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
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