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 rank 4, number 1 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
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