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
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