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 rank 3, number 1 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
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