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 rank 3, number 1 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
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