y-2*z + x-1*y-3*z2
7 rank 1, V12 x + y + z + 2*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 3*y-1*z + 3*x-1*z + x-1*y-1*z2 + y*z-2 + 2*x-1*y2*z-2 + 3*z-1 + 8*x-1*y*z-1 + 3*y-1 + 12*x-1 + y-2*z + 8*x-1*y-1*z + 2*x-1*y-2*z2 + x-1*y2*z-3 + 5*x-1*y*z-2 + 10*x-1*z-1 + 10*x-1*y-1 + 5*x-1*y-2*z + x-1*y-3*z2
11 rank 2, number 6 x + y + z + 2*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + y*z-2 + 2*x-1*y2*z-2 + 3*z-1 + 8*x-1*y*z-1 + 3*y-1 + 12*x-1 + y-2*z + 8*x-1*y-1*z + 2*x-1*y-2*z2 + x-1*y2*z-3 + 5*x-1*y*z-2 + 10*x-1*z-1 + 10*x-1*y-1 + 5*x-1*y-2*z + x-1*y-3*z2
22 ? x + y + z + 3*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 3*y-1*z + 3*x-1*z + x-1*y-1*z2 + y*z-2 + 2*x-1*y2*z-2 + 3*z-1 + 8*x-1*y*z-1 + 3*y-1 + 12*x-1 + y-2*z + 8*x-1*y-1*z + 2*x-1*y-2*z2 + x-1*y2*z-3 + 5*x-1*y*z-2 + 10*x-1*z-1 + 10*x-1*y-1 + 5*x-1*y-2*z + x-1*y-3*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 146 1 Lattice Minkowski decompositions of facet 146
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 23 2 Lattice Minkowski decompositions of facet 23
Image of facet 216 1 Lattice Minkowski decompositions of facet 216
Image of facet 9 1 irreducible and admissible
Polytope 4182
Image of polytope 4182 PALP id: 4182
grdb id: 72202
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 1 -1 -1 2 -2 2 -2 -1 0 1 -2 -1 0 1 2 -1 0 1 0 -1 0 1 0]
[ 0 0 2 -2 0 3 -1 1 -3 -2 -1 0 -2 -1 0 1 2 0 1 2 -1 -1 0 1 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
22 ? x-1*y2*z3 + y*z2 + 2*x-1*y2*z2 + 3*y*z + x-1*y2*z + 4*x-1*y*z2 + x + y + 2*z + 8*x-1*y*z + 4*x-1*y + 6*x-1*z + 2*z-1 + y-1 + 12*x-1 + 3*y-1*z-1 + 6*x-1*z-1 + 4*x-1*y-1 + y-1*z-2 + 8*x-1*y-1*z-1 + 4*x-1*y-1*z-2 + x-1*y-2*z-1 + 2*x-1*y-2*z-2 + x-1*y-2*z-3
11 rank 2, number 6 x-1*y2*z3 + y*z2 + 2*x-1*y2*z2 + 2*y*z + x-1*y2*z + 4*x-1*y*z2 + x + y + 2*z + 8*x-1*y*z + 4*x-1*y + 6*x-1*z + 2*z-1 + y-1 + 12*x-1 + 2*y-1*z-1 + 6*x-1*z-1 + 4*x-1*y-1 + y-1*z-2 + 8*x-1*y-1*z-1 + 4*x-1*y-1*z-2 + x-1*y-2*z-1 + 2*x-1*y-2*z-2 + x-1*y-2*z-3
7 rank 1, V12 x-1*y2*z3 + y*z2 + 2*x-1*y2*z2 + 3*y*z + x-1*y2*z + 4*x-1*y*z2 + x + y + 2*z + 8*x-1*y*z + 4*x-1*y + 6*x-1*z + 2*z-1 + y-1 + 12*x-1 + 2*y-1*z-1 + 6*x-1*z-1 + 4*x-1*y-1 + y-1*z-2 + 8*x-1*y-1*z-1 + 4*x-1*y-1*z-2 + x-1*y-2*z-1 + 2*x-1*y-2*z-2 + x-1*y-2*z-3
7 rank 1, V12 x-1*y2*z3 + y*z2 + 2*x-1*y2*z2 + 2*y*z + x-1*y2*z + 4*x-1*y*z2 + x + y + 2*z + 8*x-1*y*z + 4*x-1*y + 6*x-1*z + 2*z-1 + y-1 + 12*x-1 + 3*y-1*z-1 + 6*x-1*z-1 + 4*x-1*y-1 + y-1*z-2 + 8*x-1*y-1*z-1 + 4*x-1*y-1*z-2 + x-1*y-2*z-1 + 2*x-1*y-2*z-2 + x-1*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 59 2 Lattice Minkowski decompositions of facet 59
Image of facet 214 1 Lattice Minkowski decompositions of facet 214
Image of facet 23 2 Lattice Minkowski decompositions of facet 23
Polytope 4183
Image of polytope 4183 PALP id: 4183
grdb id: 72680
Integer points: [ 1 0 1 0 0 -2 1 1 -4 0 -1 -2 -3 0 -1 -2 -3 -1 1 0 -1 -2 1 0 -1]
[ 0 1 -1 0 0 2 -2 -3 2 -2 -1 0 1 -1 0 1 2 1 -2 -1 0 1 -1 0 1]
[ 0 0 0 1 -1 1 -2 -2 3 -1 0 1 2 -1 0 1 2 0 -1 0 1 2 -1 0 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + 3*x-1*y*z + x-2*y2*z + 2*x-2*y*z2 + 2*x-3*y2*z2 + x-4*y2*z3 + x*y-1 + 2*x-1*y + 6*x-1*z + 7*x-2*y*z + 5*x-3*y*z2 + 2*x*y-1*z-1 + z-1 + 6*y-1 + 9*x-1 + 10*x-2*z + 2*x*y-2*z-1 + 5*y-1*z-1 + 10*x-1*y-1 + x*y-2*z-2 + 5*y-2*z-1 + x*y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Image of facet 201 1 Lattice Minkowski decompositions of facet 201
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 30 1 Lattice Minkowski decompositions of facet 30
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 4184
Image of polytope 4184 PALP id: 4184
grdb id: 69823
Integer points: [ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 0 1 -1 1 1 -2 -2 0 -1 1 0 -1 -2 1 0 -1 -2 0 -1 0 -1 0 -1]
[ 0 0 1 -1 1 1 -2 1 -2 1 1 0 0 0 0 -1 -1 -1 -1 -2 -2 0 0 -1 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x-1*y*z + y*z-1 + 3*x-1*y + y-1*z + 3*x-1*z + 3*z-1 + 3*x-1*y*z-1 + 3*y-1 + 9*x-1 + 3*x-1*y-1*z + x-1*y*z-2 + 2*y-1*z-1 + 9*x-1*z-1 + 9*x-1*y-1 + x-1*y-2*z + 3*x-1*z-2 + 9*x-1*y-1*z-1 + 3*x-1*y-2 + 3*x-1*y-1*z-2 + 3*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
Image of facet 243 1 Lattice Minkowski decompositions of facet 243
Polytope 4185
Image of polytope 4185 PALP id: 4185
grdb id: 555254
Integer points: [ 1 0 0 2 1 -2 -3 0 -1 2 -2 -1 -1 -2 -1 0 1 -1 0 1 0 1 0 1 2]
[ 0 1 0 -1 0 2 2 -1 0 -3 1 0 1 1 0 -1 -2 1 0 -1 -1 -2 0 -1 -2]
[ 0 0 1 -1 -1 1 1 1 -1 -1 1 1 1 0 0 0 0 0 0 0 -1 -1 -1 -1 -1]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x + y + z + 2*x-1*y*z + x-2*y2*z + x2*y-1*z-1 + x*z-1 + 3*x*y-1 + 3*x-1*y + y-1*z + 3*x-1*z + 3*x-2*y*z + x-3*y2*z + 2*x2*y-2*z-1 + 4*x*y-1*z-1 + 2*z-1 + 2*x*y-2 + 6*y-1 + 6*x-1 + 2*x-2*y + x2*y-3*z-1 + 3*x*y-2*z-1 + 3*y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Polytope 4186
Image of polytope 4186 PALP id: 4186
grdb id: 544573
Integer points: [ 1 0 1 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 0 0 1]
[ 0 1 0 1 -4 -3 -2 -1 0 -3 -2 -1 0 1 -2 -1 0 1 -1 0 -2 -1 0 -1 0 0]
[ 0 0 2 -3 2 1 0 -1 -2 2 1 0 -1 -2 2 1 0 -1 2 1 1 0 -1 1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 1 irreducible and admissible
Image of facet 298 1 Lattice Minkowski decompositions of facet 298
Image of facet 9 1 irreducible and admissible
Image of facet 73 1 none
Polytope 4187
Image of polytope 4187 PALP id: 4187
grdb id: 544564
Integer points: [ 1 0 1 -6 1 0 -1 -2 -3 -4 -5 1 0 -1 -2 -3 -4 0 -1 -2 1 0 -1 -2 1 0]
[ 0 1 0 -2 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0]
[ 0 0 2 -3 4 3 2 1 0 -1 -2 3 2 1 0 -1 -2 1 0 -1 2 1 0 -1 1 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 275 1 none
Image of facet 299 1 Lattice Minkowski decompositions of facet 299
Image of facet 9 1 irreducible and admissible
Polytope 4188
Image of polytope 4188 PALP id: 4188
grdb id: 544566
Integer points: [ 1 0 0 -2 -9 -8 -7 -6 -5 -4 -3 -6 -5 -4 -3 -2 -1 -3 -2 -1 -4 -3 -2 -1 -1 0]
[ 0 1 0 -2 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0]
[ 0 0 1 1 -6 -5 -4 -3 -2 -1 0 -4 -3 -2 -1 0 1 -2 -1 0 -3 -2 -1 0 -1 0]
Degree: 26
Hilbert function: 1 + 16 t + 70 t2 + 189 t3 + 399 t4 + 726 t5 + 1196 t6 + 1835 t7 + 2669 t8 + 3724 t9 + 5026 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 275 1 none
Image of facet 14 1 none
Image of facet 299 1 Lattice Minkowski decompositions of facet 299
Polytope 4189
Image of polytope 4189 PALP id: 4189
grdb id: 521210
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0]
[ 0 1 1 -2 1 1 1 1 1 1 1 0 0 0 0 0 -1 -1 -1 1 1 1 0 0 0 -1]
[ 0 0 4 -4 -1 5 4 3 2 1 0 2 1 0 -1 -2 -1 -2 -3 3 2 1 1 0 -1 -2]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 y*z4 + x-1*y*z5 + 4*y*z3 + 6*x-1*y*z4 + 6*y*z2 + 15*x-1*y*z3 + 4*y*z + 20*x-1*y*z2 + x + y + 3*z + 15*x-1*y*z + 3*x-1*z2 + 6*x-1*y + 12*x-1*z + 3*z-1 + x-1*y*z-1 + 18*x-1 + 12*x-1*z-1 + 2*y-1*z-2 + 3*x-1*z-2 + 3*x-1*y-1*z-1 + 6*x-1*y-1*z-2 + 3*x-1*y-1*z-3 + x-1*y-2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Image of facet 13 1 irreducible and admissible
Image of facet 173 1 Lattice Minkowski decompositions of facet 173
Image of facet 241 1 Lattice Minkowski decompositions of facet 241
Polytope 4190
Image of polytope 4190 PALP id: 4190
grdb id: 521212
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0]
[ 0 1 1 0 0 -4 -1 -2 -3 0 -1 -2 -3 0 -1 -2 0 -1 0 -1 -2 1 0 -1 1 0]
[ 0 0 3 -2 2 -6 0 -2 -4 1 -1 -3 -5 0 -2 -4 -1 -3 1 -1 -3 2 0 -2 1 -1]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 y*z3 + 3*y*z2 + 3*y*z + x + y + 3*z + x-1*z2 + 4*x-1*z + 3*z-1 + 6*x-1 + 4*y-1*z-1 + 4*x-1*z-1 + 4*x-1*y-1 + 4*y-1*z-2 + x-1*z-2 + 12*x-1*y-1*z-1 + 12*x-1*y-1*z-2 + 2*y-2*z-3 + 4*x-1*y-1*z-3 + 6*x-1*y-2*z-2 + 12*x-1*y-2*z-3 + 6*x-1*y-2*z-4 + 4*x-1*y-3*z-4 + 4*x-1*y-3*z-5 + x-1*y-4*z-6
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 9 1 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 76 2 Lattice Minkowski decompositions of facet 76
Image of facet 206 1 Lattice Minkowski decompositions of facet 206
Polytope 4191
Image of polytope 4191 PALP id: 4191
grdb id: 521209
Integer points: [ 1 0 0 1 0 -6 -1 -2 -3 -4 -5 0 -1 -2 -3 -4 0 -1 -2 0 -1 -2 -3 1 0 -1]
[ 0 1 0 -2 -3 3 -2 -1 0 1 2 -2 -1 0 1 2 -1 0 1 -1 0 1 2 -1 0 1]
[ 0 0 1 -2 -2 4 -1 0 1 2 3 -1 0 1 2 3 0 1 2 -1 0 1 2 -1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 3*x-1*y*z + 3*x-2*y*z2 + 2*x-3*y2*z2 + 3*x-4*y2*z3 + x-6*y3*z4 + 6*x-1*z + 6*x-2*y*z + 12*x-3*y*z2 + 6*x-5*y2*z3 + 2*x*y-1*z-1 + 3*y-1 + 7*x-1 + 18*x-2*z + 15*x-4*y*z2 + 4*y-1*z-1 + 12*x-1*y-1 + 20*x-3*z + x*y-2*z-2 + 3*y-2*z-1 + 15*x-2*y-1 + 6*x-1*y-2*z-1 + y-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 241 1 Lattice Minkowski decompositions of facet 241
Image of facet 171 1 Lattice Minkowski decompositions of facet 171
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 1 1 irreducible and admissible
Polytope 4192
Image of polytope 4192 PALP id: 4192
grdb id: 521213
Integer points: [ 1 0 2 -4 2 -6 1 0 -1 -2 -3 -4 -5 1 0 -1 -2 -3 1 0 -1 -2 -3 1 0 -1]
[ 0 1 2 -4 3 -5 2 1 0 -1 -2 -3 -4 1 0 -1 -2 -3 2 1 0 -1 -2 1 0 -1]
[ 0 0 3 -3 4 -4 3 2 1 0 -1 -2 -3 2 1 0 -1 -2 2 1 0 -1 -2 1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 8 2 none
Image of facet 208 1 Lattice Minkowski decompositions of facet 208
Image of facet 300 1 Lattice Minkowski decompositions of facet 300
Image of facet 53 1 irreducible and admissible
Polytope 4193
Image of polytope 4193 PALP id: 4193
grdb id: 521215
Integer points: [ 1 1 0 0 1 -3 -2 -1 0 -2 -1 0 1 -1 0 -2 -1 0 1 -1 0 1 0 -1 0 0]
[ 0 2 0 3 -2 -6 -5 -4 -3 -3 -2 -1 0 0 1 -4 -3 -2 -1 -1 0 1 2 -2 -1 1]
[ 0 0 1 1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 -1 -1 -1 -1 0 0 0 1 0 0 1]
Degree: 8
Hilbert function: 1 + 7 t + 25 t2 + 63 t3 + 129 t4 + 231 t5 + 377 t6 + 575 t7 + 833 t8 + 1159 t9 + 1561 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
5 rank 1, V8 y3*z + x*y2 + 3*y2*z + 2*x*y + 3*y*z + x + 4*y + z + 2*x*z-1 + 2*x*y-1*z-1 + 4*y-1 + 3*x-1 + 7*y-1*z-1 + 6*x-1*y-1 + x*y-2*z-2 + 7*y-2*z-1 + 3*x-1*y-2 + 8*x-1*y-2*z-1 + 4*y-3*z-2 + 8*x-1*y-3*z-1 + 3*x-2*y-3*z-1 + 6*x-1*y-4*z-2 + 3*x-2*y-4*z-1 + 4*x-2*y-5*z-2 + x-3*y-6*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 167 2 Lattice Minkowski decompositions of facet 167
Polytope 4194
Image of polytope 4194 PALP id: 4194
grdb id: 521204
Integer points: [ 1 0 0 1 -2 -7 -6 -5 -4 -3 -5 -4 -3 -2 -1 -3 -2 -1 -1 0 -3 -2 -1 -1 0 1]
[ 0 1 0 -2 2 2 2 2 2 2 1 1 1 1 1 0 0 0 -1 -1 1 1 1 0 0 -1]
[ 0 0 1 2 -1 -6 -5 -4 -3 -2 -4 -3 -2 -1 0 -2 -1 0 0 1 -3 -2 -1 -1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 1 irreducible and admissible
Image of facet 290 1 none
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Polytope 4195
Image of polytope 4195 PALP id: 4195
grdb id: 521182
Integer points: [ 1 0 1 -3 1 -3 -2 -1 0 -3 -2 -1 0 1 -3 -2 -1 0 -2 -1 -1 0 1 -1 0 1]
[ 0 1 0 1 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 0 1 1 -1 -1 -1 0 0 0]
[ 0 0 2 -3 4 0 1 2 3 -1 0 1 2 3 -2 -1 0 1 -2 -1 0 1 2 -1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 301 1 Lattice Minkowski decompositions of facet 301
Image of facet 14 1 none
Polytope 4196
Image of polytope 4196 PALP id: 4196
grdb id: 521121
Integer points: [ 1 0 0 -2 -3 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 0 -6 -1 -2 -3 -4 -5 0 -1 -2 -3 -4 1 0 -1 -2 0 -1 -2 -3 0 -1]
[ 0 0 1 -2 -2 4 -1 0 1 2 3 -1 0 1 2 3 -1 0 1 2 -1 0 1 2 0 1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 14 1 none
Image of facet 302 1 Lattice Minkowski decompositions of facet 302
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Polytope 4197
Image of polytope 4197 PALP id: 4197
grdb id: 521161
Integer points: [ 1 0 0 -1 -1 -5 -2 -1 0 -3 -2 -1 0 -4 -3 -2 -1 -4 -3 -2 0 -1 0 -2 -1 0]
[ 0 1 1 0 0 -4 -1 0 1 -2 -1 0 1 -3 -2 -1 0 -3 -2 -1 0 -1 0 -2 -1 0]
[ 0 0 3 -2 2 -6 0 1 2 -2 -1 0 1 -4 -3 -2 -1 -5 -4 -3 1 -1 0 -3 -2 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 y*z3 + 3*y*z2 + 3*y*z + x + y + 2*z + x-1*z2 + 7*x-1*z + 2*z-1 + 12*x-1 + 7*x-1*z-1 + x-1*z-2 + 4*x-1*y-1*z-1 + 4*x-2*y-1 + 4*x-1*y-1*z-2 + 15*x-2*y-1*z-1 + 15*x-2*y-1*z-2 + 4*x-2*y-1*z-3 + 2*x-2*y-2*z-3 + 6*x-3*y-2*z-2 + 13*x-3*y-2*z-3 + 6*x-3*y-2*z-4 + 4*x-4*y-3*z-4 + 4*x-4*y-3*z-5 + x-5*y-4*z-6
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 2 Lattice Minkowski decompositions of facet 32
Image of facet 1 2 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 303 1 Lattice Minkowski decompositions of facet 303
Polytope 4198
Image of polytope 4198 PALP id: 4198
grdb id: 521046
Integer points: [ 1 0 0 -1 -2 -9 -3 -4 -5 -6 -7 -8 -2 -3 -4 -5 -6 -1 -2 -3 -1 -2 -3 -4 0 -1]
[ 0 1 0 0 -1 -8 -2 -3 -4 -5 -6 -7 -1 -2 -3 -4 -5 0 -1 -2 -1 -2 -3 -4 0 -1]
[ 0 0 1 1 1 -6 0 -1 -2 -3 -4 -5 0 -1 -2 -3 -4 0 -1 -2 0 -1 -2 -3 0 -1]
Degree: 28
Hilbert function: 1 + 17 t + 75 t2 + 203 t3 + 429 t4 + 781 t5 + 1287 t6 + 1975 t7 + 2873 t8 + 4009 t9 + 5411 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 291 1 none
Image of facet 14 1 none
Image of facet 195 1 Lattice Minkowski decompositions of facet 195
Polytope 4199
Image of polytope 4199 PALP id: 4199
grdb id: 433689
Integer points: [ 1 0 0 1 -1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0 0 1]
[ 0 1 0 -2 2 3 -2 2 1 0 -1 1 0 -1 -2 0 -1 -2 2 1 0 -1 1 0 -1 -1]
[ 0 0 1 0 -2 -2 3 -1 0 1 2 -1 0 1 2 -1 0 1 -1 0 1 2 -1 0 1 0]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x + y + z + 2*y*z-1 + 2*x-1*y2*z-1 + 2*x*y-1 + 6*x-1*y + 4*y-1*z + 6*x-1*z + 2*x-1*y-1*z2 + x-1*y2*z-2 + x-2*y3*z-2 + 2*z-1 + 6*x-1*y*z-1 + 5*x-2*y2*z-1 + x*y-2 + 5*y-1 + 12*x-1 + 10*x-2*y + 3*y-2*z + 10*x-1*y-1*z + 10*x-2*z + 3*x-1*y-2*z2 + 5*x-2*y-1*z2 + x-2*y-2*z3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 227 1 Lattice Minkowski decompositions of facet 227
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 4200
Image of polytope 4200 PALP id: 4200
grdb id: 433641
Integer points: [ 1 0 0 -2 1 -3 -3 -2 -1 0 -3 -2 -1 0 -3 -2 -1 -3 -2 -1 -1 0 1 -1 0 -1]
[ 0 1 0 2 -2 2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 1 1 1 -1 -1 -1 0 0 1]
[ 0 0 1 -1 2 -2 -2 -1 0 1 -2 -1 0 1 -2 -1 0 -2 -1 0 -1 0 1 -1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*x-1*y + 4*y-1*z + 2*x-1*y*z-1 + x-2*y2*z-1 + 4*y-1 + 8*x-1 + 4*y-2*z + 4*x-1*z-1 + 6*x-2*y*z-1 + 12*x-1*y-1 + x-3*y2*z-2 + 2*x-1*y-1*z-1 + 13*x-2*z-1 + 6*x-1*y-2 + 4*x-3*y*z-2 + 12*x-2*y-1*z-1 + 6*x-3*z-2 + 4*x-2*y-2*z-1 + 4*x-3*y-1*z-2 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 2 Lattice Minkowski decompositions of facet 32
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 292 1 Lattice Minkowski decompositions of facet 292
Polytope 4201
Image of polytope 4201 PALP id: 4201
grdb id: 433642
Integer points: [ 1 0 0 2 -2 2 -2 -1 0 1 -2 -1 0 1 -2 -1 0 -2 -1 1 -1 0 1 -1 0 -1]
[ 0 1 0 -1 2 -2 -2 1 0 -1 1 0 -1 -2 0 -1 -2 -1 -2 0 1 0 -1 0 -1 -1]
[ 0 0 1 -2 1 -3 1 0 -1 -2 1 0 -1 -2 1 0 -1 1 0 -1 1 0 -1 1 0 1]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x + y + z + 2*x-1*y*z + x-2*y2*z + 2*x*z-1 + 4*x-1*y + 4*x-1*z + 4*x-2*y*z + x2*y-1*z-2 + 4*x*y-1*z-1 + 6*z-1 + 5*y-1 + 12*x-1 + 2*x-1*y-1*z + 6*x-2*z + 4*x*y-1*z-2 + 12*y-1*z-1 + 12*x-1*y-1 + 4*x-2*y-1*z + x2*y-2*z-3 + 4*x*y-2*z-2 + 6*y-2*z-1 + 4*x-1*y-2 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 206 1 Lattice Minkowski decompositions of facet 206
Polytope 4202
Image of polytope 4202 PALP id: 4202
grdb id: 433519
Integer points: [ 1 1 1 0 0 -2 -2 0 -1 0 -1 -2 -1 -2 1 0 -1 1 0 -1 0 -1 -1 1 0 0]
[ 0 2 0 2 -1 -3 0 -1 -2 0 -1 -2 0 -1 0 -1 -2 1 0 -1 1 0 1 1 0 1]
[ 0 0 2 -1 -1 -1 -1 1 0 1 0 -1 0 -1 1 0 -1 1 0 -1 0 -1 -1 0 -1 -1]
Degree: 8
Hilbert function: 1 + 7 t + 25 t2 + 63 t3 + 129 t4 + 231 t5 + 377 t6 + 575 t7 + 833 t8 + 1159 t9 + 1561 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
5 rank 1, V8 x*y2 + 2*x*y*z + x*z2 + 2*x*y + 2*x*z + y2*z-1 + x + 4*y + 3*z + 3*y*z-1 + 3*y-1*z + 3*z-1 + 2*x-1*y*z-1 + 4*y-1 + 3*x-1 + y-1*z-1 + 6*x-1*z-1 + 6*x-1*y-1 + 6*x-1*y-1*z-1 + x-2*z-1 + 3*x-1*y-2 + 2*x-1*y-2*z-1 + 3*x-2*y-1*z-1 + 3*x-2*y-2*z-1 + x-2*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Polytope 4203
Image of polytope 4203 PALP id: 4203
grdb id: 433681
Integer points: [ 1 0 0 -1 1 1 -4 -3 -2 -1 0 -3 -2 -1 0 1 -2 -1 0 -2 -1 0 1 -1 0 1]
[ 0 1 0 1 -2 -4 1 0 -1 -2 -3 1 0 -1 -2 -3 1 0 -1 1 0 -1 -2 1 0 -1]
[ 0 0 1 1 0 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Image of facet 14 1 none
Image of facet 271 1 Lattice Minkowski decompositions of facet 271
Polytope 4204
Image of polytope 4204 PALP id: 4204
grdb id: 433517
Integer points: [ 1 0 1 1 0 0 -3 -1 -2 0 -1 -2 1 0 -1 0 -1 -2 1 0 -1 1 0 0 -1 0]
[ 0 1 0 -2 -2 1 1 -1 0 -1 0 1 -1 0 1 -1 0 1 -1 0 1 0 1 0 1 1]
[ 0 0 2 -2 -3 3 0 -2 -1 -1 0 1 0 1 2 -2 -1 0 -1 0 1 1 2 -1 0 1]
Degree: 8
Hilbert function: 1 + 7 t + 25 t2 + 63 t3 + 129 t4 + 231 t5 + 377 t6 + 575 t7 + 833 t8 + 1159 t9 + 1561 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
5 rank 1, V8 y*z3 + x*z2 + 3*y*z2 + 2*x*z + 3*y*z + 3*x-1*y*z2 + x + y + 5*z + 6*x-1*y*z + 2*x*y-1 + 3*x-1*y + 3*x-2*y*z + 2*x*y-1*z-1 + 3*z-1 + 7*x-1 + 3*x-2*y + 5*y-1*z-1 + 6*x-1*z-1 + x-3*y + x*y-2*z-2 + 3*y-1*z-2 + 3*x-2*z-1 + 3*x-1*y-1*z-2 + y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 52 2 Lattice Minkowski decompositions of facet 52
Image of facet 174 1 Lattice Minkowski decompositions of facet 174
Polytope 4205
Image of polytope 4205 PALP id: 4205
grdb id: 433633
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0]
[ 0 1 1 -2 1 1 -3 -2 -1 0 -2 -1 0 1 -1 0 1 0 1 -1 0 -1 0 1 0 1]
[ 0 0 3 -3 0 4 -4 -2 0 2 -3 -1 1 3 -2 0 2 -1 1 -1 1 -2 0 2 -1 1]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 y*z3 + x-1*y*z4 + 3*y*z2 + 4*x-1*y*z3 + 3*y*z + 6*x-1*y*z2 + x + y + 3*z + 4*x-1*y*z + 4*x-1*z2 + x-1*y + 12*x-1*z + 3*z-1 + 12*x-1 + 3*y-1*z-1 + 4*x-1*z-1 + 6*x-1*y-1 + 3*y-1*z-2 + 12*x-1*y-1*z-1 + 6*x-1*y-1*z-2 + y-2*z-3 + 4*x-1*y-2*z-2 + 4*x-1*y-2*z-3 + x-1*y-3*z-4
49 rank 2, number 4 y*z3 + x-1*y*z4 + 3*y*z2 + 4*x-1*y*z3 + 3*y*z + 6*x-1*y*z2 + x + y + 4*z + 4*x-1*y*z + 4*x-1*z2 + x-1*y + 12*x-1*z + 3*z-1 + 12*x-1 + 4*y-1*z-1 + 4*x-1*z-1 + 6*x-1*y-1 + 3*y-1*z-2 + 12*x-1*y-1*z-1 + 6*x-1*y-1*z-2 + y-2*z-3 + 4*x-1*y-2*z-2 + 4*x-1*y-2*z-3 + x-1*y-3*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 9 2 irreducible and admissible
Image of facet 90 2 Lattice Minkowski decompositions of facet 90
Image of facet 93 1 Lattice Minkowski decompositions of facet 93
Image of facet 206 1 Lattice Minkowski decompositions of facet 206
Polytope 4206
Image of polytope 4206 PALP id: 4206
grdb id: 433730
Integer points: [ 1 0 0 1 -2 -1 -5 -2 -3 -4 0 -1 -2 -3 -4 0 -1 -2 -3 -1 0 -1 -2 1 0 -1]
[ 0 1 0 -2 2 -2 2 -1 0 1 -2 -1 0 1 2 -1 0 1 2 1 -1 0 1 -1 0 1]
[ 0 0 1 2 -1 0 -4 -1 -2 -3 1 0 -1 -2 -3 1 0 -1 -2 0 0 -1 -2 1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*x-1*y + 4*y-1*z + 3*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 8*x-1 + 2*y-2*z + 4*x-1*z-1 + 8*x-2*y*z-1 + 8*x-1*y-1 + 2*x-2*y*z-2 + 3*x-3*y2*z-2 + 13*x-2*z-1 + x-1*y-2 + 10*x-3*y*z-2 + 4*x-2*y-1*z-1 + 3*x-4*y2*z-3 + 6*x-3*z-2 + 4*x-4*y*z-3 + x-5*y2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 1 irreducible and admissible
Image of facet 293 1 Lattice Minkowski decompositions of facet 293
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 4207
Image of polytope 4207 PALP id: 4207
grdb id: 433599
Integer points: [ 1 0 1 0 1 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 -2 1 -5 -4 -3 -2 -1 0 -4 -3 -2 -1 0 -3 -2 -1 -2 -1 0 1 -1 0]
[ 0 0 0 1 -1 2 -4 -3 -2 -1 0 1 -3 -2 -1 0 1 -2 -1 0 -2 -1 0 1 -1 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Image of facet 295 1 none
Polytope 4208
Image of polytope 4208 PALP id: 4208
grdb id: 433608
Integer points: [ 1 0 1 1 -3 -5 1 0 -1 -2 -3 -4 1 0 -1 -2 -3 1 0 -1 0 -1 -2 1 0 -1]
[ 0 1 -1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 0 0 2 -2 -3 3 2 1 0 -1 -2 2 1 0 -1 -2 1 0 -1 1 0 -1 1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x*z2 + x*y-1*z3 + 2*x*z + 3*x*y-1*z2 + x + y + 3*x*y-1*z + 4*z + 6*y-1*z2 + x*y-1 + 12*y-1*z + 6*y-1 + 6*x-1 + 15*x-1*y-1*z + 2*x-1*z-1 + 18*x-1*y-1 + 3*x-1*y-1*z-1 + 4*x-2*z-1 + 20*x-2*y-1 + 12*x-2*y-1*z-1 + x-3*z-2 + 15*x-3*y-1*z-1 + 3*x-3*y-1*z-2 + 6*x-4*y-1*z-2 + x-5*y-1*z-3
51 rank 2, number 7 x*z2 + x*y-1*z3 + 2*x*z + 3*x*y-1*z2 + x + y + 3*x*y-1*z + 5*z + 6*y-1*z2 + x*y-1 + 12*y-1*z + 6*y-1 + 8*x-1 + 15*x-1*y-1*z + 2*x-1*z-1 + 18*x-1*y-1 + 3*x-1*y-1*z-1 + 5*x-2*z-1 + 20*x-2*y-1 + 12*x-2*y-1*z-1 + x-3*z-2 + 15*x-3*y-1*z-1 + 3*x-3*y-1*z-2 + 6*x-4*y-1*z-2 + x-5*y-1*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 183 1 Lattice Minkowski decompositions of facet 183
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 241 1 Lattice Minkowski decompositions of facet 241
Polytope 4209
Image of polytope 4209 PALP id: 4209
grdb id: 433360
Integer points: [ 1 0 0 -1 0 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 -1 -1 -1 0 0]
[ 0 1 0 2 -2 3 -2 2 1 0 -1 2 1 0 -1 -2 1 0 -1 -2 -1 1 0 -1 0 -1]
[ 0 0 1 -1 1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 0 1 -1 -1 -1 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 277 1 Lattice Minkowski decompositions of facet 277
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 14 1 none
Polytope 4210
Image of polytope 4210 PALP id: 4210
grdb id: 433119
Integer points: [ 1 0 1 0 -1 -3 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 -1 0 2 3 -3 -2 -1 0 1 2 -2 -1 0 1 2 -1 0 1 -2 -1 0 1 -1 0]
[ 0 0 0 1 -1 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 200 1 Lattice Minkowski decompositions of facet 200
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 14 1 none
Image of facet 241 1 Lattice Minkowski decompositions of facet 241
Polytope 4211
Image of polytope 4211 PALP id: 4211
grdb id: 433064
Integer points: [ 1 0 0 -1 -2 -3 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -2 2 2 -4 -3 -2 -1 0 1 -3 -2 -1 0 1 -1 0 1 -2 -1 0 1 -1 0]
[ 0 0 1 0 -1 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
39 ? x + y + z + 2*x-1*y + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 6*x-1 + 6*x-1*z-1 + 7*x-2*y*z-1 + 5*x-1*y-1 + x-3*y2*z-2 + 6*x-1*y-1*z-1 + 17*x-2*z-1 + x-1*y-2 + 6*x-3*y*z-2 + 2*x-1*y-2*z-1 + 19*x-2*y-1*z-1 + 15*x-3*z-2 + 10*x-2*y-2*z-1 + 20*x-3*y-1*z-2 + 2*x-2*y-3*z-1 + 15*x-3*y-2*z-2 + 6*x-3*y-3*z-2 + x-3*y-4*z-2
52 rank 2, number 52 x + y + z + 2*x-1*y + 2*x-1*y*z-1 + x-2*y2*z-1 + 2*y-1 + 5*x-1 + 6*x-1*z-1 + 6*x-2*y*z-1 + 4*x-1*y-1 + x-3*y2*z-2 + 6*x-1*y-1*z-1 + 14*x-2*z-1 + x-1*y-2 + 6*x-3*y*z-2 + 2*x-1*y-2*z-1 + 16*x-2*y-1*z-1 + 15*x-3*z-2 + 9*x-2*y-2*z-1 + 20*x-3*y-1*z-2 + 2*x-2*y-3*z-1 + 15*x-3*y-2*z-2 + 6*x-3*y-3*z-2 + x-3*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 294 1 Lattice Minkowski decompositions of facet 294
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Polytope 4212
Image of polytope 4212 PALP id: 4212
grdb id: 433118
Integer points: [ 1 0 -1 0 -2 -3 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 1 0 1 0 -6 -5 -4 -3 -2 -1 -4 -3 -2 -1 0 -2 -1 0 -3 -2 -1 0 -1 0]
[ 0 0 0 1 -1 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 296 1 Lattice Minkowski decompositions of facet 296
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 14 1 none
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Polytope 4213
Image of polytope 4213 PALP id: 4213
grdb id: 261697
Integer points: [ 1 0 0 -2 2 1 2 -2 -1 0 1 -1 0 1 2 0 1 2 -2 -1 0 1 -1 0 1 -1]
[ 0 1 0 2 -1 0 -4 0 -1 -2 -3 0 -1 -2 -3 0 -1 -2 1 0 -1 -2 1 0 -1 1]
[ 0 0 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 1]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x + y + z + 2*x-1*y*z + x-2*y2*z + x2*y-1*z-1 + x*z-1 + 3*x*y-1 + 3*x-1*y + 3*x2*y-2*z-1 + 6*x*y-1*z-1 + 3*z-1 + 2*x*y-2 + 6*y-1 + 6*x-1 + 2*x-2*y + 3*x2*y-3*z-1 + 9*x*y-2*z-1 + 9*y-1*z-1 + 3*x-1*z-1 + x2*y-4*z-1 + 4*x*y-3*z-1 + 6*y-2*z-1 + 4*x-1*y-1*z-1 + x-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 4214
Image of polytope 4214 PALP id: 4214
grdb id: 261714
Integer points: [ 1 0 0 -1 -1 2 2 -3 -2 -1 0 1 -2 -1 0 1 -2 -1 0 1 2 -1 0 1 0 1]
[ 0 1 0 1 1 -2 -4 1 0 -1 -2 -3 1 0 -1 -2 1 0 -1 -2 -3 1 0 -1 0 -1]
[ 0 0 1 1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 -1 -1 -1 -1 -1 0 0 0 -1 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
11 rank 2, number 6 x + y + z + x-1*y*z + 2*x*y-1 + 2*x-1*y + x2*y-2*z-1 + 3*x*y-1*z-1 + 3*z-1 + x-1*y*z-1 + 2*x*y-2 + 6*y-1 + 6*x-1 + 2*x-2*y + 2*x2*y-3*z-1 + 8*x*y-2*z-1 + 12*y-1*z-1 + 8*x-1*z-1 + 2*x-2*y*z-1 + x2*y-4*z-1 + 5*x*y-3*z-1 + 10*y-2*z-1 + 10*x-1*y-1*z-1 + 5*x-2*z-1 + x-3*y*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 216 1 Lattice Minkowski decompositions of facet 216
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Polytope 4215
Image of polytope 4215 PALP id: 4215
grdb id: 261648
Integer points: [ 1 0 0 2 -2 2 -4 0 1 0 -1 1 0 -1 -2 -3 -1 -2 -3 1 1 0 -1 0 -1 -2]
[ 0 1 0 -1 2 -2 2 -2 -1 0 1 -2 -1 0 1 2 -1 0 1 0 -1 0 1 -1 0 1]
[ 0 0 1 -2 1 -3 3 -1 -2 -1 0 -2 -1 0 1 2 0 1 2 -1 -1 0 1 0 1 2]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x + y + z + 3*x-1*y*z + x-2*y2*z + 2*x-2*y*z2 + 2*x-3*y2*z2 + x-4*y2*z3 + 2*x*z-1 + 4*x-1*y + 4*x-1*z + 8*x-2*y*z + 4*x-3*y*z2 + x2*y-1*z-2 + 3*x*y-1*z-1 + 6*z-1 + 2*y-1 + 12*x-1 + 6*x-2*z + 4*x*y-1*z-2 + 8*y-1*z-1 + 4*x-1*y-1 + x2*y-2*z-3 + 2*x*y-2*z-2 + y-2*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Image of facet 214 1 Lattice Minkowski decompositions of facet 214
Polytope 4216
Image of polytope 4216 PALP id: 4216
grdb id: 261645
Integer points: [ 1 1 0 0 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 1 1 1]
[ 0 2 0 3 -1 2 -2 -4 0 -2 1 -1 -3 0 -2 1 -1 -3 2 0 -2 1 -1 0 1 -1]
[ 0 0 1 1 1 1 -2 -2 0 -1 1 0 -1 1 0 0 -1 -2 1 0 -1 1 0 -1 0 -1]
Degree: 8
Hilbert function: 1 + 7 t + 25 t2 + 63 t3 + 129 t4 + 231 t5 + 377 t6 + 575 t7 + 833 t8 + 1159 t9 + 1561 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
5 rank 1, V8 y3*z + x*y2 + 3*y2*z + 2*x*y + 3*y*z + x-1*y2*z + x + 4*y + z + 3*x-1*y*z + 2*x*z-1 + 3*x-1*z + 2*x*y-1*z-1 + 4*y-1 + 3*x-1 + x-1*y-1*z + 5*y-1*z-1 + 6*x-1*y-1 + x*y-2*z-2 + 5*y-2*z-1 + 3*x-1*y-2 + 3*x-1*y-2*z-1 + 2*y-3*z-2 + 3*x-1*y-3*z-1 + x-1*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 52 1 Lattice Minkowski decompositions of facet 52
Image of facet 108 2 Lattice Minkowski decompositions of facet 108
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 4217
Image of polytope 4217 PALP id: 4217
grdb id: 261497
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 1 1 1 0 -2 -2 1 -2 -1 -1 -1 -1 0 0 0 0 1 1 1 -1 -1 0 0 0 1]
[ 0 0 2 -1 -2 -2 0 3 -1 1 0 -1 -2 2 1 0 -1 2 1 0 0 -1 1 0 -1 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 y*z2 + x-1*y*z3 + 2*y*z + 4*x-1*y*z2 + x + y + 3*z + 6*x-1*y*z + 3*x-1*z2 + 4*x-1*y + 10*x-1*z + 2*z-1 + x-1*y*z-1 + 2*y-1 + 12*x-1 + 3*x-1*y-1*z + 2*y-1*z-1 + 6*x-1*z-1 + 8*x-1*y-1 + x-1*z-2 + 7*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-1*z-2 + 2*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 273 1 Lattice Minkowski decompositions of facet 273
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 4218
Image of polytope 4218 PALP id: 4218
grdb id: 260631
Integer points: [ 1 0 0 1 0 -2 1 -2 1 0 0 0 -1 -1 -1 -1 -2 -2 1 1 0 0 0 -1 -1 -1]
[ 0 1 0 0 1 1 -2 -2 -1 -2 -1 0 -2 -1 0 1 -1 0 -1 0 -1 0 1 -1 0 1]
[ 0 0 1 -2 -2 0 0 3 -1 1 0 -1 2 1 0 -1 2 1 0 -1 1 0 -1 2 1 0]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x + y + z + 2*x*z-1 + 2*y*z-1 + 2*x*y-1 + 2*x-1*y + 4*y-1*z + 4*x-1*z + 2*x-1*y-1*z2 + x*z-2 + y*z-2 + 2*x*y-1*z-1 + 5*z-1 + 2*x-1*y*z-1 + x*y-2 + 7*y-1 + 7*x-1 + x-2*y + 3*y-2*z + 8*x-1*y-1*z + 3*x-2*z + 3*x-1*y-2*z2 + 3*x-2*y-1*z2 + x-2*y-2*z3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 231 1 Lattice Minkowski decompositions of facet 231
Polytope 4219
Image of polytope 4219 PALP id: 4219
grdb id: 260624
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 1 1 -1 1 -2 1 -2 -2 -2 -1 -1 -1 -1 0 0 0 0 1 1 -1 -1 0 0 0 1]
[ 0 0 2 -2 0 -3 3 0 -2 -1 -2 -1 0 1 -1 0 1 2 1 2 -1 0 -1 0 1 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 y*z2 + x-1*y*z3 + 2*y*z + 3*x-1*y*z2 + x + y + 3*z + 3*x-1*y*z + 3*x-1*z2 + x-1*y + 9*x-1*z + 2*z-1 + 2*y-1 + 9*x-1 + 3*x-1*y-1*z + 3*y-1*z-1 + 3*x-1*z-1 + 9*x-1*y-1 + y-1*z-2 + 9*x-1*y-1*z-1 + x-1*y-2 + 3*x-1*y-1*z-2 + 3*x-1*y-2*z-1 + 3*x-1*y-2*z-2 + x-1*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 243 1 Lattice Minkowski decompositions of facet 243
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Polytope 4220
Image of polytope 4220 PALP id: 4220
grdb id: 261600
Integer points: [ 1 0 0 -2 1 -3 -3 1 0 -1 -2 1 0 -1 -2 -3 0 -1 -2 -1 1 0 -1 1 0 -1]
[ 0 1 0 2 -2 2 0 -4 -3 -2 -1 -3 -2 -1 0 1 -1 0 1 1 -2 -1 0 -1 0 1]
[ 0 0 1 -1 2 -2 -2 2 1 0 -1 2 1 0 -1 -2 1 0 -1 0 1 0 -1 1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
51 rank 2, number 7 x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*x-1*y + 2*x*y-2*z + 6*y-1*z + 2*x*y-3*z2 + 2*x-1*y*z-1 + x-2*y2*z-1 + 4*y-1 + 10*x-1 + 9*y-2*z + x*y-4*z2 + 2*x-1*z-1 + 6*x-2*y*z-1 + 14*x-1*y-1 + 4*y-3*z + x-3*y2*z-2 + 9*x-2*z-1 + 6*x-1*y-2 + 2*x-3*y*z-2 + 4*x-2*y-1*z-1 + x-3*z-2
18 rank 1, V14 x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*x-1*y + 2*x*y-2*z + 5*y-1*z + 2*x*y-3*z2 + 2*x-1*y*z-1 + x-2*y2*z-1 + 4*y-1 + 8*x-1 + 8*y-2*z + x*y-4*z2 + 2*x-1*z-1 + 5*x-2*y*z-1 + 12*x-1*y-1 + 4*y-3*z + x-3*y2*z-2 + 8*x-2*z-1 + 6*x-1*y-2 + 2*x-3*y*z-2 + 4*x-2*y-1*z-1 + x-3*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 297 1 Lattice Minkowski decompositions of facet 297
Polytope 4221
Image of polytope 4221 PALP id: 4221
grdb id: 261560
Integer points: [ 1 0 0 0 0 -1 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 0 1 1 -2 2 2 -4 1 0 -1 -2 -3 1 0 -1 -2 -3 0 -1 1 0 -1 -2 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
62 rank 2, number 9 x + y + z + y-1*z + 2*x-1*z + x-1*y-1*z2 + 2*z-1 + 3*y-1 + 6*x-1 + 6*x-1*y-1*z + x-2*y-1*z2 + 3*y-1*z-1 + 6*x-1*z-1 + 14*x-1*y-1 + 6*x-2*y-1*z + y-1*z-2 + 2*x-1*z-2 + 16*x-1*y-1*z-1 + 15*x-2*y-1 + 9*x-1*y-1*z-2 + 20*x-2*y-1*z-1 + 2*x-1*y-1*z-3 + 15*x-2*y-1*z-2 + 6*x-2*y-1*z-3 + x-2*y-1*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 304 1 Lattice Minkowski decompositions of facet 304
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Image of facet 9 1 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 4222
Image of polytope 4222 PALP id: 4222
grdb id: 261134
Integer points: [ 1 0 1 0 -2 1 -4 1 -3 -2 -1 0 -3 -2 -1 0 1 -1 0 1 -2 -1 0 -1 0 1]
[ 0 1 -1 0 1 -2 1 -4 0 -1 -2 -3 1 0 -1 -2 -3 0 -1 -2 1 0 -1 1 0 -1]
[ 0 0 0 1 2 -2 2 -3 1 0 -1 -2 2 1 0 -1 -2 1 0 -1 1 0 -1 1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*x-1*y*z + x-2*y*z2 + x*y-1 + 5*x-1*z + 2*x-2*y*z + 2*x-3*y*z2 + 2*x*y-1*z-1 + 7*y-1 + 5*x-1 + 9*x-2*z + x-4*y*z2 + 3*x*y-2*z-1 + 4*y-1*z-1 + 15*x-1*y-1 + 5*x-3*z + x*y-2*z-2 + 11*y-2*z-1 + 10*x-2*y-1 + 3*x*y-3*z-2 + 10*x-1*y-2*z-1 + 5*y-3*z-2 + x*y-4*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 271 1 Lattice Minkowski decompositions of facet 271
Polytope 4223
Image of polytope 4223 PALP id: 4223
grdb id: 261536
Integer points: [ 1 0 0 0 0 -1 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 -2 2 2 -4 1 0 -1 -2 -3 1 0 -1 -2 -3 -1 1 0 -1 -2 1 0 -1]
[ 0 0 1 -1 1 -2 -3 3 -2 -1 0 1 2 -2 -1 0 1 2 0 -1 0 1 2 -1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + z-1 + 5*x-1*y*z-1 + 2*y-1 + 9*x-1 + y-2*z + 7*x-1*y-1*z + 2*x-1*y-2*z2 + 2*x-1*y*z-2 + 8*x-1*z-1 + 12*x-1*y-1 + 8*x-1*y-2*z + 2*x-1*y-3*z2 + x-2*y2*z-3 + 6*x-2*y*z-2 + 15*x-2*z-1 + 20*x-2*y-1 + 15*x-2*y-2*z + 6*x-2*y-3*z2 + x-2*y-4*z3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 212 1 Lattice Minkowski decompositions of facet 212
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 200 1 Lattice Minkowski decompositions of facet 200
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 4224
Image of polytope 4224 PALP id: 4224
grdb id: 68371
Integer points: [ 1 0 0 1 0 -2 1 -3 1 -2 -1 0 -2 -1 0 1 -1 0 1 -1 0 1 -1 0 1 1]
[ 0 1 0 0 -1 2 -2 2 -2 1 0 -1 1 0 -1 -2 0 -1 -2 1 0 -1 1 0 -1 -1]
[ 0 0 1 -1 1 1 0 1 -3 0 -1 -2 1 0 -1 -2 1 0 -1 0 -1 -2 1 0 -1 0]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x + y + z + 2*x-1*y*z + x-2*y2*z + x*z-1 + 2*x*y-1 + 4*x-1*y + y-1*z + 3*x-1*z + 3*x-2*y*z + x-3*y2*z + 4*x*y-1*z-1 + 5*z-1 + x*y-2 + 6*y-1 + 9*x-1 + 4*x-2*y + 2*x*y-1*z-2 + 3*x*y-2*z-1 + 9*y-1*z-1 + 6*x-1*z-1 + 3*x*y-2*z-2 + 4*y-1*z-2 + x*y-2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 107 1 Lattice Minkowski decompositions of facet 107
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 4225
Image of polytope 4225 PALP id: 4225
grdb id: 67721
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 1 1 -1 1 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 0 1 -1 -1 -1 0 0]
[ 0 0 1 -1 0 2 -2 2 -2 -1 0 1 -2 -1 0 1 -2 -1 0 1 -1 -1 0 1 -1 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + y*z-1 + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + 3*z-1 + 2*x-1*y*z-1 + 4*y-1 + 7*x-1 + 6*x-1*y-1*z + x-1*y-2*z2 + x-1*y*z-2 + 2*y-1*z-1 + 8*x-1*z-1 + 12*x-1*y-1 + 4*x-1*y-2*z + 3*x-1*z-2 + 10*x-1*y-1*z-1 + 6*x-1*y-2 + 3*x-1*y-1*z-2 + 4*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 3 Lattice Minkowski decompositions of facet 11
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 273 1 Lattice Minkowski decompositions of facet 273
Polytope 4226
Image of polytope 4226 PALP id: 4226
grdb id: 67006
Integer points: [ 1 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 -1 1 0 1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0]
[ 0 0 1 1 0 1 -1 1 -4 0 -1 -2 -3 1 0 -1 -2 -3 0 -1 -2 0 -1 -2 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
20 rank 1, V16 x + y + z + x-1*y + y-1*z + x-1*z + 3*z-1 + x-1*y*z-1 + 4*y-1 + 5*x-1 + 2*x-1*y-1*z + 5*y-1*z-1 + 7*x-1*z-1 + 9*x-1*y-1 + x-1*y-2*z + 2*y-1*z-2 + 3*x-1*z-2 + 15*x-1*y-1*z-1 + 5*x-1*y-2 + 11*x-1*y-1*z-2 + 10*x-1*y-2*z-1 + 3*x-1*y-1*z-3 + 10*x-1*y-2*z-2 + 5*x-1*y-2*z-3 + x-1*y-2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 271 1 Lattice Minkowski decompositions of facet 271
Polytope 4227
Image of polytope 4227 PALP id: 4227
grdb id: 551994
Integer points: [ 1 0 0 -1 2 0 -2 0 -2 2 -1 -2 -1 0 1 -1 0 1 -1 0 1 -1 0 1 2 1]
[ 0 1 0 1 -1 -1 1 1 -1 -1 1 0 0 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1]
[ 0 0 1 1 -1 1 1 -1 1 -3 0 1 0 -1 -2 1 0 -1 0 -1 -2 1 0 -1 -2 0]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x + y + z + x-1*y*z + x2*y-1*z-1 + 3*x*z-1 + y*z-1 + 2*x*y-1 + 2*x-1*y + y-1*z + 3*x-1*z + x-2*y*z + 2*x2*y-1*z-2 + 2*x*z-2 + 6*x*y-1*z-1 + 6*z-1 + 6*y-1 + 6*x-1 + 2*x-1*y-1*z + 2*x-2*z + x2*y-1*z-3 + 4*x*y-1*z-2 + 6*y-1*z-1 + 4*x-1*y-1 + x-2*y-1*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Image of facet 127 2 Lattice Minkowski decompositions of facet 127
Polytope 4228
Image of polytope 4228 PALP id: 4228
grdb id: 547402
Integer points: [ 1 1 1 -11 -9 -7 -5 -3 -1 -8 -6 -4 -2 0 -5 -3 -1 1 -2 0 -5 -3 -1 1 -2 0 1]
[ 0 2 0 -6 -5 -4 -3 -2 -1 -4 -3 -2 -1 0 -2 -1 0 1 0 1 -3 -2 -1 0 -1 0 1]
[ 0 0 2 -4 -3 -2 -1 0 1 -3 -2 -1 0 1 -2 -1 0 1 -1 0 -2 -1 0 1 -1 0 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Image of facet 305 1 none
Polytope 4229
Image of polytope 4229 PALP id: 4229
grdb id: 547403
Integer points: [ 1 0 1 -15 -13 -11 -9 -7 -5 -3 -1 -10 -8 -6 -4 -2 0 -5 -3 -1 -7 -5 -3 -1 1 -2 0]
[ 0 1 0 -8 -7 -6 -5 -4 -3 -2 -1 -5 -4 -3 -2 -1 0 -2 -1 0 -4 -3 -2 -1 0 -1 0]
[ 0 0 2 -6 -5 -4 -3 -2 -1 0 1 -4 -3 -2 -1 0 1 -2 -1 0 -3 -2 -1 0 1 -1 0]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 208 1 Lattice Minkowski decompositions of facet 208
Image of facet 1 1 irreducible and admissible
Image of facet 306 1 none
Image of facet 14 1 none
Polytope 4230
Image of polytope 4230 PALP id: 4230
grdb id: 544534
Integer points: [ 1 1 1 -3 -3 0 -1 -2 0 -1 -2 -3 -1 -2 -3 -2 -3 1 0 -1 1 0 -1 0 -1 -1 1]
[ 0 2 0 0 -4 -1 -2 -3 0 -1 -2 -3 0 -1 -2 0 -1 0 -1 -2 1 0 -1 1 0 1 1]
[ 0 0 2 -2 -2 1 0 -1 1 0 -1 -2 0 -1 -2 -1 -2 1 0 -1 1 0 -1 0 -1 -1 0]
Degree: 8
Hilbert function: 1 + 7 t + 25 t2 + 63 t3 + 129 t4 + 231 t5 + 377 t6 + 575 t7 + 833 t8 + 1159 t9 + 1561 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
5 rank 1, V8 x*y2 + 2*x*y*z + x*z2 + 2*x*y + 2*x*z + x + 4*y + 4*z + 4*y-1*z + 2*x-1*y*z-1 + 4*y-1 + 6*x-1 + 6*x-1*z-1 + 12*x-1*y-1 + 6*x-1*y-1*z-1 + 4*x-2*z-1 + 6*x-1*y-2 + 2*x-1*y-2*z-1 + 12*x-2*y-1*z-1 + x-3*z-2 + 12*x-2*y-2*z-1 + 4*x-3*y-1*z-2 + 4*x-2*y-3*z-1 + 6*x-3*y-2*z-2 + 4*x-3*y-3*z-2 + x-3*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 32 2 Lattice Minkowski decompositions of facet 32
Image of facet 206 1 Lattice Minkowski decompositions of facet 206
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 4231
Image of polytope 4231 PALP id: 4231
grdb id: 544530
Integer points: [ 1 1 0 -3 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 1]
[ 0 2 0 0 -6 -5 -4 -3 -2 -1 -4 -3 -2 -1 0 -2 -1 0 -3 -2 -1 0 1 -1 0 1 1]
[ 0 0 1 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 -1 0 0 0 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 212 1 Lattice Minkowski decompositions of facet 212
Image of facet 14 2 none
Image of facet 241 1 Lattice Minkowski decompositions of facet 241
Polytope 4232
Image of polytope 4232 PALP id: 4232
grdb id: 544529
Integer points: [ 1 0 1 -4 1 0 -1 -2 -3 1 0 -1 -2 -3 1 0 -1 -2 1 0 -1 1 0 -1 1 0 1]
[ 0 1 0 1 -4 -3 -2 -1 0 -3 -2 -1 0 1 -2 -1 0 1 -1 0 1 -2 -1 0 -1 0 0]
[ 0 0 2 -4 6 4 2 0 -2 5 3 1 -1 -3 4 2 0 -2 3 1 -1 3 1 -1 2 0 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 1 irreducible and admissible
Image of facet 307 1 Lattice Minkowski decompositions of facet 307
Image of facet 13 1 irreducible and admissible
Image of facet 73 1 none
Polytope 4233
Image of polytope 4233 PALP id: 4233
grdb id: 544524
Integer points: [ 1 0 0 -3 -3 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 -6 -5 -4 -3 -2 -1 0 -4 -3 -2 -1 0 1 -2 -1 0 1 -3 -2 -1 0 -1 0]
[ 0 0 1 -3 4 3 2 1 0 -1 -2 3 2 1 0 -1 -2 2 1 0 -1 2 1 0 -1 1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 275 1 none
Image of facet 308 1 Lattice Minkowski decompositions of facet 308
Image of facet 14 1 none
Polytope 4234
Image of polytope 4234 PALP id: 4234
grdb id: 544539
Integer points: [ 1 0 0 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 0 0 0]
[ 0 1 1 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 0 0 1 1 1 -1 -1 -1 0 0 0]
[ 0 0 4 -2 -6 -3 -4 -5 0 -1 -2 -3 -4 2 1 0 -1 -2 3 2 1 -1 -2 -3 1 0 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 13 1 irreducible and admissible
Image of facet 14 2 none
Image of facet 309 1 Lattice Minkowski decompositions of facet 309
Polytope 4235
Image of polytope 4235 PALP id: 4235
grdb id: 544536
Integer points: [ 1 1 1 -3 -7 -5 -3 -1 -6 -4 -2 0 -5 -3 -1 1 -4 -2 0 -1 -3 -1 1 -2 0 -1 1]
[ 0 2 0 0 -4 -3 -2 -1 -3 -2 -1 0 -2 -1 0 1 -1 0 1 1 -2 -1 0 -1 0 0 1]
[ 0 0 2 -2 -2 -1 0 1 -2 -1 0 1 -2 -1 0 1 -2 -1 0 -1 -1 0 1 -1 0 -1 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
11 rank 2, number 6 x*y2 + 2*x*y*z + x*z2 + 2*x*y + 2*x*z + x + 4*y + 4*z + 2*x-1*y*z-1 + 10*x-1 + 4*x-1*y-1*z + 2*x-1*z-1 + 4*x-1*y-1 + 8*x-2*z-1 + 12*x-2*y-1 + 4*x-2*y-1*z-1 + x-3*z-2 + 14*x-3*y-1*z-1 + 6*x-3*y-2 + 2*x-3*y-2*z-1 + 4*x-4*y-1*z-2 + 12*x-4*y-2*z-1 + 6*x-5*y-2*z-2 + 4*x-5*y-3*z-1 + 4*x-6*y-3*z-2 + x-7*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 32 2 Lattice Minkowski decompositions of facet 32
Image of facet 310 1 Lattice Minkowski decompositions of facet 310
Polytope 4236
Image of polytope 4236 PALP id: 4236
grdb id: 544531
Integer points: [ 1 0 1 -3 -9 -4 -5 -6 -7 -8 -1 -2 -3 -4 -5 -6 0 -1 -2 -3 -1 -2 -3 -4 1 0 -1]
[ 0 1 0 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0 0 0 -1 -1 -1 -1 0 0 0]
[ 0 0 2 0 -6 -1 -2 -3 -4 -5 1 0 -1 -2 -3 -4 1 0 -1 -2 0 -1 -2 -3 1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Image of facet 14 1 none
Image of facet 311 1 Lattice Minkowski decompositions of facet 311
Polytope 4237
Image of polytope 4237 PALP id: 4237
grdb id: 520915
Integer points: [ 1 1 1 -3 1 -3 0 -1 -2 1 0 -1 -2 -3 0 -1 -2 1 0 -1 1 0 -1 1 0 -1 1]
[ 0 2 0 -4 2 -2 1 0 -1 1 0 -1 -2 -3 -1 -2 -3 2 1 0 1 0 -1 0 -1 -2 1]
[ 0 0 2 -2 2 -2 1 0 -1 2 1 0 -1 -2 1 0 -1 1 0 -1 1 0 -1 1 0 -1 0]
Degree: 8
Hilbert function: 1 + 7 t + 25 t2 + 63 t3 + 129 t4 + 231 t5 + 377 t6 + 575 t7 + 833 t8 + 1159 t9 + 1561 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
5 rank 1, V8 x*y2*z2 + 2*x*y2*z + 2*x*y*z2 + x*y2 + 4*x*y*z + x*z2 + 2*x*y + 2*x*z + 4*y*z + x + 4*y + 8*z + 4*y-1*z + 4*y-1 + 6*x-1 + 2*x-1*z-1 + 12*x-1*y-1 + 4*x-1*y-1*z-1 + 6*x-1*y-2 + 2*x-1*y-2*z-1 + 4*x-2*y-1*z-1 + 8*x-2*y-2*z-1 + 4*x-2*y-3*z-1 + x-3*y-2*z-2 + 2*x-3*y-3*z-2 + x-3*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 2 Lattice Minkowski decompositions of facet 32
Image of facet 36 2 Lattice Minkowski decompositions of facet 36
Image of facet 214 1 Lattice Minkowski decompositions of facet 214
Polytope 4238
Image of polytope 4238 PALP id: 4238
grdb id: 520931
Integer points: [ 1 0 0 -2 3 -2 -1 0 1 2 -2 -1 0 1 2 -2 -1 0 1 -1 -1 0 1 2 -1 0 1]
[ 0 1 0 2 -6 -1 -2 -3 -4 -5 0 -1 -2 -3 -4 1 0 -1 -2 1 0 -1 -2 -3 1 0 -1]
[ 0 0 1 1 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 0 1 -1 -1 -1 -1 0 0 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 277 1 Lattice Minkowski decompositions of facet 277
Image of facet 14 2 none
Polytope 4239
Image of polytope 4239 PALP id: 4239
grdb id: 520906
Integer points: [ 1 0 0 0 -2 -2 0 0 0 -1 -1 -1 -1 -1 -1 -2 -2 -2 -2 -2 0 0 0 -1 -1 -1 -1]
[ 0 1 1 -3 1 -5 0 -1 -2 1 0 -1 -2 -3 -4 0 -1 -2 -3 -4 1 0 -1 1 0 -1 -2]
[ 0 0 2 -2 2 -4 1 0 -1 2 1 0 -1 -2 -3 1 0 -1 -2 -3 1 0 -1 1 0 -1 -2]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 y*z2 + 2*y*z + 2*x-1*y*z2 + x + y + 4*z + 2*x-1*y*z + x-2*y*z2 + 10*x-1*z + 6*y-1 + 6*x-1 + 6*x-2*z + 2*y-1*z-1 + 20*x-1*y-1 + 4*y-2*z-1 + 6*x-1*y-1*z-1 + 15*x-2*y-1 + 20*x-1*y-2*z-1 + y-3*z-2 + 2*x-1*y-2*z-2 + 20*x-2*y-2*z-1 + 10*x-1*y-3*z-2 + 15*x-2*y-3*z-2 + 2*x-1*y-4*z-3 + 6*x-2*y-4*z-3 + x-2*y-5*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Image of facet 312 1 Lattice Minkowski decompositions of facet 312
Image of facet 13 1 irreducible and admissible
Polytope 4240
Image of polytope 4240 PALP id: 4240
grdb id: 520890
Integer points: [ 1 1 1 -3 -5 -1 0 -2 -1 0 1 -3 -2 -1 0 -4 -3 -2 -1 -4 0 1 -1 0 1 -2 -1]
[ 0 2 0 0 -2 -2 -1 -2 -1 0 1 -2 -1 0 1 -2 -1 0 1 -1 -1 0 -1 0 1 -1 0]
[ 0 0 2 -2 -2 2 2 1 1 1 1 0 0 0 0 -1 -1 -1 -1 -2 1 1 0 0 0 -1 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
22 ? x*y2 + 2*x*y*z + x*z2 + 2*x*y + 2*x*z + x + 6*y + 8*z + 2*y-1*z2 + 2*y-1*z + 2*x-1*y*z-1 + 15*x-1 + 10*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 4*x-1*y-1 + 8*x-2*z-1 + 16*x-2*y-1 + 4*x-2*y-2*z + 2*x-2*y-1*z-1 + x-3*z-2 + 10*x-3*y-1*z-1 + 6*x-3*y-2 + 2*x-4*y-1*z-2 + 4*x-4*y-2*z-1 + x-5*y-2*z-2
11 rank 2, number 6 x*y2 + 2*x*y*z + x*z2 + 2*x*y + 2*x*z + x + 4*y + 6*z + 2*y-1*z2 + 2*y-1*z + 2*x-1*y*z-1 + 10*x-1 + 8*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 4*x-1*y-1 + 6*x-2*z-1 + 12*x-2*y-1 + 4*x-2*y-2*z + 2*x-2*y-1*z-1 + x-3*z-2 + 8*x-3*y-1*z-1 + 6*x-3*y-2 + 2*x-4*y-1*z-2 + 4*x-4*y-2*z-1 + x-5*y-2*z-2
7 rank 1, V12 x*y2 + 2*x*y*z + x*z2 + 2*x*y + 2*x*z + x + 5*y + 7*z + 2*y-1*z2 + 2*y-1*z + 2*x-1*y*z-1 + 12*x-1 + 9*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*z-1 + 4*x-1*y-1 + 7*x-2*z-1 + 14*x-2*y-1 + 4*x-2*y-2*z + 2*x-2*y-1*z-1 + x-3*z-2 + 9*x-3*y-1*z-1 + 6*x-3*y-2 + 2*x-4*y-1*z-2 + 4*x-4*y-2*z-1 + x-5*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 4 Lattice Minkowski decompositions of facet 16
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 313 1 Lattice Minkowski decompositions of facet 313
Polytope 4241
Image of polytope 4241 PALP id: 4241
grdb id: 520868
Integer points: [ 1 0 1 -3 -5 1 0 -1 -2 -3 -4 1 0 -1 -2 -3 -4 0 -1 -2 1 0 -1 -2 1 0 -1]
[ 0 1 0 0 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0 0]
[ 0 0 2 -2 -2 4 3 2 1 0 -1 3 2 1 0 -1 -2 1 0 -1 2 1 0 -1 1 0 -1]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x*z2 + 2*x*y-1*z3 + x*y-2*z4 + 2*x*z + 2*x*y-1*z2 + x + y + 4*z + 9*y-1*z2 + 6*y-2*z3 + 6*y-1*z + 5*x-1 + 17*x-1*y-1*z + 15*x-1*y-2*z2 + 2*x-1*z-1 + 6*x-1*y-1 + 3*x-2*z-1 + 17*x-2*y-1 + 20*x-2*y-2*z + 2*x-2*y-1*z-1 + x-3*z-2 + 9*x-3*y-1*z-1 + 15*x-3*y-2 + 2*x-4*y-1*z-2 + 6*x-4*y-2*z-1 + x-5*y-2*z-2
151 ? x*z2 + 2*x*y-1*z3 + x*y-2*z4 + 2*x*z + 2*x*y-1*z2 + x + y + 6*z + 11*y-1*z2 + 6*y-2*z3 + 6*y-1*z + 8*x-1 + 22*x-1*y-1*z + 15*x-1*y-2*z2 + 2*x-1*z-1 + 6*x-1*y-1 + 4*x-2*z-1 + 21*x-2*y-1 + 20*x-2*y-2*z + 2*x-2*y-1*z-1 + x-3*z-2 + 10*x-3*y-1*z-1 + 15*x-3*y-2 + 2*x-4*y-1*z-2 + 6*x-4*y-2*z-1 + x-5*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 314 1 Lattice Minkowski decompositions of facet 314
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Polytope 4242
Image of polytope 4242 PALP id: 4242
grdb id: 520815
Integer points: [ 1 0 0 0 -2 -9 -3 -4 -5 -6 -7 -8 -1 -2 -3 -4 -5 -6 -1 -2 -3 -1 -2 -3 -4 0 -1]
[ 0 1 0 -1 -2 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0]
[ 0 0 1 1 1 -6 0 -1 -2 -3 -4 -5 1 0 -1 -2 -3 -4 0 -1 -2 0 -1 -2 -3 0 -1]
Degree: 24
Hilbert function: 1 + 15 t + 65 t2 + 175 t3 + 369 t4 + 671 t5 + 1105 t6 + 1695 t7 + 2465 t8 + 3439 t9 + 4641 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 195 1 Lattice Minkowski decompositions of facet 195
Image of facet 14 1 none
Image of facet 299 1 Lattice Minkowski decompositions of facet 299
Polytope 4243
Image of polytope 4243 PALP id: 4243
grdb id: 432471
Integer points: [ 1 1 1 -1 -1 -3 1 0 -1 -2 1 0 -1 -2 0 1 0 -1 -2 1 0 -1 1 0 0 1 0]
[ 0 2 0 0 -2 -2 2 1 0 -1 1 0 -1 -2 -1 2 1 0 -1 1 0 -1 0 -1 1 1 0]
[ 0 0 2 -2 0 -2 2 1 0 -1 2 1 0 -1 1 1 0 -1 -2 1 0 -1 1 0 -1 0 -1]
Degree: 8
Hilbert function: 1 + 7 t + 25 t2 + 63 t3 + 129 t4 + 231 t5 + 377 t6 + 575 t7 + 833 t8 + 1159 t9 + 1561 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
5 rank 1, V8 x*y2*z2 + 2*x*y2*z + 2*x*y*z2 + x*y2 + 4*x*y*z + x*z2 + 2*x*y + 2*x*z + 4*y*z + x + 6*y + 6*z + 2*y*z-1 + 2*y-1*z + 2*z-1 + 2*y-1 + 6*x-1 + 6*x-1*z-1 + 6*x-1*y-1 + x-1*z-2 + 4*x-1*y-1*z-1 + x-1*y-2 + 4*x-2*y-1*z-1 + 2*x-2*y-1*z-2 + 2*x-2*y-2*z-1 + x-3*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 36 2 Lattice Minkowski decompositions of facet 36
Image of facet 127 2 Lattice Minkowski decompositions of facet 127
Polytope 4244
Image of polytope 4244 PALP id: 4244
grdb id: 432671
Integer points: [ 1 0 1 1 0 -1 -4 0 -2 -1 0 1 -3 -2 -1 0 -3 -2 -1 0 1 -1 0 1 -2 -1 0]
[ 0 1 -2 0 1 -2 1 -2 -1 -1 -1 -1 0 0 0 0 1 1 1 -1 -1 0 0 0 1 1 1]
[ 0 0 0 2 2 -2 -2 -1 -2 -1 0 1 -2 -1 0 1 -1 0 1 -1 0 -1 0 1 -1 0 1]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x*z2 + y*z2 + 2*x*z + 2*y*z + x + y + 2*x*y-1*z + 6*z + 4*x-1*y*z + 2*x*y-1 + 4*x-1*y + x*y-2 + 7*y-1 + 12*x-1 + 6*x-2*y + 2*y-1*z-1 + 4*x-1*z-1 + 2*x-2*y*z-1 + 2*y-2*z-1 + 8*x-1*y-1*z-1 + 10*x-2*z-1 + 4*x-3*y*z-1 + x-1*y-2*z-2 + 3*x-2*y-1*z-2 + 3*x-3*z-2 + x-4*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 273 1 Lattice Minkowski decompositions of facet 273
Polytope 4245
Image of polytope 4245 PALP id: 4245
grdb id: 432661
Integer points: [ 1 0 0 0 0 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 1 -1 -1 -3 3 2 1 0 -1 -2 2 1 0 -1 -2 0 2 1 0 -1 -2 1 0 -1 0]
[ 0 0 2 -2 0 -4 2 1 0 -1 -2 -3 1 0 -1 -2 -3 -1 2 1 0 -1 -2 1 0 -1 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
11 rank 2, number 6 y*z2 + 2*x-1*y2*z2 + x-2*y3*z2 + 2*y*z + 2*x-1*y2*z + x + y + 2*z + 8*x-1*y*z + 6*x-2*y2*z + 8*x-1*y + 2*z-1 + y-1 + 12*x-1 + 15*x-2*y + 2*y-1*z-1 + 12*x-1*z-1 + y-1*z-2 + 8*x-1*y-1*z-1 + 20*x-2*z-1 + 8*x-1*y-1*z-2 + 2*x-1*y-2*z-2 + 15*x-2*y-1*z-2 + 2*x-1*y-2*z-3 + 6*x-2*y-2*z-3 + x-2*y-3*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 212 2 Lattice Minkowski decompositions of facet 212
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Polytope 4246
Image of polytope 4246 PALP id: 4246
grdb id: 432558
Integer points: [ 1 0 0 1 -1 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 2 2 -4 1 0 -1 -2 -3 1 0 -1 -2 -3 0 -1 -2 1 0 -1 -2 1 0 -1]
[ 0 0 1 0 -2 -3 3 -2 -1 0 1 2 -2 -1 0 1 2 -1 0 1 -1 0 1 2 -1 0 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + 2*y*z-1 + x*y-1 + 3*y-1*z + x-1*y2*z-2 + 3*z-1 + 5*x-1*y*z-1 + 6*y-1 + 9*x-1 + 3*y-2*z + 7*x-1*y-1*z + 2*x-1*y-2*z2 + 3*x-1*y*z-2 + 12*x-1*z-1 + 18*x-1*y-1 + 12*x-1*y-2*z + 3*x-1*y-3*z2 + x-2*y2*z-3 + 6*x-2*y*z-2 + 15*x-2*z-1 + 20*x-2*y-1 + 15*x-2*y-2*z + 6*x-2*y-3*z2 + x-2*y-4*z3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 241 1 Lattice Minkowski decompositions of facet 241
Image of facet 200 1 Lattice Minkowski decompositions of facet 200
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 4247
Image of polytope 4247 PALP id: 4247
grdb id: 432244
Integer points: [ 1 0 0 0 -2 -3 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 2 2 -4 -3 -2 -1 0 1 -3 -2 -1 0 1 -2 -1 0 1 -2 -1 0 1 -1 0]
[ 0 0 1 1 -1 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 0 -1 -1 -1 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 14 1 none
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 302 1 Lattice Minkowski decompositions of facet 302
Polytope 4248
Image of polytope 4248 PALP id: 4248
grdb id: 432464
Integer points: [ 1 1 1 -3 -3 -5 3 2 2 1 0 -1 0 -1 -2 -1 -2 -3 -4 -4 2 1 1 0 -1 -1 -2]
[ 0 2 0 0 -2 -2 2 2 1 1 1 1 0 0 0 -1 -1 -1 -1 -2 1 1 0 0 0 -1 -1]
[ 0 0 2 -2 0 -2 2 1 2 1 0 -1 1 0 -1 1 0 -1 -2 -1 1 0 1 0 -1 0 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x3*y2*z2 + 2*x2*y2*z + 2*x2*y*z2 + 2*x2*y*z + x*y2 + 7*x*y*z + x*z2 + 2*x*y + 2*x*z + x + 7*y + 7*z + 2*x-1*y*z-1 + 12*x-1 + 2*x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + 7*x-2*z-1 + 7*x-2*y-1 + 2*x-2*y-1*z-1 + x-3*z-2 + 7*x-3*y-1*z-1 + x-3*y-2 + 2*x-4*y-1*z-2 + 2*x-4*y-2*z-1 + x-5*y-2*z-2
11 rank 2, number 6 x3*y2*z2 + 2*x2*y2*z + 2*x2*y*z2 + 2*x2*y*z + x*y2 + 6*x*y*z + x*z2 + 2*x*y + 2*x*z + x + 6*y + 6*z + 2*x-1*y*z-1 + 10*x-1 + 2*x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + 6*x-2*z-1 + 6*x-2*y-1 + 2*x-2*y-1*z-1 + x-3*z-2 + 6*x-3*y-1*z-1 + x-3*y-2 + 2*x-4*y-1*z-2 + 2*x-4*y-2*z-1 + x-5*y-2*z-2
22 ? x3*y2*z2 + 2*x2*y2*z + 2*x2*y*z2 + 2*x2*y*z + x*y2 + 8*x*y*z + x*z2 + 2*x*y + 2*x*z + x + 8*y + 8*z + 2*x-1*y*z-1 + 15*x-1 + 2*x-1*y-1*z + 2*x-1*z-1 + 2*x-1*y-1 + 8*x-2*z-1 + 8*x-2*y-1 + 2*x-2*y-1*z-1 + x-3*z-2 + 8*x-3*y-1*z-1 + x-3*y-2 + 2*x-4*y-1*z-2 + 2*x-4*y-2*z-1 + x-5*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 6 Lattice Minkowski decompositions of facet 16
Image of facet 315 1 Lattice Minkowski decompositions of facet 315
Polytope 4249
Image of polytope 4249 PALP id: 4249
grdb id: 259467
Integer points: [ 1 1 0 0 -2 -2 1 1 0 -1 1 0 -1 1 0 -1 -2 1 0 -1 1 0 0 -1 1 0 -1]
[ 0 2 0 2 -2 0 -2 0 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0 0 1 1 0 0 1 1 1]
[ 0 0 1 1 1 1 -2 -2 -1 0 -1 0 1 -2 -1 0 1 -1 0 1 0 1 -1 0 -1 0 1]
Degree: 8
Hilbert function: 1 + 7 t + 25 t2 + 63 t3 + 129 t4 + 231 t5 + 377 t6 + 575 t7 + 833 t8 + 1159 t9 + 1561 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
5 rank 1, V8 x*y2 + y2*z + 2*x*y + 2*y*z + 2*x*y*z-1 + x + 4*y + z + 2*x-1*y*z + 4*x*z-1 + 4*x-1*z + x*z-2 + 2*x*y-1*z-1 + 3*z-1 + 4*y-1 + 3*x-1 + 2*x-1*y-1*z + x-2*z + 2*x*y-1*z-2 + 6*y-1*z-1 + 6*x-1*y-1 + 2*x-2*y-1*z + x*y-2*z-2 + 3*y-2*z-1 + 3*x-1*y-2 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Image of facet 36 2 Lattice Minkowski decompositions of facet 36
Image of facet 125 1 Lattice Minkowski decompositions of facet 125
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 4250
Image of polytope 4250 PALP id: 4250
grdb id: 259468
Integer points: [ 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 1 1 1 1 1]
[ 0 2 0 2 -2 0 -2 0 -2 -1 -1 -1 0 -1 -1 -1 0 0 0 1 1 1 0 1 1 1 2]
[ 0 0 2 2 -2 -2 0 0 -1 -2 -1 0 -1 -1 0 1 -1 0 1 -1 0 1 1 0 1 2 1]
Degree: 8
Hilbert function: 1 + 7 t + 25 t2 + 63 t3 + 129 t4 + 231 t5 + 377 t6 + 575 t7 + 833 t8 + 1159 t9 + 1561 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
5 rank 1, V8 x*y2*z2 + 2*x*y2*z + 2*x*y*z2 + x*y2 + 4*x*y*z + x*z2 + 2*x*y + 2*x*z + 2*y*z + x + 4*y + 4*z + 2*y*z-1 + 2*y-1*z + 4*z-1 + 4*y-1 + x-1 + 2*y-1*z-1 + 2*x-1*z-1 + 2*x-1*y-1 + x-1*z-2 + 4*x-1*y-1*z-1 + x-1*y-2 + 2*x-1*y-1*z-2 + 2*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 36 6 Lattice Minkowski decompositions of facet 36
Polytope 4251
Image of polytope 4251 PALP id: 4251
grdb id: 259464
Integer points: [ 1 0 0 -2 0 -3 3 0 -2 -1 -2 -1 0 1 -1 0 1 2 1 2 -1 0 -1 0 1 1 2]
[ 0 1 0 2 -1 2 -4 -1 1 0 1 0 -1 -2 0 -1 -2 -3 -2 -3 1 0 1 0 -1 -1 -2]
[ 0 0 1 1 1 1 -2 -2 0 -1 1 0 -1 -2 1 0 -1 -2 0 -1 0 -1 1 0 -1 0 -1]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x + y + z + 2*x-1*y*z + x-2*y2*z + 3*x*y-1 + 3*x-1*y + y-1*z + 3*x-1*z + 3*x-2*y*z + x-3*y2*z + 2*x2*y-2*z-1 + 4*x*y-1*z-1 + 2*z-1 + 3*x*y-2 + 9*y-1 + 9*x-1 + 3*x-2*y + 3*x2*y-3*z-1 + 9*x*y-2*z-1 + 9*y-1*z-1 + 3*x-1*z-1 + x3*y-4*z-2 + 3*x2*y-3*z-2 + 3*x*y-2*z-2 + y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Image of facet 35 1 Lattice Minkowski decompositions of facet 35
Image of facet 243 1 Lattice Minkowski decompositions of facet 243
Polytope 4252
Image of polytope 4252 PALP id: 4252
grdb id: 259188
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0]
[ 0 1 0 1 -1 1 -2 -2 1 0 0 0 0 -1 -1 -1 -1 -1 -2 -2 -2 -2 0 0 -1 -1 -1]
[ 0 0 1 1 1 -1 1 -4 0 1 0 -1 -2 1 0 -1 -2 -3 0 -1 -2 -3 0 -1 0 -1 -2]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x-1*y*z + 2*x-1*y + y-1*z + 3*x-1*z + 3*z-1 + x-1*y*z-1 + 4*y-1 + 9*x-1 + 3*x-1*y-1*z + 5*y-1*z-1 + 9*x-1*z-1 + 12*x-1*y-1 + x-1*y-2*z + 2*y-1*z-2 + 3*x-1*z-2 + 18*x-1*y-1*z-1 + 5*x-1*y-2 + 12*x-1*y-1*z-2 + 10*x-1*y-2*z-1 + 3*x-1*y-1*z-3 + 10*x-1*y-2*z-2 + 5*x-1*y-2*z-3 + x-1*y-2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 277 1 Lattice Minkowski decompositions of facet 277
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Polytope 4253
Image of polytope 4253 PALP id: 4253
grdb id: 259203
Integer points: [ 1 0 0 1 1 0 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0 0]
[ 0 1 0 0 -1 1 1 -4 0 -1 -2 -3 1 0 -1 -2 -3 0 -1 -2 1 0 -1 -2 1 0 -1]
[ 0 0 1 -1 0 -2 -2 3 -1 0 1 2 -2 -1 0 1 2 -1 0 1 -1 0 1 2 -1 0 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + x*z-1 + 2*y*z-1 + x*y-1 + 3*y-1*z + y*z-2 + 5*z-1 + 2*x-1*y*z-1 + 7*y-1 + 6*x-1 + 3*y-2*z + 6*x-1*y-1*z + 2*x-1*y-2*z2 + 2*x-1*y*z-2 + 9*x-1*z-1 + 15*x-1*y-1 + 11*x-1*y-2*z + 3*x-1*y-3*z2 + x-2*y*z-2 + 5*x-2*z-1 + 10*x-2*y-1 + 10*x-2*y-2*z + 5*x-2*y-3*z2 + x-2*y-4*z3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 271 1 Lattice Minkowski decompositions of facet 271
Polytope 4254
Image of polytope 4254 PALP id: 4254
grdb id: 65832
Integer points: [ 1 0 0 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0]
[ 0 1 0 -1 0 -1 2 -3 2 0 1 -2 -1 0 1 2 -2 -1 0 1 -1 0 1 -2 -1 0 1]
[ 0 0 1 0 -1 2 -1 2 -3 1 0 2 1 0 -1 -2 1 0 -1 -2 1 0 -1 1 0 -1 -2]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x + y + z + x*z-1 + 3*y*z-1 + x-1*y2*z-1 + x*y-1 + 3*x-1*y + 3*y-1*z + 3*x-1*z + x-1*y-1*z2 + 2*y*z-2 + 2*x-1*y2*z-2 + 6*z-1 + 8*x-1*y*z-1 + 6*y-1 + 12*x-1 + 2*y-2*z + 8*x-1*y-1*z + 2*x-1*y-2*z2 + x-1*y2*z-3 + 5*x-1*y*z-2 + 10*x-1*z-1 + 10*x-1*y-1 + 5*x-1*y-2*z + x-1*y-3*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 216 1 Lattice Minkowski decompositions of facet 216
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Polytope 4255
Image of polytope 4255 PALP id: 4255
grdb id: 547399
Integer points: [ 1 0 0 -5 -4 -3 -2 -1 -4 -3 -2 -1 0 -3 -2 -1 0 -2 -1 0 -1 0 -2 -1 0 -1 0 0]
[ 0 1 1 -4 -3 -2 -1 0 -3 -2 -1 0 1 -2 -1 0 1 -1 0 1 0 1 -2 -1 0 -1 0 0]
[ 0 0 5 -10 -7 -4 -1 2 -8 -5 -2 1 4 -6 -3 0 3 -4 -1 2 -2 1 -5 -2 1 -3 0 -1]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 73 2 none
Image of facet 43 1 irreducible and admissible
Image of facet 316 1 Lattice Minkowski decompositions of facet 316
Polytope 4256
Image of polytope 4256 PALP id: 4256
grdb id: 544493
Integer points: [ 1 0 0 -1 -9 -8 -7 -6 -5 -4 -3 -2 -6 -5 -4 -3 -2 -1 -3 -2 -1 -4 -3 -2 -1 0 -1 0]
[ 0 1 0 -2 -2 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 -1 0 0]
[ 0 0 1 2 -6 -5 -4 -3 -2 -1 0 1 -4 -3 -2 -1 0 1 -2 -1 0 -3 -2 -1 0 1 -1 0]
Degree: 22
Hilbert function: 1 + 14 t + 60 t2 + 161 t3 + 339 t4 + 616 t5 + 1014 t6 + 1555 t7 + 2261 t8 + 3154 t9 + 4256 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 208 1 Lattice Minkowski decompositions of facet 208
Image of facet 317 1 none
Image of facet 14 1 none
Polytope 4257
Image of polytope 4257 PALP id: 4257
grdb id: 520706
Integer points: [ 1 0 0 1 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 -1 0 0 0 0]
[ 0 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 1]
[ 0 0 2 -1 2 -4 1 0 -1 -2 -3 1 0 -1 -2 -3 0 -1 -2 2 1 0 -1 -2 1 0 -1 1]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 y*z2 + 2*y*z + x + y + 3*z + 2*x-1*z2 + 8*x-1*z + x*y-1*z-1 + 3*z-1 + 3*y-1 + 12*x-1 + 3*x-1*y-1*z + x-2*y-1*z2 + 6*y-1*z-1 + 8*x-1*z-1 + 12*x-1*y-1 + 6*x-2*y-1*z + 3*y-1*z-2 + 2*x-1*z-2 + 18*x-1*y-1*z-1 + 15*x-2*y-1 + 12*x-1*y-1*z-2 + 20*x-2*y-1*z-1 + 3*x-1*y-1*z-3 + 15*x-2*y-1*z-2 + 6*x-2*y-1*z-3 + x-2*y-1*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 212 1 Lattice Minkowski decompositions of facet 212
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Image of facet 241 1 Lattice Minkowski decompositions of facet 241
Polytope 4258
Image of polytope 4258 PALP id: 4258
grdb id: 520677
Integer points: [ 1 0 0 -1 -3 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 2 0 -6 -1 -2 -3 -4 -5 1 0 -1 -2 -3 -4 1 0 -1 -2 0 -1 -2 -3 1 0 -1]
[ 0 0 1 -2 -2 4 -1 0 1 2 3 -2 -1 0 1 2 3 -1 0 1 2 -1 0 1 2 -1 0 1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 318 1 Lattice Minkowski decompositions of facet 318
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Image of facet 14 1 none
Polytope 4259
Image of polytope 4259 PALP id: 4259
grdb id: 431910
Integer points: [ 1 0 0 -2 2 -4 2 -1 0 1 -3 -2 -1 0 1 2 -3 -2 -1 0 1 -1 0 1 -2 -1 0 1]
[ 0 1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0]
[ 0 0 1 2 -2 2 -4 1 0 -1 2 1 0 -1 -2 -3 1 0 -1 -2 -3 1 0 -1 1 0 -1 -2]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
11 rank 2, number 6 x + y + z + 2*x*z-1 + 2*x-1*z + x2*y-1*z-2 + 2*x*z-2 + 4*x*y-1*z-1 + 6*z-1 + 6*y-1 + 6*x-1 + 4*x-1*y-1*z + 2*x-2*z + x-2*y-1*z2 + 2*x2*y-1*z-3 + 10*x*y-1*z-2 + 20*y-1*z-1 + 20*x-1*y-1 + 10*x-2*y-1*z + 2*x-3*y-1*z2 + x2*y-1*z-4 + 6*x*y-1*z-3 + 15*y-1*z-2 + 20*x-1*y-1*z-1 + 15*x-2*y-1 + 6*x-3*y-1*z + x-4*y-1*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 49 1 Lattice Minkowski decompositions of facet 49
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Image of facet 312 1 Lattice Minkowski decompositions of facet 312
Polytope 4260
Image of polytope 4260 PALP id: 4260
grdb id: 431891
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0]
[ 0 1 1 -2 -2 1 1 -2 -1 -1 -1 -1 0 0 0 0 0 1 1 1 1 -1 -1 0 0 0 1 1]
[ 0 0 3 -4 -2 4 -1 -3 -3 -2 -1 0 -2 -1 0 1 2 0 1 2 3 -2 -1 -1 0 1 1 2]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 y*z3 + x-1*y*z4 + 3*y*z2 + 5*x-1*y*z3 + 3*y*z + 10*x-1*y*z2 + x + y + 3*z + 10*x-1*y*z + 3*x-1*z2 + 5*x-1*y + 12*x-1*z + 3*z-1 + x-1*y*z-1 + 18*x-1 + 2*y-1*z-1 + 12*x-1*z-1 + 3*x-1*y-1 + 2*y-1*z-2 + 3*x-1*z-2 + 9*x-1*y-1*z-1 + 9*x-1*y-1*z-2 + 3*x-1*y-1*z-3 + x-1*y-2*z-2 + 2*x-1*y-2*z-3 + x-1*y-2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 9 1 irreducible and admissible
Image of facet 146 1 Lattice Minkowski decompositions of facet 146
Image of facet 277 1 Lattice Minkowski decompositions of facet 277
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Polytope 4261
Image of polytope 4261 PALP id: 4261
grdb id: 431894
Integer points: [ 1 0 0 -1 0 -2 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0 -1 -1 -1 -1 0 0 0]
[ 0 1 0 2 -3 2 -5 1 0 -1 -2 -3 -4 1 0 -1 -2 -3 -4 -1 -2 1 0 -1 -2 1 0 -1]
[ 0 0 1 2 -2 3 -4 2 1 0 -1 -2 -3 2 1 0 -1 -2 -3 0 -1 1 0 -1 -2 1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x-1*y2*z2 + x-2*y2*z3 + 2*y*z + 2*x-1*y*z2 + x + y + z + 5*x-1*y*z + 7*x-2*y*z2 + 10*x-1*z + 3*y-1 + 9*x-1 + 21*x-2*z + 2*y-1*z-1 + 20*x-1*y-1 + 3*y-2*z-1 + 7*x-1*y-1*z-1 + 35*x-2*y-1 + 20*x-1*y-2*z-1 + y-3*z-2 + 2*x-1*y-2*z-2 + 35*x-2*y-2*z-1 + 10*x-1*y-3*z-2 + 21*x-2*y-3*z-2 + 2*x-1*y-4*z-3 + 7*x-2*y-4*z-3 + x-2*y-5*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 195 1 Lattice Minkowski decompositions of facet 195
Image of facet 22 1 Lattice Minkowski decompositions of facet 22
Image of facet 9 1 irreducible and admissible
Image of facet 319 1 Lattice Minkowski decompositions of facet 319
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 4262
Image of polytope 4262 PALP id: 4262
grdb id: 431807
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 1 0 2 2 -1 -6 -5 -4 -3 -2 -4 -3 -2 -1 0 -2 -1 0 1 0 1 -3 -2 -1 -1 0 1]
[ 0 0 1 -1 -2 2 2 2 2 2 2 1 1 1 1 1 0 0 0 0 -1 -1 1 1 1 0 0 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + 2*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 4*y-1*z + 3*x-1*z + x-1*y-1*z2 + x-1*y2*z-2 + 5*x-1*y*z-1 + 4*y-1 + 12*x-1 + 5*y-2*z + 13*x-1*y-1*z + 5*x-1*y-2*z2 + 4*x-1*z-1 + 15*x-1*y-1 + 2*y-3*z + 21*x-1*y-2*z + 10*x-1*y-3*z2 + 6*x-1*y-2 + 15*x-1*y-3*z + 10*x-1*y-4*z2 + 4*x-1*y-4*z + 5*x-1*y-5*z2 + x-1*y-6*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 298 1 Lattice Minkowski decompositions of facet 298
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 4263
Image of polytope 4263 PALP id: 4263
grdb id: 431653
Integer points: [ 1 0 0 -1 -1 -3 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 2 -2 -4 2 -3 -2 -1 0 1 -3 -2 -1 0 1 2 -1 0 1 -2 -1 0 1 -1 0 1]
[ 0 0 1 -2 2 2 -4 1 0 -1 -2 -3 2 1 0 -1 -2 -3 1 0 -1 1 0 -1 -2 1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 6*x-1*y*z-1 + 10*x-1 + 6*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*y*z-2 + 6*x-1*z-1 + 6*x-1*y-1 + 2*x-1*y-2*z + 2*x-2*y2*z-3 + 11*x-2*y*z-2 + 23*x-2*z-1 + 23*x-2*y-1 + 11*x-2*y-2*z + 2*x-2*y-3*z2 + x-3*y2*z-4 + 6*x-3*y*z-3 + 15*x-3*z-2 + 20*x-3*y-1*z-1 + 15*x-3*y-2 + 6*x-3*y-3*z + x-3*y-4*z2
20 rank 1, V16 x + y + z + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 5*x-1*y*z-1 + 8*x-1 + 5*x-1*y-1*z + x-1*y-2*z2 + 2*x-1*y*z-2 + 6*x-1*z-1 + 6*x-1*y-1 + 2*x-1*y-2*z + 2*x-2*y2*z-3 + 10*x-2*y*z-2 + 20*x-2*z-1 + 20*x-2*y-1 + 10*x-2*y-2*z + 2*x-2*y-3*z2 + x-3*y2*z-4 + 6*x-3*y*z-3 + 15*x-3*z-2 + 20*x-3*y-1*z-1 + 15*x-3*y-2 + 6*x-3*y-3*z + x-3*y-4*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 2 irreducible and admissible
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Image of facet 320 1 Lattice Minkowski decompositions of facet 320
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Polytope 4264
Image of polytope 4264 PALP id: 4264
grdb id: 431504
Integer points: [ 1 0 0 -1 -1 -3 -3 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -2 2 3 -4 2 1 0 -1 -2 -3 2 1 0 -1 -2 -3 1 0 -1 1 0 -1 -2 0 -1]
[ 0 0 1 0 -1 -2 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
10 rank 1, V18 x + y + z + x-1*y2*z-1 + 3*x-1*y + 5*x-1*y*z-1 + 3*x-2*y2*z-1 + 2*y-1 + 7*x-1 + x-3*y3*z-2 + 9*x-1*z-1 + 14*x-2*y*z-1 + 5*x-1*y-1 + 7*x-3*y2*z-2 + 7*x-1*y-1*z-1 + 26*x-2*z-1 + x-1*y-2 + 21*x-3*y*z-2 + 2*x-1*y-2*z-1 + 24*x-2*y-1*z-1 + 35*x-3*z-2 + 11*x-2*y-2*z-1 + 35*x-3*y-1*z-2 + 2*x-2*y-3*z-1 + 21*x-3*y-2*z-2 + 7*x-3*y-3*z-2 + x-3*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 195 1 Lattice Minkowski decompositions of facet 195
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 299 1 Lattice Minkowski decompositions of facet 299
Polytope 4265
Image of polytope 4265 PALP id: 4265
grdb id: 431508
Integer points: [ 1 0 0 -1 -1 -3 -3 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 1 1 1 -6 -5 -4 -3 -2 -1 0 -4 -3 -2 -1 0 1 -2 -1 0 -3 -2 -1 0 -1 0]
[ 0 0 1 0 -1 -2 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 0]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 299 1 Lattice Minkowski decompositions of facet 299
Image of facet 14 1 none
Image of facet 195 1 Lattice Minkowski decompositions of facet 195
Polytope 4266
Image of polytope 4266 PALP id: 4266
grdb id: 258004
Integer points: [ 1 0 0 2 -1 2 -2 -2 1 0 -1 1 0 -1 -2 0 -1 -2 -1 -2 1 0 -1 1 0 -1 0 -1]
[ 0 1 0 -1 2 -2 2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 1 1 -1 -1 -1 0 0 0 1 1]
[ 0 0 1 -1 -1 -1 -1 3 0 1 2 -1 0 1 2 -1 0 1 -1 0 0 1 2 -1 0 1 -1 0]
Degree: 8
Hilbert function: 1 + 7 t + 25 t2 + 63 t3 + 129 t4 + 231 t5 + 377 t6 + 575 t7 + 833 t8 + 1159 t9 + 1561 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
5 rank 1, V8 x + y + z + x2*y-1*z-1 + 3*x*z-1 + 3*y*z-1 + x-1*y2*z-1 + 4*x*y-1 + 4*x-1*y + 5*y-1*z + 5*x-1*z + 2*x-1*y-1*z2 + x2*y-2*z-1 + 4*x*y-1*z-1 + 6*z-1 + 4*x-1*y*z-1 + x-2*y2*z-1 + 4*x*y-2 + 12*y-1 + 12*x-1 + 4*x-2*y + 6*y-2*z + 12*x-1*y-1*z + 6*x-2*z + 4*x-1*y-2*z2 + 4*x-2*y-1*z2 + x-2*y-2*z3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 90 1 Lattice Minkowski decompositions of facet 90
Image of facet 107 2 Lattice Minkowski decompositions of facet 107
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 206 1 Lattice Minkowski decompositions of facet 206
Polytope 4267
Image of polytope 4267 PALP id: 4267
grdb id: 258031
Integer points: [ 1 0 0 0 -2 2 -4 2 -3 -2 -1 0 1 -3 -2 -1 0 1 -1 -2 -1 0 1 2 -1 0 1 1]
[ 0 1 0 0 2 -2 2 -4 1 0 -1 -2 -3 2 1 0 -1 -2 1 1 0 -1 -2 -3 1 0 -1 -1]
[ 0 0 1 -1 -1 1 -3 3 -2 -1 0 1 2 -2 -1 0 1 2 0 -2 -1 0 1 2 -1 0 1 0]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x + y + x2*y-2*z + 3*x*y-1*z + z + 2*x2*y-3*z2 + 2*x*y-2*z2 + x2*y-4*z3 + 2*x*y-1 + 2*x-1*y + 8*x*y-2*z + 8*y-1*z + 6*x*y-3*z2 + z-1 + 3*x-1*y*z-1 + x-2*y2*z-1 + 12*y-1 + 12*x-1 + 15*y-2*z + 8*x-1*z-1 + 8*x-2*y*z-1 + 20*x-1*y-1 + 2*x-2*y*z-2 + 2*x-3*y2*z-2 + 15*x-2*z-1 + 6*x-3*y*z-2 + x-4*y2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 2 irreducible and admissible
Image of facet 212 2 Lattice Minkowski decompositions of facet 212
Image of facet 30 2 Lattice Minkowski decompositions of facet 30
Polytope 4268
Image of polytope 4268 PALP id: 4268
grdb id: 258029
Integer points: [ 1 0 0 2 -1 -2 -2 2 1 -1 0 1 2 -1 0 1 -1 0 -1 0 1 -2 -1 0 1 -2 -1 0]
[ 0 1 0 -2 2 3 0 -4 -1 0 -1 -2 -3 1 0 -1 2 1 -1 -2 -3 1 0 -1 -2 2 1 0]
[ 0 0 1 1 -2 -2 1 1 1 1 1 1 1 0 0 0 -1 -1 1 1 1 0 0 0 0 -1 -1 -1]
Degree: 8
Hilbert function: 1 + 7 t + 25 t2 + 63 t3 + 129 t4 + 231 t5 + 377 t6 + 575 t7 + 833 t8 + 1159 t9 + 1561 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
5 rank 1, V8 x + y + x2*y-2*z + 2*x*y-1*z + z + 2*y*z-1 + 2*x-1*y2*z-1 + 4*x*y-1 + 4*x-1*y + 2*x2*y-3*z + 6*x*y-2*z + 6*y-1*z + 2*x-1*z + x-1*y2*z-2 + x-2*y3*z-2 + 3*z-1 + 6*x-1*y*z-1 + 3*x-2*y2*z-1 + 3*x*y-2 + 9*y-1 + 9*x-1 + 3*x-2*y + x2*y-4*z + 4*x*y-3*z + 6*y-2*z + 4*x-1*y-1*z + x-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 192 1 Lattice Minkowski decompositions of facet 192
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 127 1 Lattice Minkowski decompositions of facet 127
Polytope 4269
Image of polytope 4269 PALP id: 4269
grdb id: 257760
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 1 0 2 -1 2 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 0 1 1 1 -1 -1 -1 0 0 1]
[ 0 0 1 -1 2 -2 2 -2 -1 0 1 -2 -1 0 1 -2 -1 0 1 -2 -1 0 -1 0 1 -1 0 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + 2*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + x-1*y2*z-2 + 4*z-1 + 7*x-1*y*z-1 + 4*y-1 + 12*x-1 + 7*x-1*y-1*z + x-1*y-2*z2 + 4*x-1*y*z-2 + 2*y-1*z-1 + 15*x-1*z-1 + 15*x-1*y-1 + 4*x-1*y-2*z + 6*x-1*z-2 + 13*x-1*y-1*z-1 + 6*x-1*y-2 + 4*x-1*y-1*z-2 + 4*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 32 2 Lattice Minkowski decompositions of facet 32
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 303 1 Lattice Minkowski decompositions of facet 303
Polytope 4270
Image of polytope 4270 PALP id: 4270
grdb id: 257604
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 1 0 1 1 -1 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 0 -1 -1 -1 -1 0 0]
[ 0 0 1 0 -1 2 2 -4 1 0 -1 -2 -3 1 0 -1 -2 -3 1 0 -1 -2 1 0 -1 -2 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
18 rank 1, V14 x + y + z + x-1*y + 2*y-1*z + 2*x-1*z + x-1*y-1*z2 + 3*z-1 + x-1*y*z-1 + 6*y-1 + 7*x-1 + 7*x-1*y-1*z + x-1*y-2*z2 + 6*y-1*z-1 + 8*x-1*z-1 + 18*x-1*y-1 + 6*x-1*y-2*z + 2*y-1*z-2 + 3*x-1*z-2 + 22*x-1*y-1*z-1 + 15*x-1*y-2 + 13*x-1*y-1*z-2 + 20*x-1*y-2*z-1 + 3*x-1*y-1*z-3 + 15*x-1*y-2*z-2 + 6*x-1*y-2*z-3 + x-1*y-2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 302 1 Lattice Minkowski decompositions of facet 302
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Polytope 4271
Image of polytope 4271 PALP id: 4271
grdb id: 257945
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 1 0 2 2 -1 0 -4 -1 -2 -3 1 0 -1 -2 -3 1 0 -1 -2 1 0 0 -1 -2 1 0 -1]
[ 0 0 1 -1 -2 2 -2 2 -1 0 1 -2 -1 0 1 2 -1 0 1 2 0 1 -1 0 1 -1 0 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + 2*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 3*y-1*z + 3*x-1*z + x-1*y-1*z2 + x-1*y2*z-2 + 2*z-1 + 6*x-1*y*z-1 + 4*y-1 + 12*x-1 + 2*y-2*z + 10*x-1*y-1*z + 3*x-1*y-2*z2 + 2*x-1*y*z-2 + 9*x-1*z-1 + 15*x-1*y-1 + 11*x-1*y-2*z + 3*x-1*y-3*z2 + x-1*z-2 + 4*x-1*y-1*z-1 + 6*x-1*y-2 + 4*x-1*y-3*z + x-1*y-4*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 301 1 Lattice Minkowski decompositions of facet 301
Polytope 4272
Image of polytope 4272 PALP id: 4272
grdb id: 257862
Integer points: [ 1 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0]
[ 0 1 0 1 1 -1 1 -4 0 -2 -1 0 1 -3 -2 -1 0 1 -3 -2 -1 0 -1 0 1 -2 -1 0]
[ 0 0 1 0 -2 2 -3 2 1 2 1 0 -1 2 1 0 -1 -2 1 0 -1 -2 1 0 -1 1 0 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + 2*y*z-1 + x-1*y + 3*y-1*z + 2*x-1*z + x-1*y-1*z2 + y*z-2 + 4*z-1 + 3*x-1*y*z-1 + 5*y-1 + 9*x-1 + 2*y-2*z + 9*x-1*y-1*z + 3*x-1*y-2*z2 + 3*x-1*y*z-2 + 12*x-1*z-1 + 18*x-1*y-1 + 12*x-1*y-2*z + 3*x-1*y-3*z2 + x-1*y*z-3 + 5*x-1*z-2 + 10*x-1*y-1*z-1 + 10*x-1*y-2 + 5*x-1*y-3*z + x-1*y-4*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 277 1 Lattice Minkowski decompositions of facet 277
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 4273
Image of polytope 4273 PALP id: 4273
grdb id: 544474
Integer points: [ 1 0 0 -1 -9 -2 -3 -4 -5 -6 -7 -8 -1 -2 -3 -4 -5 -6 0 -1 -2 -3 0 -1 -2 -3 -4 0 -1]
[ 0 1 1 0 -8 -1 -2 -3 -4 -5 -6 -7 0 -1 -2 -3 -4 -5 1 0 -1 -2 0 -1 -2 -3 -4 0 -1]
[ 0 0 2 2 -6 1 0 -1 -2 -3 -4 -5 1 0 -1 -2 -3 -4 1 0 -1 -2 1 0 -1 -2 -3 0 -1]
Degree: 20
Hilbert function: 1 + 13 t + 55 t2 + 147 t3 + 309 t4 + 561 t5 + 923 t6 + 1415 t7 + 2057 t8 + 2869 t9 + 3871 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 208 1 Lattice Minkowski decompositions of facet 208
Image of facet 1 2 irreducible and admissible
Image of facet 14 1 none
Image of facet 321 1 Lattice Minkowski decompositions of facet 321
Polytope 4274
Image of polytope 4274 PALP id: 4274
grdb id: 520538
Integer points: [ 1 0 0 1 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 -1 0 0 0 1 0]
[ 0 1 1 -2 1 1 1 1 1 1 1 0 0 0 0 0 -1 -1 -1 1 1 1 1 1 0 0 0 -1 1]
[ 0 0 2 -2 4 -2 3 2 1 0 -1 2 1 0 -1 -2 0 -1 -2 3 2 1 0 -1 1 0 -1 -1 1]
Degree: 8
Hilbert function: 1 + 7 t + 25 t2 + 63 t3 + 129 t4 + 231 t5 + 377 t6 + 575 t7 + 833 t8 + 1159 t9 + 1561 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
5 rank 1, V8 y*z2 + 2*x-1*y*z3 + x-2*y*z4 + 2*y*z + 8*x-1*y*z2 + 6*x-2*y*z3 + x + y + 4*z + 12*x-1*y*z + 3*x-1*z2 + 15*x-2*y*z2 + 8*x-1*y + 12*x-1*z + 20*x-2*y*z + 2*x*y-1*z-1 + 4*z-1 + 2*x-1*y*z-1 + 3*y-1 + 18*x-1 + 15*x-2*y + 6*y-1*z-1 + 12*x-1*z-1 + 6*x-2*y*z-1 + x*y-2*z-2 + 3*y-1*z-2 + 3*x-1*z-2 + x-2*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Image of facet 212 1 Lattice Minkowski decompositions of facet 212
Image of facet 241 1 Lattice Minkowski decompositions of facet 241
Polytope 4275
Image of polytope 4275 PALP id: 4275
grdb id: 520517
Integer points: [ 1 0 0 -1 -3 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 0 -1 -1 -1 -1 0 0 0]
[ 0 1 1 0 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0 0 0 1 -1 -1 -1 -1 0 0 0]
[ 0 0 2 -2 -4 2 1 0 -1 -2 -3 2 1 0 -1 -2 -3 2 1 0 -1 1 1 0 -1 -2 1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 322 1 Lattice Minkowski decompositions of facet 322
Image of facet 14 1 none
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Polytope 4276
Image of polytope 4276 PALP id: 4276
grdb id: 520484
Integer points: [ 1 0 0 1 1 -6 -5 -4 -3 -2 -1 0 -4 -3 -2 -1 0 1 -2 -1 0 -3 -2 -1 0 1 -1 0 1]
[ 0 1 0 -2 -4 3 2 1 0 -1 -2 -3 2 1 0 -1 -2 -3 1 0 -1 2 1 0 -1 -2 1 0 -1]
[ 0 0 1 0 -2 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 -1 0 0 0]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 215 1 Lattice Minkowski decompositions of facet 215
Image of facet 299 1 Lattice Minkowski decompositions of facet 299
Image of facet 14 1 none
Polytope 4277
Image of polytope 4277 PALP id: 4277
grdb id: 431397
Integer points: [ 1 0 0 0 0 -2 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -2 1 -4 3 2 1 0 -1 -2 -3 2 1 0 -1 -2 -3 0 -1 2 1 0 -1 -2 1 0 -1]
[ 0 0 1 1 -2 3 -4 -3 -2 -1 0 1 2 -3 -2 -1 0 1 2 -1 0 -2 -1 0 1 2 -1 0 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
11 rank 2, number 6 x + y + z + 2*y*z-1 + 2*y-1*z + y*z-2 + 2*x-1*y2*z-2 + 3*z-1 + 8*x-1*y*z-1 + 3*y-1 + 12*x-1 + y-2*z + 8*x-1*y-1*z + 2*x-1*y-2*z2 + 2*x-1*y2*z-3 + 10*x-1*y*z-2 + 20*x-1*z-1 + 20*x-1*y-1 + 10*x-1*y-2*z + 2*x-1*y-3*z2 + x-2*y3*z-4 + 7*x-2*y2*z-3 + 21*x-2*y*z-2 + 35*x-2*z-1 + 35*x-2*y-1 + 21*x-2*y-2*z + 7*x-2*y-3*z2 + x-2*y-4*z3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 9 1 irreducible and admissible
Image of facet 215 1 Lattice Minkowski decompositions of facet 215
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Image of facet 319 1 Lattice Minkowski decompositions of facet 319
Polytope 4278
Image of polytope 4278 PALP id: 4278
grdb id: 431130
Integer points: [ 1 0 0 0 -1 -3 -3 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 -1 2 3 -4 2 1 0 -1 -2 -3 2 1 0 -1 -2 -3 1 0 -1 -2 1 0 -1 -2 0 -1]
[ 0 0 1 1 -1 -2 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0 0 0 -1 -1 -1 -1 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 3 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 195 1 Lattice Minkowski decompositions of facet 195
Image of facet 308 1 Lattice Minkowski decompositions of facet 308
Image of facet 14 1 none
Polytope 4279
Image of polytope 4279 PALP id: 4279
grdb id: 257048
Integer points: [ 1 0 0 -1 0 3 -3 0 -2 -1 0 -1 0 1 0 1 2 -2 -1 -2 -1 0 1 -1 0 1 2 1 2]
[ 0 1 0 1 -2 -2 1 1 1 1 1 0 0 0 -1 -1 -1 1 1 0 0 0 0 -1 -1 -1 -1 -2 -2]
[ 0 0 1 1 1 -2 1 -2 1 0 -1 1 0 -1 1 0 -1 0 -1 1 0 -1 -2 1 0 -1 -2 0 -1]
Degree: 8
Hilbert function: 1 + 7 t + 25 t2 + 63 t3 + 129 t4 + 231 t5 + 377 t6 + 575 t7 + 833 t8 + 1159 t9 + 1561 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
5 rank 1, V8 x + y + z + x-1*y*z + 2*x2*y-1*z-1 + 4*x*z-1 + 2*y*z-1 + 4*x*y-1 + 4*x-1*y + 2*y-1*z + 4*x-1*z + 2*x-2*y*z + x3*y-2*z-2 + 3*x2*y-1*z-2 + 3*x*z-2 + y*z-2 + 3*x2*y-2*z-1 + 9*x*y-1*z-1 + 9*z-1 + 3*x-1*y*z-1 + 3*x*y-2 + 9*y-1 + 9*x-1 + 3*x-2*y + y-2*z + 3*x-1*y-1*z + 3*x-2*z + x-3*y*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 35 4 Lattice Minkowski decompositions of facet 35
Image of facet 243 1 Lattice Minkowski decompositions of facet 243
Polytope 4280
Image of polytope 4280 PALP id: 4280
grdb id: 257095
Integer points: [ 1 0 0 -1 -2 0 3 -2 -1 -2 -1 0 1 -2 -1 0 1 2 -1 0 1 2 -1 0 1 -1 0 1 2]
[ 0 1 0 1 1 1 -2 -2 1 0 0 0 0 -1 -1 -1 -1 -1 -2 -2 -2 -2 0 0 0 -1 -1 -1 -1]
[ 0 0 1 1 1 -1 -4 1 0 1 0 -1 -2 1 0 -1 -2 -3 0 -1 -2 -3 1 0 -1 1 0 -1 -2]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x + y + z + x-1*y*z + 3*x*z-1 + y*z-1 + 2*x-1*y + 3*x-1*z + x-2*y*z + 2*x2*y-1*z-2 + 3*x*z-2 + 6*x*y-1*z-1 + 9*z-1 + 6*y-1 + 9*x-1 + 2*x-1*y-1*z + 3*x-2*z + 3*x2*y-1*z-3 + 12*x*y-1*z-2 + 18*y-1*z-1 + 12*x-1*y-1 + 3*x-2*y-1*z + x3*y-2*z-4 + 5*x2*y-2*z-3 + 10*x*y-2*z-2 + 10*y-2*z-1 + 5*x-1*y-2 + x-2*y-2*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 277 1 Lattice Minkowski decompositions of facet 277
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Polytope 4281
Image of polytope 4281 PALP id: 4281
grdb id: 547396
Integer points: [ 1 1 1 -5 0 -1 -2 -3 -4 1 0 -1 -2 -3 1 0 -1 1 0 -1 -2 -3 1 0 -1 1 1 0 -1 1]
[ 0 3 0 -6 -1 -2 -3 -4 -5 1 0 -1 -2 -3 2 1 0 0 -1 -2 -3 -4 1 0 -1 2 0 -1 -2 1]
[ 0 0 3 -3 2 1 0 -1 -2 2 1 0 -1 -2 1 0 -1 2 1 0 -1 -2 1 0 -1 0 1 0 -1 0]
Degree: 6
Hilbert function: 1 + 6 t + 20 t2 + 49 t3 + 99 t4 + 176 t5 + 286 t6 + 435 t7 + 629 t8 + 874 t9 + 1176 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
19 rank 1, V6 x*y3 + 3*x*y2*z + 3*x*y*z2 + x*z3 + 3*x*y2 + 6*x*y*z + 3*x*z2 + 3*x*y + 3*x*z + x + 6*y + 12*z + 6*y-1*z2 + 12*y-1*z + 6*y-1 + 3*x-1*z-1 + 18*x-1*y-1 + 15*x-1*y-2*z + 6*x-1*y-1*z-1 + 18*x-1*y-2 + 3*x-1*y-2*z-1 + 12*x-2*y-2*z-1 + 20*x-2*y-3 + 12*x-2*y-3*z-1 + 3*x-3*y-3*z-2 + 15*x-3*y-4*z-1 + 3*x-3*y-4*z-2 + 6*x-4*y-5*z-2 + x-5*y-6*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 241 2 Lattice Minkowski decompositions of facet 241
Image of facet 52 2 Lattice Minkowski decompositions of facet 52
Polytope 4282
Image of polytope 4282 PALP id: 4282
grdb id: 547395
Integer points: [ 1 0 0 -9 -8 -7 -6 -5 -4 -3 -2 -1 -6 -5 -4 -3 -2 -1 0 -3 -2 -1 0 -4 -3 -2 -1 0 -1 0]
[ 0 1 1 -8 -7 -6 -5 -4 -3 -2 -1 0 -5 -4 -3 -2 -1 0 1 -2 -1 0 1 -4 -3 -2 -1 0 -1 0]
[ 0 0 3 -6 -5 -4 -3 -2 -1 0 1 2 -4 -3 -2 -1 0 1 2 -2 -1 0 1 -3 -2 -1 0 1 -1 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 9 1 irreducible and admissible
Image of facet 323 1 none
Image of facet 324 1 Lattice Minkowski decompositions of facet 324
Image of facet 14 1 none
Polytope 4283
Image of polytope 4283 PALP id: 4283
grdb id: 544447
Integer points: [ 1 1 -2 1 -2 -1 0 -2 -1 0 1 -2 -1 0 1 -1 0 -1 0 1 -1 0 1 -1 0 1 0 1 0 1]
[ 0 3 -3 0 0 1 2 -1 0 1 2 -2 -1 0 1 -2 -1 0 1 2 -1 0 1 -2 -1 0 0 1 -1 0]
[ 0 0 0 3 -3 -2 -1 -2 -1 0 1 -1 0 1 2 1 2 -2 -1 0 -1 0 1 0 1 2 -1 0 0 1]
Degree: 6
Hilbert function: 1 + 6 t + 20 t2 + 49 t3 + 99 t4 + 176 t5 + 286 t6 + 435 t7 + 629 t8 + 874 t9 + 1176 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
19 rank 1, V6 x*y3 + 3*x*y2*z + 3*x*y*z2 + x*z3 + 3*x*y2 + 6*x*y*z + 3*x*z2 + 3*x*y + 3*x*z + 3*y2*z-1 + x + 9*y + 9*z + 3*y-1*z2 + 6*y*z-1 + 6*y-1*z + 3*z-1 + 3*y-1 + 3*x-1*y*z-2 + 9*x-1*z-1 + 9*x-1*y-1 + 3*x-1*y-2*z + 3*x-1*z-2 + 6*x-1*y-1*z-1 + 3*x-1*y-2 + x-2*z-3 + 3*x-2*y-1*z-2 + 3*x-2*y-2*z-1 + x-2*y-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 243 1 Lattice Minkowski decompositions of facet 243
Image of facet 52 4 Lattice Minkowski decompositions of facet 52
Polytope 4284
Image of polytope 4284 PALP id: 4284
grdb id: 544458
Integer points: [ 1 0 0 -3 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 -1 -1 -1 -1 0 0 0]
[ 0 1 1 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0 0 0 0 1 1 -1 -1 -1 -1 0 0 0]
[ 0 0 3 0 -6 -1 -2 -3 -4 -5 1 0 -1 -2 -3 -4 2 1 0 -1 -2 2 1 0 -1 -2 -3 1 0 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 9 1 irreducible and admissible
Image of facet 325 1 Lattice Minkowski decompositions of facet 325
Image of facet 14 2 none
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Polytope 4285
Image of polytope 4285 PALP id: 4285
grdb id: 520428
Integer points: [ 1 1 0 0 1 -3 0 -1 -2 1 0 -1 -2 1 0 -1 1 0 -1 -2 1 0 -1 1 0 1 0 -1 1 0]
[ 0 3 0 3 -3 -3 -3 -3 -3 -1 -1 -1 -1 1 1 1 -2 -2 -2 -2 0 0 0 2 2 -1 -1 -1 1 1]
[ 0 0 1 1 -3 1 -2 -1 0 -2 -1 0 1 -1 0 1 -2 -1 0 1 -1 0 1 0 1 -1 0 1 0 1]
Degree: 6
Hilbert function: 1 + 6 t + 20 t2 + 49 t3 + 99 t4 + 176 t5 + 286 t6 + 435 t7 + 629 t8 + 874 t9 + 1176 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
19 rank 1, V6 x*y3 + y3*z + 3*x*y2 + 3*y2*z + 3*x*y + 3*y*z + 3*x*y*z-1 + x + 6*y + z + 3*x-1*y*z + 6*x*z-1 + 6*x-1*z + 3*x*y-1*z-1 + 6*y-1 + 3*x-1*y-1*z + 3*x*y-1*z-2 + 9*y-1*z-1 + 9*x-1*y-1 + 3*x-2*y-1*z + 3*x*y-2*z-2 + 9*y-2*z-1 + 9*x-1*y-2 + 3*x-2*y-2*z + x*y-3*z-3 + 4*y-3*z-2 + 6*x-1*y-3*z-1 + 4*x-2*y-3 + x-3*y-3*z
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 192 2 Lattice Minkowski decompositions of facet 192
Image of facet 52 2 Lattice Minkowski decompositions of facet 52
Image of facet 60 1 Lattice Minkowski decompositions of facet 60
Polytope 4286
Image of polytope 4286 PALP id: 4286
grdb id: 520416
Integer points: [ 1 1 1 -2 1 -2 -1 0 -1 0 1 0 1 -2 -1 0 1 -1 0 1 0 1 1 -1 0 -1 0 1 0 1]
[ 0 2 0 -3 2 -1 -2 -1 -2 -1 0 -1 0 -2 -1 0 1 -1 0 1 0 1 1 0 1 0 1 2 1 2]
[ 0 0 3 -3 3 -3 -1 1 -2 0 2 -1 1 -3 -1 1 3 -2 0 2 -1 1 0 -1 1 -2 0 2 -1 1]
Degree: 6
Hilbert function: 1 + 6 t + 20 t2 + 49 t3 + 99 t4 + 176 t5 + 286 t6 + 435 t7 + 629 t8 + 874 t9 + 1176 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
19 rank 1, V6 x*y2*z3 + 3*x*y2*z2 + 2*x*y*z3 + 3*x*y2*z + 6*x*y*z2 + x*z3 + x*y2 + 6*x*y*z + 3*x*z2 + 2*x*y + 3*x*z + 3*y*z + x + 6*y + 6*z + 3*y*z-1 + 3*y-1*z + 6*z-1 + 6*y-1 + 3*y-1*z-1 + 3*x-1*z-1 + 3*x-1*z-2 + 6*x-1*y-1*z-1 + 6*x-1*y-1*z-2 + 3*x-1*y-2*z-1 + 3*x-1*y-2*z-2 + x-2*y-1*z-3 + 2*x-2*y-2*z-3 + x-2*y-3*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 52 2 Lattice Minkowski decompositions of facet 52
Image of facet 125 3 Lattice Minkowski decompositions of facet 125
Polytope 4287
Image of polytope 4287 PALP id: 4287
grdb id: 520423
Integer points: [ 1 0 0 1 1 -6 -5 -4 -3 -2 -1 0 -4 -3 -2 -1 0 1 -2 -1 0 1 -3 -2 -1 0 1 -1 0 1]
[ 0 1 0 -1 -4 3 2 1 0 -1 -2 -3 2 1 0 -1 -2 -3 1 0 -1 -2 2 1 0 -1 -2 1 0 -1]
[ 0 0 1 1 -2 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0 0 0 -1 -1 -1 -1 -1 0 0 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 3 1 Lattice Minkowski decompositions of facet 3
Image of facet 308 1 Lattice Minkowski decompositions of facet 308
Image of facet 14 2 none
Image of facet 215 1 Lattice Minkowski decompositions of facet 215
Polytope 4288
Image of polytope 4288 PALP id: 4288
grdb id: 520369
Integer points: [ 1 0 0 -2 -3 -3 -3 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 2 2 -6 -5 -4 -3 -2 -1 0 1 -4 -3 -2 -1 0 1 -2 -1 0 1 -3 -2 -1 0 1 -1 0]
[ 0 0 1 -1 -2 -2 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0 0 0 -1 -1 -1 -1 -1 0 0]
Degree: 18
Hilbert function: 1 + 12 t + 50 t2 + 133 t3 + 279 t4 + 506 t5 + 832 t6 + 1275 t7 + 1853 t8 + 2584 t9 + 3486 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 321 1 Lattice Minkowski decompositions of facet 321
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Image of facet 208 1 Lattice Minkowski decompositions of facet 208
Image of facet 14 1 none
Polytope 4289
Image of polytope 4289 PALP id: 4289
grdb id: 431045
Integer points: [ 1 0 0 1 1 -2 -2 1 0 0 0 0 -1 -1 -1 -1 -1 -2 -2 -2 -2 1 1 0 0 0 -1 -1 -1 -1]
[ 0 1 0 0 -2 -2 3 -1 1 0 -1 -2 2 1 0 -1 -2 2 1 0 -1 0 -1 1 0 -1 2 1 0 -1]
[ 0 0 1 -2 0 3 -2 -1 -2 -1 0 1 -2 -1 0 1 2 -1 0 1 2 -1 0 -1 0 1 -1 0 1 2]
Degree: 8
Hilbert function: 1 + 7 t + 25 t2 + 63 t3 + 129 t4 + 231 t5 + 377 t6 + 575 t7 + 833 t8 + 1159 t9 + 1561 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
5 rank 1, V8 x + y + z + 2*x*z-1 + 4*y*z-1 + 2*x-1*y2*z-1 + 2*x*y-1 + 6*x-1*y + 4*y-1*z + 6*x-1*z + 2*x-1*y-1*z2 + x*z-2 + 3*y*z-2 + 3*x-1*y2*z-2 + x-2*y3*z-2 + 2*x*y-1*z-1 + 9*z-1 + 12*x-1*y*z-1 + 5*x-2*y2*z-1 + x*y-2 + 9*y-1 + 18*x-1 + 10*x-2*y + 3*y-2*z + 12*x-1*y-1*z + 10*x-2*z + 3*x-1*y-2*z2 + 5*x-2*y-1*z2 + x-2*y-2*z3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Image of facet 277 1 Lattice Minkowski decompositions of facet 277
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Polytope 4290
Image of polytope 4290 PALP id: 4290
grdb id: 431005
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0]
[ 0 1 1 1 0 1 -4 0 -1 -2 -3 1 0 -1 -2 -3 1 0 -1 -2 1 0 -1 0 -1 -2 1 0 -1 0]
[ 0 0 2 -1 -2 3 -2 2 1 0 -1 2 1 0 -1 -2 1 0 -1 -2 0 -1 -2 1 0 -1 1 0 -1 -1]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 y*z2 + x-1*y*z3 + 2*y*z + 4*x-1*y*z2 + x + y + 4*z + 6*x-1*y*z + 5*x-1*z2 + 4*x-1*y + 16*x-1*z + 2*z-1 + x-1*y*z-1 + 5*y-1 + 18*x-1 + 10*x-1*y-1*z + 4*y-1*z-1 + 8*x-1*z-1 + 24*x-1*y-1 + x-1*z-2 + 2*y-2*z-1 + 18*x-1*y-1*z-1 + 10*x-1*y-2 + 4*x-1*y-1*z-2 + 16*x-1*y-2*z-1 + 6*x-1*y-2*z-2 + 5*x-1*y-3*z-1 + 4*x-1*y-3*z-2 + x-1*y-4*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 1 irreducible and admissible
Image of facet 307 1 Lattice Minkowski decompositions of facet 307
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 103 1 Lattice Minkowski decompositions of facet 103
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 4291
Image of polytope 4291 PALP id: 4291
grdb id: 431051
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0]
[ 0 1 1 1 1 -2 -2 1 1 1 0 0 0 0 0 -1 -1 -1 -1 -1 -2 -2 -2 1 0 0 0 -1 -1 -1]
[ 0 0 2 3 -1 -4 0 2 1 0 2 1 0 -1 -2 1 0 -1 -2 -3 -1 -2 -3 1 1 0 -1 0 -1 -2]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 y*z2 + x-1*y*z3 + 2*y*z + 4*x-1*y*z2 + x + y + 3*z + 6*x-1*y*z + 3*x-1*z2 + 4*x-1*y + 12*x-1*z + 3*z-1 + x-1*y*z-1 + 2*y-1 + 18*x-1 + 3*x-1*y-1*z + 4*y-1*z-1 + 12*x-1*z-1 + 12*x-1*y-1 + 2*y-1*z-2 + 3*x-1*z-2 + 18*x-1*y-1*z-1 + x-1*y-2 + 12*x-1*y-1*z-2 + 4*x-1*y-2*z-1 + 3*x-1*y-1*z-3 + 6*x-1*y-2*z-2 + 4*x-1*y-2*z-3 + x-1*y-2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 1 1 irreducible and admissible
Image of facet 59 1 Lattice Minkowski decompositions of facet 59
Image of facet 309 1 Lattice Minkowski decompositions of facet 309
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Polytope 4292
Image of polytope 4292 PALP id: 4292
grdb id: 431027
Integer points: [ 1 0 0 -2 1 1 -5 0 -1 -2 -3 -4 1 0 -1 -2 -3 -4 0 -1 -2 -3 -1 1 0 -1 -2 1 0 -1]
[ 0 1 0 2 -2 -4 2 -3 -2 -1 0 1 -3 -2 -1 0 1 2 -1 0 1 2 1 -2 -1 0 1 -1 0 1]
[ 0 0 1 -1 2 2 -4 1 0 -1 -2 -3 2 1 0 -1 -2 -3 1 0 -1 -2 0 1 0 -1 -2 1 0 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + 2*x*y-1*z + z + x*y-2*z2 + 2*x-1*y + 2*x*y-2*z + 6*y-1*z + 2*x*y-3*z2 + 3*x-1*y*z-1 + x-2*y2*z-1 + 6*y-1 + 12*x-1 + 11*y-2*z + x*y-4*z2 + 6*x-1*z-1 + 10*x-2*y*z-1 + 24*x-1*y-1 + 6*y-3*z + 2*x-2*y*z-2 + 3*x-3*y2*z-2 + 26*x-2*z-1 + 15*x-1*y-2 + 14*x-3*y*z-2 + 20*x-2*y-1*z-1 + 3*x-4*y2*z-3 + 15*x-3*z-2 + 6*x-4*y*z-3 + x-5*y2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 322 1 Lattice Minkowski decompositions of facet 322
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 11 1 Lattice Minkowski decompositions of facet 11
Polytope 4293
Image of polytope 4293 PALP id: 4293
grdb id: 430976
Integer points: [ 1 0 1 0 1 1 -6 0 -1 -2 -3 -4 -5 1 0 -1 -2 -3 -4 1 0 -1 -2 0 -1 -2 -3 1 0 -1]
[ 0 1 -1 0 -2 -4 3 -3 -2 -1 0 1 2 -3 -2 -1 0 1 2 -2 -1 0 1 -1 0 1 2 -1 0 1]
[ 0 0 0 1 -2 -3 4 -2 -1 0 1 2 3 -2 -1 0 1 2 3 -1 0 1 2 -1 0 1 2 -1 0 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
7 rank 1, V12 x + y + z + 3*x-1*y*z + 3*x-2*y*z2 + 2*x-3*y2*z2 + 3*x-4*y2*z3 + x-6*y3*z4 + x*y-1 + 9*x-1*z + 7*x-2*y*z + 15*x-3*y*z2 + 7*x-5*y2*z3 + 2*x*y-1*z-1 + 9*y-1 + 9*x-1 + 30*x-2*z + 21*x-4*y*z2 + 3*x*y-2*z-1 + 5*y-1*z-1 + 30*x-1*y-1 + 35*x-3*z + x*y-2*z-2 + 15*y-2*z-1 + 35*x-2*y-1 + 3*x*y-3*z-2 + 21*x-1*y-2*z-1 + 7*y-3*z-2 + x*y-4*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 195 1 Lattice Minkowski decompositions of facet 195
Image of facet 308 1 Lattice Minkowski decompositions of facet 308
Image of facet 25 1 Lattice Minkowski decompositions of facet 25
Image of facet 44 1 Lattice Minkowski decompositions of facet 44
Polytope 4294
Image of polytope 4294 PALP id: 4294
grdb id: 544439
Integer points: [ 1 1 1 -1 -7 -2 -3 -4 -5 -6 0 -1 -2 -3 -4 -5 0 -1 -2 -3 1 0 -1 0 -1 -2 -3 1 0 -1 1]
[ 0 2 0 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0 0 0 1 1 1 -1 -1 -1 -1 0 0 0 1]
[ 0 0 2 2 -4 1 0 -1 -2 -3 2 1 0 -1 -2 -3 1 0 -1 -2 1 0 -1 1 0 -1 -2 1 0 -1 0]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x*y2 + 2*x*y*z + x*z2 + 2*x*y + 2*x*z + x + 6*y + 8*z + 2*y-1*z2 + 2*y-1*z + 4*x-1*y*z-1 + 19*x-1 + 12*x-1*y-1*z + x-1*y-2*z2 + 4*x-1*z-1 + 6*x-1*y-1 + 18*x-2*z-1 + 28*x-2*y-1 + 6*x-2*y-2*z + 6*x-2*y-1*z-1 + 6*x-3*z-2 + 32*x-3*y-1*z-1 + 15*x-3*y-2 + 2*x-3*y-1*z-2 + 18*x-4*y-1*z-2 + 20*x-4*y-2*z-1 + 4*x-5*y-1*z-3 + 15*x-5*y-2*z-2 + 6*x-6*y-2*z-3 + x-7*y-2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 32 1 Lattice Minkowski decompositions of facet 32
Image of facet 326 1 Lattice Minkowski decompositions of facet 326
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Polytope 4295
Image of polytope 4295 PALP id: 4295
grdb id: 544441
Integer points: [ 1 0 1 -1 -9 -2 -3 -4 -5 -6 -7 -8 0 -1 -2 -3 -4 -5 -6 0 -1 -2 -3 0 -1 -2 -3 -4 1 0 -1]
[ 0 1 0 -2 -2 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 2 2 -6 1 0 -1 -2 -3 -4 -5 2 1 0 -1 -2 -3 -4 1 0 -1 -2 1 0 -1 -2 -3 1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 208 1 Lattice Minkowski decompositions of facet 208
Image of facet 14 1 none
Image of facet 327 1 Lattice Minkowski decompositions of facet 327
Polytope 4296
Image of polytope 4296 PALP id: 4296
grdb id: 520331
Integer points: [ 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 1 1 1]
[ 0 2 0 -2 -2 2 -2 -2 -2 -1 -1 -1 -1 0 0 0 1 1 -1 -1 -1 -1 0 0 0 1 1 2 0 1 1]
[ 0 0 2 2 -2 -2 -1 0 1 -2 -1 0 1 -2 -1 0 -2 -1 -1 0 1 2 -1 0 1 -1 0 -1 1 0 1]
Degree: 6
Hilbert function: 1 + 6 t + 20 t2 + 49 t3 + 99 t4 + 176 t5 + 286 t6 + 435 t7 + 629 t8 + 874 t9 + 1176 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
19 rank 1, V6 x*y2 + 2*x*y*z + x*z2 + 2*x*y + 2*x*z + 2*y2*z-1 + x + 6*y + 6*z + 2*y-1*z2 + 6*y*z-1 + 6*y-1*z + x-1*y2*z-2 + 6*z-1 + 4*x-1*y*z-1 + 6*y-1 + 6*x-1 + 4*x-1*y-1*z + x-1*y-2*z2 + 4*x-1*y*z-2 + 2*y-1*z-1 + 12*x-1*z-1 + 12*x-1*y-1 + 4*x-1*y-2*z + 6*x-1*z-2 + 12*x-1*y-1*z-1 + 6*x-1*y-2 + 4*x-1*y-1*z-2 + 4*x-1*y-2*z-1 + x-1*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 206 1 Lattice Minkowski decompositions of facet 206
Image of facet 127 3 Lattice Minkowski decompositions of facet 127
Polytope 4297
Image of polytope 4297 PALP id: 4297
grdb id: 520329
Integer points: [ 1 0 0 1 1 -4 -1 0 1 -2 -1 0 1 -3 -2 -1 0 1 -3 -2 -1 0 0 1 -1 0 1 -2 -1 0 1]
[ 0 1 1 0 -4 1 1 0 -1 1 0 -1 -2 1 0 -1 -2 -3 0 -1 -2 -3 1 0 1 0 -1 1 0 -1 -2]
[ 0 0 2 2 -2 -2 1 1 1 0 0 0 0 -1 -1 -1 -1 -1 -2 -2 -2 -2 1 1 0 0 0 -1 -1 -1 -1]
Degree: 8
Hilbert function: 1 + 7 t + 25 t2 + 63 t3 + 129 t4 + 231 t5 + 377 t6 + 575 t7 + 833 t8 + 1159 t9 + 1561 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
5 rank 1, V8 x*z2 + y*z2 + 2*x*z + 2*y*z + x + y + 4*x*y-1*z + 8*z + 4*x-1*y*z + 4*x*y-1 + 4*x-1*y + 6*x*y-2 + 18*y-1 + 18*x-1 + 6*x-2*y + 2*x*y-2*z-1 + 6*y-1*z-1 + 6*x-1*z-1 + 2*x-2*y*z-1 + 4*x*y-3*z-1 + 16*y-2*z-1 + 24*x-1*y-1*z-1 + 16*x-2*z-1 + 4*x-3*y*z-1 + x*y-4*z-2 + 5*y-3*z-2 + 10*x-1*y-2*z-2 + 10*x-2*y-1*z-2 + 5*x-3*z-2 + x-4*y*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 2 Lattice Minkowski decompositions of facet 32
Image of facet 129 1 Lattice Minkowski decompositions of facet 129
Image of facet 307 1 Lattice Minkowski decompositions of facet 307
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Polytope 4298
Image of polytope 4298 PALP id: 4298
grdb id: 520332
Integer points: [ 1 0 1 1 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 0 0 1 1 1 -1 -1 -1 0 0 0 1 1 1]
[ 0 1 0 -4 3 -1 2 1 0 2 1 0 -1 -2 1 0 -1 -2 -3 -1 -2 -3 2 1 0 1 0 -1 0 -1 -2]
[ 0 0 2 -2 2 -2 1 0 -1 2 1 0 -1 -2 2 1 0 -1 -2 1 0 -1 1 0 -1 1 0 -1 1 0 -1]
Degree: 8
Hilbert function: 1 + 7 t + 25 t2 + 63 t3 + 129 t4 + 231 t5 + 377 t6 + 575 t7 + 833 t8 + 1159 t9 + 1561 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
5 rank 1, V8 x*z2 + 3*y*z2 + 3*x-1*y2*z2 + x-2*y3*z2 + 2*x*z + 4*y*z + 2*x-1*y2*z + x + y + 4*x*y-1*z + 12*z + 12*x-1*y*z + 4*x-2*y2*z + 4*x*y-1 + 4*x-1*y + 6*x*y-2 + 18*y-1 + 18*x-1 + 6*x-2*y + 2*x*y-2*z-1 + 4*y-1*z-1 + 2*x-1*z-1 + 4*x*y-3*z-1 + 12*y-2*z-1 + 12*x-1*y-1*z-1 + 4*x-2*z-1 + x*y-4*z-2 + 3*y-3*z-2 + 3*x-1*y-2*z-2 + x-2*y-1*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 2 Lattice Minkowski decompositions of facet 32
Image of facet 35 2 Lattice Minkowski decompositions of facet 35
Image of facet 309 1 Lattice Minkowski decompositions of facet 309
Polytope 4299
Image of polytope 4299 PALP id: 4299
grdb id: 520330
Integer points: [ 1 0 0 0 -2 -2 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 1 -3 -5 3 2 1 0 -1 -2 -3 -4 2 1 0 -1 -2 -3 -4 0 -1 -2 2 1 0 -1 -2 1 0 -1]
[ 0 0 2 -2 -4 4 3 2 1 0 -1 -2 -3 3 2 1 0 -1 -2 -3 1 0 -1 2 1 0 -1 -2 1 0 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
11 rank 2, number 6 x-2*y3*z4 + 2*x-1*y2*z3 + y*z2 + 2*x-1*y2*z2 + 8*x-2*y2*z3 + 2*y*z + 12*x-1*y*z2 + x + y + 4*z + 8*x-1*y*z + 28*x-2*y*z2 + 30*x-1*z + 6*y-1 + 12*x-1 + 56*x-2*z + 2*y-1*z-1 + 40*x-1*y-1 + 4*y-2*z-1 + 8*x-1*y-1*z-1 + 70*x-2*y-1 + 30*x-1*y-2*z-1 + y-3*z-2 + 2*x-1*y-2*z-2 + 56*x-2*y-2*z-1 + 12*x-1*y-3*z-2 + 28*x-2*y-3*z-2 + 2*x-1*y-4*z-3 + 8*x-2*y-4*z-3 + x-2*y-5*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 208 1 Lattice Minkowski decompositions of facet 208
Image of facet 328 1 Lattice Minkowski decompositions of facet 328
Image of facet 13 1 irreducible and admissible
Image of facet 22 2 Lattice Minkowski decompositions of facet 22
Polytope 4300
Image of polytope 4300 PALP id: 4300
grdb id: 520319
Integer points: [ 1 1 1 -1 -1 -5 0 -2 -1 0 1 -3 -2 -1 0 -4 -3 -2 -1 0 -4 -3 -2 0 1 -1 0 1 -2 -1 0]
[ 0 2 0 2 -2 -2 -1 -2 -1 0 1 -2 -1 0 1 -2 -1 0 1 2 -1 0 1 -1 0 -1 0 1 -1 0 1]
[ 0 0 2 -2 2 -2 2 1 1 1 1 0 0 0 0 -1 -1 -1 -1 -1 -2 -2 -2 1 1 0 0 0 -1 -1 -1]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x*y2 + 2*x*y*z + x*z2 + 2*x*y + 2*x*z + 2*y2*z-1 + x + 8*y + 8*z + 2*y-1*z2 + 2*y*z-1 + 2*y-1*z + x-1*y2*z-2 + 10*x-1*y*z-1 + 19*x-1 + 10*x-1*y-1*z + x-1*y-2*z2 + 4*x-1*z-1 + 4*x-1*y-1 + 4*x-2*y*z-2 + 18*x-2*z-1 + 18*x-2*y-1 + 4*x-2*y-2*z + 2*x-2*y-1*z-1 + 6*x-3*z-2 + 14*x-3*y-1*z-1 + 6*x-3*y-2 + 4*x-4*y-1*z-2 + 4*x-4*y-2*z-1 + x-5*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 3 Lattice Minkowski decompositions of facet 16
Image of facet 32 2 Lattice Minkowski decompositions of facet 32
Image of facet 329 1 Lattice Minkowski decompositions of facet 329
Polytope 4301
Image of polytope 4301 PALP id: 4301
grdb id: 520292
Integer points: [ 1 0 1 -3 -7 1 0 -1 -2 -3 -4 -5 -6 1 0 -1 -2 -3 -4 -5 0 -1 -2 1 0 -1 -2 -3 1 0 -1]
[ 0 1 0 0 -2 -2 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 2 -2 -4 4 3 2 1 0 -1 -2 -3 3 2 1 0 -1 -2 -3 1 0 -1 2 1 0 -1 -2 1 0 -1]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
40 rank 2, number 10 x*z2 + 2*x*y-1*z3 + x*y-2*z4 + 2*x*z + 2*x*y-1*z2 + x + y + 6*z + 13*y-1*z2 + 8*y-2*z3 + 8*y-1*z + 10*x-1 + 34*x-1*y-1*z + 28*x-1*y-2*z2 + 2*x-1*z-1 + 12*x-1*y-1 + 6*x-2*z-1 + 46*x-2*y-1 + 56*x-2*y-2*z + 8*x-2*y-1*z-1 + x-3*z-2 + 34*x-3*y-1*z-1 + 70*x-3*y-2 + 2*x-3*y-1*z-2 + 13*x-4*y-1*z-2 + 56*x-4*y-2*z-1 + 2*x-5*y-1*z-3 + 28*x-5*y-2*z-2 + 8*x-6*y-2*z-3 + x-7*y-2*z-4
20 rank 1, V16 x*z2 + 2*x*y-1*z3 + x*y-2*z4 + 2*x*z + 2*x*y-1*z2 + x + y + 5*z + 12*y-1*z2 + 8*y-2*z3 + 8*y-1*z + 8*x-1 + 30*x-1*y-1*z + 28*x-1*y-2*z2 + 2*x-1*z-1 + 12*x-1*y-1 + 5*x-2*z-1 + 40*x-2*y-1 + 56*x-2*y-2*z + 8*x-2*y-1*z-1 + x-3*z-2 + 30*x-3*y-1*z-1 + 70*x-3*y-2 + 2*x-3*y-1*z-2 + 12*x-4*y-1*z-2 + 56*x-4*y-2*z-1 + 2*x-5*y-1*z-3 + 28*x-5*y-2*z-2 + 8*x-6*y-2*z-3 + x-7*y-2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 2 Lattice Minkowski decompositions of facet 16
Image of facet 1 2 irreducible and admissible
Image of facet 330 1 Lattice Minkowski decompositions of facet 330
Image of facet 208 1 Lattice Minkowski decompositions of facet 208
Polytope 4302
Image of polytope 4302 PALP id: 4302
grdb id: 430778
Integer points: [ 1 0 0 1 1 -2 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 0 0 0 0 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -1 0 -4 3 2 1 0 -1 -2 -3 2 1 0 -1 -2 -3 1 0 -1 -2 2 1 0 -1 -2 1 0 -1]
[ 0 0 1 0 -1 3 -4 -3 -2 -1 0 1 2 -3 -2 -1 0 1 2 -2 -1 0 1 -2 -1 0 1 2 -1 0 1]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x + y + z + x*z-1 + 3*y*z-1 + x*y-1 + 3*y-1*z + 3*y*z-2 + 2*x-1*y2*z-2 + 9*z-1 + 8*x-1*y*z-1 + 9*y-1 + 12*x-1 + 3*y-2*z + 8*x-1*y-1*z + 2*x-1*y-2*z2 + 3*x-1*y2*z-3 + 15*x-1*y*z-2 + 30*x-1*z-1 + 30*x-1*y-1 + 15*x-1*y-2*z + 3*x-1*y-3*z2 + x-2*y3*z-4 + 7*x-2*y2*z-3 + 21*x-2*y*z-2 + 35*x-2*z-1 + 35*x-2*y-1 + 21*x-2*y-2*z + 7*x-2*y-3*z2 + x-2*y-4*z3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Image of facet 308 1 Lattice Minkowski decompositions of facet 308
Image of facet 215 1 Lattice Minkowski decompositions of facet 215
Polytope 4303
Image of polytope 4303 PALP id: 4303
grdb id: 520261
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0]
[ 0 1 1 1 1 -4 0 -1 -2 -3 1 0 -1 -2 -3 1 0 -1 -2 1 0 -1 1 0 0 -1 -2 1 0 -1 1 0]
[ 0 0 3 -1 4 -6 2 0 -2 -4 3 1 -1 -3 -5 2 0 -2 -4 1 -1 -3 0 -2 1 -1 -3 2 0 -2 1 -1]
Degree: 8
Hilbert function: 1 + 7 t + 25 t2 + 63 t3 + 129 t4 + 231 t5 + 377 t6 + 575 t7 + 833 t8 + 1159 t9 + 1561 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
5 rank 1, V8 y*z3 + x-1*y*z4 + 3*y*z2 + 5*x-1*y*z3 + 3*y*z + 10*x-1*y*z2 + x + y + 4*z + 10*x-1*y*z + 5*x-1*z2 + 5*x-1*y + 20*x-1*z + 4*z-1 + x-1*y*z-1 + 30*x-1 + 5*y-1*z-1 + 20*x-1*z-1 + 10*x-1*y-1 + 5*y-1*z-2 + 5*x-1*z-2 + 30*x-1*y-1*z-1 + 30*x-1*y-1*z-2 + 2*y-2*z-3 + 10*x-1*y-1*z-3 + 10*x-1*y-2*z-2 + 20*x-1*y-2*z-3 + 10*x-1*y-2*z-4 + 5*x-1*y-3*z-4 + 5*x-1*y-3*z-5 + x-1*y-4*z-6
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 9 1 irreducible and admissible
Image of facet 146 1 Lattice Minkowski decompositions of facet 146
Image of facet 316 1 Lattice Minkowski decompositions of facet 316
Image of facet 103 2 Lattice Minkowski decompositions of facet 103
Polytope 4304
Image of polytope 4304 PALP id: 4304
grdb id: 520244
Integer points: [ 1 0 0 -1 -3 -3 -3 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 2 2 -6 1 0 -1 -2 -3 -4 -5 2 1 0 -1 -2 -3 -4 1 0 -1 -2 1 0 -1 -2 -3 1 0 -1]
[ 0 0 1 -2 -4 4 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 -1 0 1 2 -2 -1 0 1 2 -1 0 1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 1 1 irreducible and admissible
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 331 1 Lattice Minkowski decompositions of facet 331
Image of facet 208 1 Lattice Minkowski decompositions of facet 208
Image of facet 14 1 none
Polytope 4305
Image of polytope 4305 PALP id: 4305
grdb id: 520236
Integer points: [ 1 0 0 -1 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0]
[ 0 1 0 2 3 -6 -5 -4 -3 -2 -1 0 1 2 -4 -3 -2 -1 0 1 2 -2 -1 0 1 -3 -2 -1 0 1 -1 0]
[ 0 0 1 -1 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 -1 -1 -1 -1 -1 0 0]
Degree: 16
Hilbert function: 1 + 11 t + 45 t2 + 119 t3 + 249 t4 + 451 t5 + 741 t6 + 1135 t7 + 1649 t8 + 2299 t9 + 3101 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 324 1 Lattice Minkowski decompositions of facet 324
Image of facet 14 1 none
Image of facet 332 1 Lattice Minkowski decompositions of facet 332
Polytope 4306
Image of polytope 4306 PALP id: 4306
grdb id: 430676
Integer points: [ 1 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0]
[ 0 1 0 -1 2 2 -4 0 1 -2 -1 0 1 2 -3 -2 -1 0 1 2 -3 -2 -1 0 1 -1 0 1 -2 -1 0 1]
[ 0 0 1 2 -1 -4 2 1 0 2 1 0 -1 -2 2 1 0 -1 -2 -3 1 0 -1 -2 -3 1 0 -1 1 0 -1 -2]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x + y + z + 3*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 3*y-1*z + 3*x-1*z + x-1*y-1*z2 + 2*y*z-2 + 3*x-1*y2*z-2 + 6*z-1 + 12*x-1*y*z-1 + 6*y-1 + 18*x-1 + 2*y-2*z + 12*x-1*y-1*z + 3*x-1*y-2*z2 + 3*x-1*y2*z-3 + 15*x-1*y*z-2 + 30*x-1*z-1 + 30*x-1*y-1 + 15*x-1*y-2*z + 3*x-1*y-3*z2 + x-1*y2*z-4 + 6*x-1*y*z-3 + 15*x-1*z-2 + 20*x-1*y-1*z-1 + 15*x-1*y-2 + 6*x-1*y-3*z + x-1*y-4*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Image of facet 20 1 Lattice Minkowski decompositions of facet 20
Image of facet 325 1 Lattice Minkowski decompositions of facet 325
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Polytope 4307
Image of polytope 4307 PALP id: 4307
grdb id: 544419
Integer points: [ 1 0 0 -3 -3 -3 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 1 -2 -2 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 2 2 -6 1 0 -1 -2 -3 -4 -5 2 1 0 -1 -2 -3 -4 2 1 0 -1 -2 1 1 0 -1 -2 -3 1 0 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 208 1 Lattice Minkowski decompositions of facet 208
Image of facet 1 1 irreducible and admissible
Image of facet 333 1 Lattice Minkowski decompositions of facet 333
Image of facet 14 2 none
Polytope 4308
Image of polytope 4308 PALP id: 4308
grdb id: 544417
Integer points: [ 1 0 0 3 -6 2 1 0 -1 -2 -3 -4 -5 2 1 0 -1 -2 -3 -4 1 0 -1 -2 2 1 0 -1 -2 -3 1 0 -1]
[ 0 1 0 -6 3 -5 -4 -3 -2 -1 0 1 2 -4 -3 -2 -1 0 1 2 -2 -1 0 1 -3 -2 -1 0 1 2 -1 0 1]
[ 0 0 1 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 -1 -1 -1 -1 -1 -1 0 0 0]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 324 1 Lattice Minkowski decompositions of facet 324
Image of facet 14 2 none
Image of facet 334 1 Lattice Minkowski decompositions of facet 334
Polytope 4309
Image of polytope 4309 PALP id: 4309
grdb id: 520190
Integer points: [ 1 0 0 -2 3 -2 2 1 0 -1 2 1 0 -1 -2 1 0 -1 -2 0 -1 -2 -1 -2 2 1 0 -1 1 0 -1 0 -1 -1]
[ 0 1 0 -2 -2 3 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 0 1 1 1 2 2 -1 -1 -1 -1 0 0 0 1 1 2]
[ 0 0 1 3 -2 -2 -1 0 1 2 -2 -1 0 1 2 -2 -1 0 1 -2 -1 0 -2 -1 -1 0 1 2 -1 0 1 -1 0 -1]
Degree: 6
Hilbert function: 1 + 6 t + 20 t2 + 49 t3 + 99 t4 + 176 t5 + 286 t6 + 435 t7 + 629 t8 + 874 t9 + 1176 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
19 rank 1, V6 x + y + z + 2*x2*y-1*z-1 + 6*x*z-1 + 6*y*z-1 + 2*x-1*y2*z-1 + 6*x*y-1 + 6*x-1*y + 6*y-1*z + 6*x-1*z + 2*x-1*y-1*z2 + x3*y-2*z-2 + 5*x2*y-1*z-2 + 10*x*z-2 + 10*y*z-2 + 5*x-1*y2*z-2 + x-2*y3*z-2 + 5*x2*y-2*z-1 + 20*x*y-1*z-1 + 30*z-1 + 20*x-1*y*z-1 + 5*x-2*y2*z-1 + 10*x*y-2 + 30*y-1 + 30*x-1 + 10*x-2*y + 10*y-2*z + 20*x-1*y-1*z + 10*x-2*z + 5*x-1*y-2*z2 + 5*x-2*y-1*z2 + x-2*y-2*z3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 129 3 Lattice Minkowski decompositions of facet 129
Image of facet 316 1 Lattice Minkowski decompositions of facet 316
Polytope 4310
Image of polytope 4310 PALP id: 4310
grdb id: 520191
Integer points: [ 1 0 0 -2 3 -5 -4 -3 -2 -1 0 1 2 -4 -3 -2 -1 0 1 2 -3 -2 -1 0 1 -1 -2 -1 0 1 2 -1 0 1]
[ 0 1 0 2 -6 2 1 0 -1 -2 -3 -4 -5 2 1 0 -1 -2 -3 -4 2 1 0 -1 -2 1 1 0 -1 -2 -3 1 0 -1]
[ 0 0 1 -1 4 -4 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 -2 -1 0 1 2 0 -2 -1 0 1 2 -1 0 1]
Degree: 10
Hilbert function: 1 + 8 t + 30 t2 + 77 t3 + 159 t4 + 286 t5 + 468 t6 + 715 t7 + 1037 t8 + 1444 t9 + 1946 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
9 rank 1, V10 x + y + 3*x*y-1*z + z + 2*x2*y-3*z2 + 3*x*y-2*z2 + 3*x2*y-4*z3 + x3*y-6*z4 + 2*x-1*y + 8*x*y-2*z + 12*y-1*z + 18*x*y-3*z2 + 8*x2*y-5*z3 + 3*x-1*y*z-1 + x-2*y2*z-1 + 12*y-1 + 18*x-1 + 45*y-2*z + 28*x*y-4*z2 + 8*x-1*z-1 + 12*x-2*y*z-1 + 60*x-1*y-1 + 56*y-3*z + 2*x-2*y*z-2 + 3*x-3*y2*z-2 + 45*x-2*z-1 + 70*x-1*y-2 + 18*x-3*y*z-2 + 56*x-2*y-1*z-1 + 3*x-4*y2*z-3 + 28*x-3*z-2 + 8*x-4*y*z-3 + x-5*y2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 208 1 Lattice Minkowski decompositions of facet 208
Image of facet 1 1 irreducible and admissible
Image of facet 333 1 Lattice Minkowski decompositions of facet 333
Image of facet 25 2 Lattice Minkowski decompositions of facet 25
Polytope 4311
Image of polytope 4311 PALP id: 4311
grdb id: 547390
Integer points: [ 1 1 1 -3 -2 -1 0 -2 -1 0 1 -1 0 1 0 1 -2 -1 0 1 -1 0 1 0 1 1 -1 0 1 0 1 1 0 1 1]
[ 0 4 0 -4 -3 -2 -1 -2 -1 0 1 0 1 2 2 3 -3 -2 -1 0 -1 0 1 1 2 3 -2 -1 0 0 1 2 -1 0 1]
[ 0 0 4 -4 -2 0 2 -3 -1 1 3 -2 0 2 -1 1 -3 -1 1 3 -2 0 2 -1 1 0 -2 0 2 -1 1 0 -1 1 0]
Degree: 4
Hilbert function: 1 + 5 t + 15 t2 + 35 t3 + 69 t4 + 121 t5 + 195 t6 + 295 t7 + 425 t8 + 589 t9 + 791 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
15 rank 1, V4 x*y4 + 4*x*y3*z + 6*x*y2*z2 + 4*x*y*z3 + x*z4 + 4*x*y3 + 12*x*y2*z + 12*x*y*z2 + 4*x*z3 + 6*x*y2 + 12*x*y*z + 6*x*z2 + 4*x*y + 4*x*z + 4*y2*z-1 + x + 12*y + 12*z + 4*y-1*z2 + 12*y*z-1 + 12*y-1*z + 12*z-1 + 12*y-1 + 4*y-1*z-1 + 6*x-1*z-2 + 12*x-1*y-1*z-1 + 6*x-1*y-2 + 12*x-1*y-1*z-2 + 12*x-1*y-2*z-1 + 6*x-1*y-2*z-2 + 4*x-2*y-2*z-3 + 4*x-2*y-3*z-2 + 4*x-2*y-3*z-3 + x-3*y-4*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 206 4 Lattice Minkowski decompositions of facet 206
Polytope 4312
Image of polytope 4312 PALP id: 4312
grdb id: 547389
Integer points: [ 1 1 1 -7 0 -1 -2 -3 -4 -5 -6 1 0 -1 -2 -3 -4 -5 1 0 -1 -2 -3 1 0 -1 1 0 -1 -2 -3 1 0 -1 1]
[ 0 2 2 -6 1 0 -1 -2 -3 -4 -5 2 1 0 -1 -2 -3 -4 2 1 0 -1 -2 2 1 0 1 0 -1 -2 -3 1 0 -1 1]
[ 0 0 4 -4 3 2 1 0 -1 -2 -3 3 2 1 0 -1 -2 -3 2 1 0 -1 -2 1 0 -1 2 1 0 -1 -2 1 0 -1 0]
Degree: 8
Hilbert function: 1 + 7 t + 25 t2 + 63 t3 + 129 t4 + 231 t5 + 377 t6 + 575 t7 + 833 t8 + 1159 t9 + 1561 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
5 rank 1, V8 x*y2*z4 + 4*x*y2*z3 + 6*x*y2*z2 + 4*x*y2*z + 2*x*y*z2 + 8*y*z3 + x*y2 + 4*x*y*z + 24*y*z2 + 2*x*y + 24*y*z + x + 8*y + 8*z + 28*x-1*z2 + 60*x-1*z + 36*x-1 + 4*x-1*z-1 + 12*x-1*y-1 + 56*x-2*y-1*z + 4*x-1*y-1*z-1 + 80*x-2*y-1 + 24*x-2*y-1*z-1 + 8*x-2*y-2*z-1 + 70*x-3*y-2 + 60*x-3*y-2*z-1 + 6*x-3*y-2*z-2 + 2*x-3*y-3*z-2 + 56*x-4*y-3*z-1 + 24*x-4*y-3*z-2 + 28*x-5*y-4*z-2 + 4*x-5*y-4*z-3 + 8*x-6*y-5*z-3 + x-7*y-6*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 2 Lattice Minkowski decompositions of facet 32
Image of facet 208 1 Lattice Minkowski decompositions of facet 208
Image of facet 335 1 Lattice Minkowski decompositions of facet 335
Polytope 4313
Image of polytope 4313 PALP id: 4313
grdb id: 544405
Integer points: [ 1 1 1 -3 -3 1 0 0 0 0 -1 -1 -1 -1 -1 -2 -2 -2 -2 -2 -2 -3 -3 -3 -3 -3 1 1 0 0 0 -1 -1 -1 -1]
[ 0 2 0 -4 2 1 -1 0 1 2 -2 -1 0 1 2 -3 -2 -1 0 1 2 -3 -2 -1 0 1 0 1 -1 0 1 -2 -1 0 1]
[ 0 0 2 2 -4 1 2 1 0 -1 2 1 0 -1 -2 2 1 0 -1 -2 -3 1 0 -1 -2 -3 1 0 1 0 -1 1 0 -1 -2]
Degree: 8
Hilbert function: 1 + 7 t + 25 t2 + 63 t3 + 129 t4 + 231 t5 + 377 t6 + 575 t7 + 833 t8 + 1159 t9 + 1561 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
5 rank 1, V8 x*y2 + 2*x*y*z + x*z2 + 2*x*y + 2*x*z + 4*y2*z-1 + x + 12*y + 12*z + 4*y-1*z2 + 4*y*z-1 + 4*y-1*z + 6*x-1*y2*z-2 + 24*x-1*y*z-1 + 36*x-1 + 24*x-1*y-1*z + 6*x-1*y-2*z2 + 2*x-1*y*z-2 + 6*x-1*z-1 + 6*x-1*y-1 + 2*x-1*y-2*z + 4*x-2*y2*z-3 + 20*x-2*y*z-2 + 40*x-2*z-1 + 40*x-2*y-1 + 20*x-2*y-2*z + 4*x-2*y-3*z2 + x-3*y2*z-4 + 6*x-3*y*z-3 + 15*x-3*z-2 + 20*x-3*y-1*z-1 + 15*x-3*y-2 + 6*x-3*y-3*z + x-3*y-4*z2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 32 2 Lattice Minkowski decompositions of facet 32
Image of facet 336 1 Lattice Minkowski decompositions of facet 336
Image of facet 119 1 Lattice Minkowski decompositions of facet 119
Polytope 4314
Image of polytope 4314 PALP id: 4314
grdb id: 544406
Integer points: [ 1 1 -3 1 -3 -3 -3 -3 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 0 0 1 1 1 -1 -1 -1 0 0 0 1 1 1]
[ 0 2 -2 2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 0 0 1 1 1 1 1 2 2 2 -1 -1 -1 0 0 0 1 1 1]
[ 0 0 0 4 -4 -3 -2 -1 -3 -2 -1 0 1 -2 -1 0 1 2 -1 0 1 2 3 1 2 3 -2 -1 0 -1 0 1 0 1 2]
Degree: 8
Hilbert function: 1 + 7 t + 25 t2 + 63 t3 + 129 t4 + 231 t5 + 377 t6 + 575 t7 + 833 t8 + 1159 t9 + 1561 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
5 rank 1, V8 x*y2*z4 + 4*x*y2*z3 + 6*x*y2*z2 + 4*x*y2*z + 2*x*y*z2 + 4*y*z3 + x*y2 + 4*x*y*z + 16*y*z2 + 2*x*y + 24*y*z + x + 16*y + 4*z + 6*x-1*z2 + 4*y*z-1 + 24*x-1*z + 4*z-1 + 36*x-1 + 24*x-1*z-1 + 2*x-1*y-1 + 4*x-2*y-1*z + 6*x-1*z-2 + 4*x-1*y-1*z-1 + 16*x-2*y-1 + 2*x-1*y-1*z-2 + 24*x-2*y-1*z-1 + 16*x-2*y-1*z-2 + x-3*y-2 + 4*x-2*y-1*z-3 + 4*x-3*y-2*z-1 + 6*x-3*y-2*z-2 + 4*x-3*y-2*z-3 + x-3*y-2*z-4
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 32 4 Lattice Minkowski decompositions of facet 32
Image of facet 337 1 Lattice Minkowski decompositions of facet 337
Polytope 4315
Image of polytope 4315 PALP id: 4315
grdb id: 544404
Integer points: [ 1 0 1 1 -9 0 -1 -2 -3 -4 -5 -6 -7 -8 1 0 -1 -2 -3 -4 -5 -6 0 -1 -2 -3 1 0 -1 -2 -3 -4 1 0 -1]
[ 0 1 0 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 2 4 -6 3 2 1 0 -1 -2 -3 -4 -5 3 2 1 0 -1 -2 -3 -4 1 0 -1 -2 2 1 0 -1 -2 -3 1 0 -1]
Degree: 14
Hilbert function: 1 + 10 t + 40 t2 + 105 t3 + 219 t4 + 396 t5 + 650 t6 + 995 t7 + 1445 t8 + 2014 t9 + 2716 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 16 1 Lattice Minkowski decompositions of facet 16
Image of facet 1 1 irreducible and admissible
Image of facet 338 1 Lattice Minkowski decompositions of facet 338
Image of facet 339 1 Lattice Minkowski decompositions of facet 339
Image of facet 14 1 none
Polytope 4316
Image of polytope 4316 PALP id: 4316
grdb id: 544400
Integer points: [ 1 0 0 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0]
[ 0 1 0 -6 4 3 2 1 0 -1 -2 -3 -4 -5 3 2 1 0 -1 -2 -3 -4 2 1 0 -1 -2 2 1 0 -1 -2 -3 1 0 -1]
[ 0 0 1 4 -6 -5 -4 -3 -2 -1 0 1 2 3 -4 -3 -2 -1 0 1 2 3 -2 -1 0 1 2 -3 -2 -1 0 1 2 -1 0 1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 1 irreducible and admissible
Image of facet 339 1 Lattice Minkowski decompositions of facet 339
Image of facet 340 1 Lattice Minkowski decompositions of facet 340
Image of facet 14 2 none
Polytope 4317
Image of polytope 4317 PALP id: 4317
grdb id: 547387
Integer points: [ 1 1 1 -5 -4 -3 -2 -1 0 -4 -3 -2 -1 0 1 -3 -2 -1 0 1 -2 -1 0 1 -1 0 1 0 1 -2 -1 0 1 -1 0 1 0 1 1]
[ 0 2 2 -4 -3 -2 -1 0 1 -3 -2 -1 0 1 2 -2 -1 0 1 2 -1 0 1 2 0 1 2 1 2 -2 -1 0 1 -1 0 1 0 1 1]
[ 0 0 6 -6 -4 -2 0 2 4 -5 -3 -1 1 3 5 -4 -2 0 2 4 -3 -1 1 3 -2 0 2 -1 1 -3 -1 1 3 -2 0 2 -1 1 0]
Degree: 6
Hilbert function: 1 + 6 t + 20 t2 + 49 t3 + 99 t4 + 176 t5 + 286 t6 + 435 t7 + 629 t8 + 874 t9 + 1176 t10 + ...
Polynomials:
Period sequence Fano variety Laurent polynomial
19 rank 1, V6 x*y2*z6 + 6*x*y2*z5 + 15*x*y2*z4 + 20*x*y2*z3 + 15*x*y2*z2 + 2*x*y*z3 + 6*y*z4 + 6*x*y2*z + 6*x*y*z2 + 30*y*z3 + x*y2 + 6*x*y*z + 60*y*z2 + 2*x*y + 60*y*z + x + 30*y + 6*z + 15*x-1*z2 + 6*y*z-1 + 60*x-1*z + 6*z-1 + 90*x-1 + 60*x-1*z-1 + 15*x-1*z-2 + 6*x-1*y-1*z-1 + 20*x-2*y-1 + 6*x-1*y-1*z-2 + 60*x-2*y-1*z-1 + 60*x-2*y-1*z-2 + 20*x-2*y-1*z-3 + 2*x-2*y-2*z-3 + 15*x-3*y-2*z-2 + 30*x-3*y-2*z-3 + 15*x-3*y-2*z-4 + 6*x-4*y-3*z-4 + 6*x-4*y-3*z-5 + x-5*y-4*z-6
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 341 1 Lattice Minkowski decompositions of facet 341
Image of facet 119 3 Lattice Minkowski decompositions of facet 119
Polytope 4318
Image of polytope 4318 PALP id: 4318
grdb id: 547388
Integer points: [ 1 0 3 -9 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 2 1 0 -1 -2 -3 -4 -5 -6 1 0 -1 -2 -3 2 1 0 -1 -2 -3 -4 1 0 -1]
[ 0 1 4 -8 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 3 2 1 0 -1 -2 -3 -4 -5 2 1 0 -1 -2 2 1 0 -1 -2 -3 -4 1 0 -1]
[ 0 0 6 -6 5 4 3 2 1 0 -1 -2 -3 -4 -5 4 3 2 1 0 -1 -2 -3 -4 2 1 0 -1 -2 3 2 1 0 -1 -2 -3 1 0 -1]
Degree: 12
Hilbert function: 1 + 9 t + 35 t2 + 91 t3 + 189 t4 + 341 t5 + 559 t6 + 855 t7 + 1241 t8 + 1729 t9 + 2331 t10 + ...
Polynomials: none
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 14 2 none
Image of facet 342 1 Lattice Minkowski decompositions of facet 342
Image of facet 343 1 Lattice Minkowski decompositions of facet 343