![Image of polytope 4181](http://coates.ma.ic.ac.uk/fanosearch/wp-content/uploads/2010/09/3DReflexivePolytope.4181.png) |
PALP id: |
4181 |
grdb id: |
72684 |
Integer points: |
[ 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0] [ 0 1 0 1 -2 -1 2 2 -3 0 1 -2 -1 0 1 2 -2 -1 0 1 -1 0 1 -1 0] [ 0 0 1 -2 1 2 -1 -3 2 1 0 2 1 0 -1 -2 1 0 -1 -2 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 |
x + y + z + 3*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + y*z-2 + 2*x-1*y2*z-2 + 3*z-1 + 8*x-1*y*z-1 + 3*y-1 + 12*x-1 + y-2*z + 8*x-1*y-1*z + 2*x-1*y-2*z2 + x-1*y2*z-3 + 5*x-1*y*z-2 + 10*x-1*z-1 + 10*x-1*y-1 + 5*x-1*y-2*z + x-1*y-3*z2 |
7 |
rank 1, V12 |
x + y + z + 2*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 3*y-1*z + 3*x-1*z + x-1*y-1*z2 + y*z-2 + 2*x-1*y2*z-2 + 3*z-1 + 8*x-1*y*z-1 + 3*y-1 + 12*x-1 + y-2*z + 8*x-1*y-1*z + 2*x-1*y-2*z2 + x-1*y2*z-3 + 5*x-1*y*z-2 + 10*x-1*z-1 + 10*x-1*y-1 + 5*x-1*y-2*z + x-1*y-3*z2 |
11 |
rank 2, number 6 |
x + y + z + 2*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 2*y-1*z + 3*x-1*z + x-1*y-1*z2 + y*z-2 + 2*x-1*y2*z-2 + 3*z-1 + 8*x-1*y*z-1 + 3*y-1 + 12*x-1 + y-2*z + 8*x-1*y-1*z + 2*x-1*y-2*z2 + x-1*y2*z-3 + 5*x-1*y*z-2 + 10*x-1*z-1 + 10*x-1*y-1 + 5*x-1*y-2*z + x-1*y-3*z2 |
22 |
rank 3, number 1 |
x + y + z + 3*y*z-1 + x-1*y2*z-1 + 3*x-1*y + 3*y-1*z + 3*x-1*z + x-1*y-1*z2 + y*z-2 + 2*x-1*y2*z-2 + 3*z-1 + 8*x-1*y*z-1 + 3*y-1 + 12*x-1 + y-2*z + 8*x-1*y-1*z + 2*x-1*y-2*z2 + x-1*y2*z-3 + 5*x-1*y*z-2 + 10*x-1*z-1 + 10*x-1*y-1 + 5*x-1*y-2*z + x-1*y-3*z2 |
|
Facets: |
Facet |
Multiplicity |
Admissible lattice Minkowksi decompositions |
![Image of facet 0](http://coates.ma.ic.ac.uk/fanosearch/wp-content/uploads/2010/09/facet.0.png) |
1 |
irreducible and admissible
|
![Image of facet 146](http://coates.ma.ic.ac.uk/fanosearch/wp-content/uploads/2010/09/facet.146.png) |
1 |
|
![Image of facet 20](http://coates.ma.ic.ac.uk/fanosearch/wp-content/uploads/2010/09/facet.20.png) |
1 |
|
![Image of facet 23](http://coates.ma.ic.ac.uk/fanosearch/wp-content/uploads/2010/09/facet.23.png) |
2 |
|
![Image of facet 216](http://coates.ma.ic.ac.uk/fanosearch/wp-content/uploads/2010/09/facet.216.png) |
1 |
|
![Image of facet 9](http://coates.ma.ic.ac.uk/fanosearch/wp-content/uploads/2010/09/facet.9.png) |
1 |
irreducible and admissible
|
|