Polytope 3504
Image of polytope 3504 PALP id: 3504
grdb id: 610803
Integer points: [ 1 1 -1 -1 0 0 -1 -1 2 2 1 1 1 0 0 0 -1 -1 -1]
[ 0 2 -2 0 0 1 -3 0 2 3 1 1 2 -1 0 1 -2 -1 -1]
[ 0 0 0 0 1 1 -1 -1 1 1 0 1 1 0 0 0 -1 -1 0]
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 x2*y3*z + x2*y2*z + 2*x*y2*z + x*y2 + 2*x*y*z + 2*x*y + y*z + x + 2*y + z + 3*y-1 + x-1 + x-1*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2 + 3*x-1*y-2*z-1 + x-1*y-3*z-1
22 rank 3, number 1 x2*y3*z + x2*y2*z + 2*x*y2*z + x*y2 + 2*x*y*z + 2*x*y + y*z + x + 3*y + z + 3*y-1 + x-1 + x-1*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2 + 3*x-1*y-2*z-1 + x-1*y-3*z-1
7 rank 1, V12 x2*y3*z + x2*y2*z + 2*x*y2*z + x*y2 + 2*x*y*z + 2*x*y + y*z + x + 3*y + z + 2*y-1 + x-1 + x-1*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2 + 3*x-1*y-2*z-1 + x-1*y-3*z-1
11 rank 2, number 6 x2*y3*z + x2*y2*z + 2*x*y2*z + x*y2 + 2*x*y*z + 2*x*y + y*z + x + 2*y + z + 2*y-1 + x-1 + x-1*z-1 + 2*x-1*y-1 + 3*x-1*y-1*z-1 + x-1*y-2 + 3*x-1*y-2*z-1 + x-1*y-3*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 15 1 Lattice Minkowski decompositions of facet 15
Image of facet 11 2 Lattice Minkowski decompositions of facet 11
Image of facet 44 2 Lattice Minkowski decompositions of facet 44
Image of facet 23 2 Lattice Minkowski decompositions of facet 23
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