Polytope 4074
Image of polytope 4074 PALP id: 4074
grdb id: 566716
Integer points: [ 1 0 0 -2 2 0 2 0 -3 -1 -2 -1 -1 -2 -1 0 1 -1 0 1 0 1 1]
[ 0 1 0 2 -2 0 -3 -1 2 0 1 0 1 1 0 -1 -2 1 0 -1 -1 -2 -1]
[ 0 0 1 1 -1 -1 -1 1 1 -1 1 1 1 0 0 0 0 0 0 0 -1 -1 -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
22 rank 3, number 1 x + y + z + 2*x-1*y*z + x-2*y2*z + 3*x*y-1 + 3*x-1*y + y-1*z + 3*x-1*z + 3*x-2*y*z + x-3*y2*z + x2*y-2*z-1 + 2*x*y-1*z-1 + z-1 + 2*x*y-2 + 6*y-1 + 6*x-1 + 2*x-2*y + x2*y-3*z-1 + 3*x*y-2*z-1 + 3*y-1*z-1 + x-1*z-1
11 rank 2, number 6 x + y + z + 2*x-1*y*z + x-2*y2*z + 2*x*y-1 + 2*x-1*y + y-1*z + 3*x-1*z + 3*x-2*y*z + x-3*y2*z + x2*y-2*z-1 + 2*x*y-1*z-1 + z-1 + 2*x*y-2 + 6*y-1 + 6*x-1 + 2*x-2*y + x2*y-3*z-1 + 3*x*y-2*z-1 + 3*y-1*z-1 + x-1*z-1
7 rank 1, V12 x + y + z + 2*x-1*y*z + x-2*y2*z + 3*x*y-1 + 2*x-1*y + y-1*z + 3*x-1*z + 3*x-2*y*z + x-3*y2*z + x2*y-2*z-1 + 2*x*y-1*z-1 + z-1 + 2*x*y-2 + 6*y-1 + 6*x-1 + 2*x-2*y + x2*y-3*z-1 + 3*x*y-2*z-1 + 3*y-1*z-1 + x-1*z-1
7 rank 1, V12 x + y + z + 2*x-1*y*z + x-2*y2*z + 2*x*y-1 + 3*x-1*y + y-1*z + 3*x-1*z + 3*x-2*y*z + x-3*y2*z + x2*y-2*z-1 + 2*x*y-1*z-1 + z-1 + 2*x*y-2 + 6*y-1 + 6*x-1 + 2*x-2*y + x2*y-3*z-1 + 3*x*y-2*z-1 + 3*y-1*z-1 + x-1*z-1
Facets:
Facet Multiplicity Admissible lattice Minkowksi decompositions
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 125 1 Lattice Minkowski decompositions of facet 125
Image of facet 23 2 Lattice Minkowski decompositions of facet 23
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