Polytope 4168
Image of polytope 4168 PALP id: 4168
grdb id: 264855
Integer points: [ 1 0 0 -2 -2 2 -4 2 -3 -2 -1 0 1 -3 -2 -1 0 1 -1 -1 0 1 -1 0 1]
[ 0 1 0 2 1 -3 2 -4 1 0 -1 -2 -3 2 1 0 -1 -2 1 0 -1 -2 1 0 -1]
[ 0 0 1 -1 -2 2 -3 3 -2 -1 0 1 2 -2 -1 0 1 2 0 -1 0 1 -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
11 rank 2, number 6 x + y + 2*x*y-1*z + z + x2*y-3*z2 + 2*x*y-2*z2 + x2*y-4*z3 + 2*x-1*y + 4*x*y-2*z + 8*y-1*z + 6*x*y-3*z2 + 2*x-1*y*z-1 + x-2*y2*z-1 + 6*y-1 + 12*x-1 + 15*y-2*z + 4*x-1*z-1 + 8*x-2*y*z-1 + 20*x-1*y-1 + x-2*y*z-2 + 2*x-3*y2*z-2 + 15*x-2*z-1 + 6*x-3*y*z-2 + x-4*y2*z-3
22 rank 3, number 1 x + y + 3*x*y-1*z + z + x2*y-3*z2 + 2*x*y-2*z2 + x2*y-4*z3 + 2*x-1*y + 4*x*y-2*z + 8*y-1*z + 6*x*y-3*z2 + 3*x-1*y*z-1 + x-2*y2*z-1 + 6*y-1 + 12*x-1 + 15*y-2*z + 4*x-1*z-1 + 8*x-2*y*z-1 + 20*x-1*y-1 + x-2*y*z-2 + 2*x-3*y2*z-2 + 15*x-2*z-1 + 6*x-3*y*z-2 + x-4*y2*z-3
7 rank 1, V12 x + y + 2*x*y-1*z + z + x2*y-3*z2 + 2*x*y-2*z2 + x2*y-4*z3 + 2*x-1*y + 4*x*y-2*z + 8*y-1*z + 6*x*y-3*z2 + 3*x-1*y*z-1 + x-2*y2*z-1 + 6*y-1 + 12*x-1 + 15*y-2*z + 4*x-1*z-1 + 8*x-2*y*z-1 + 20*x-1*y-1 + x-2*y*z-2 + 2*x-3*y2*z-2 + 15*x-2*z-1 + 6*x-3*y*z-2 + x-4*y2*z-3
7 rank 1, V12 x + y + 3*x*y-1*z + z + x2*y-3*z2 + 2*x*y-2*z2 + x2*y-4*z3 + 2*x-1*y + 4*x*y-2*z + 8*y-1*z + 6*x*y-3*z2 + 2*x-1*y*z-1 + x-2*y2*z-1 + 6*y-1 + 12*x-1 + 15*y-2*z + 4*x-1*z-1 + 8*x-2*y*z-1 + 20*x-1*y-1 + x-2*y*z-2 + 2*x-3*y2*z-2 + 15*x-2*z-1 + 6*x-3*y*z-2 + x-4*y2*z-3
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 1 1 irreducible and admissible
Image of facet 23 2 Lattice Minkowski decompositions of facet 23
Image of facet 212 1 Lattice Minkowski decompositions of facet 212
Image of facet 13 1 irreducible and admissible
Image of facet 173 1 Lattice Minkowski decompositions of facet 173
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