As a an example, let’s take the 101th example on this list.
str = getKreuzerSkarkeDim3(); |
polytopes = parseKS str; |
#polytopes |
tope = polytopes_100 |
header = tope_0 |
A = matrixFromString tope_1 |
The first line gives some information about the example, see Kreuzer-Skarke headers for more details. The polytope is the convex hull of the columns of the matrix A.
One can use the packages Polyhedra and NormalToricVarieties to investigate these polyhedra, and the associated toric varieties.
needsPackage "Polyhedra" |
P = convexHull A |
P2 = polar P |
# latticePoints P |
# latticePoints P2 |
# vertices P |
# vertices P2 |
isReflexive P |
needsPackage "NormalToricVarieties" |
V0 = normalToricVariety normalFan P |
dim V0 |
max V0 |
rays V0 |
V = makeSimplicial V0 |
isSimplicial V |
isProjective V |
isSmooth V |
dim V |