Polytope 3867
Image of polytope 3867 PALP id: 3867
grdb id: 29624
Integer points: [ 1 0 0 1 1 1 1 -2 -2 1 -3 0 -1 -2 0 -1 0 -1 1 0 -1]
[ 0 1 0 0 -1 -1 -2 2 1 -2 2 -1 0 1 0 1 -1 0 -1 0 1]
[ 0 0 1 -1 0 -2 -1 1 2 -2 2 -1 0 1 -1 0 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
7 rank 1, V12 x + y + z + 2*x-1*y*z + x-2*y2*z + x-2*y*z2 + x-3*y2*z2 + x*z-1 + x*y-1 + 3*x-1*y + 3*x-1*z + 4*x-2*y*z + 3*x*y-1*z-1 + 3*z-1 + 3*y-1 + 6*x-1 + x*y-1*z-2 + x*y-2*z-1 + 4*y-1*z-1 + x*y-2*z-2
7 rank 1, V12 x + y + z + 3*x-1*y*z + x-2*y2*z + x-2*y*z2 + x-3*y2*z2 + x*z-1 + x*y-1 + 3*x-1*y + 3*x-1*z + 4*x-2*y*z + 2*x*y-1*z-1 + 3*z-1 + 3*y-1 + 6*x-1 + x*y-1*z-2 + x*y-2*z-1 + 4*y-1*z-1 + x*y-2*z-2
11 rank 2, number 6 x + y + z + 2*x-1*y*z + x-2*y2*z + x-2*y*z2 + x-3*y2*z2 + x*z-1 + x*y-1 + 3*x-1*y + 3*x-1*z + 4*x-2*y*z + 2*x*y-1*z-1 + 3*z-1 + 3*y-1 + 6*x-1 + x*y-1*z-2 + x*y-2*z-1 + 4*y-1*z-1 + x*y-2*z-2
22 rank 3, number 1 x + y + z + 3*x-1*y*z + x-2*y2*z + x-2*y*z2 + x-3*y2*z2 + x*z-1 + x*y-1 + 3*x-1*y + 3*x-1*z + 4*x-2*y*z + 3*x*y-1*z-1 + 3*z-1 + 3*y-1 + 6*x-1 + x*y-1*z-2 + x*y-2*z-1 + 4*y-1*z-1 + x*y-2*z-2
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
Image of facet 0 2 irreducible and admissible
Image of facet 24 2 Lattice Minkowski decompositions of facet 24
Image of facet 90 2 Lattice Minkowski decompositions of facet 90
Image of facet 20 2 Lattice Minkowski decompositions of facet 20
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