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ReflexivePolytopesDB :: getKreuzerSkarkeDim3

getKreuzerSkarkeDim3 -- download Kreuzer-Skarke dim 3 reflexive polytopes database of 4319 examples

Synopsis

Description

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

See also