Macaulay2 » Documentation
Packages » LatticePolytopes :: listSmooth3D

next | previous | forward | backward | up | index | toc

listSmooth3D -- gives the list of all smooth 3-polytopes with up to 16 lattice points

Synopsis

Usage:

listSmooth3D()
Outputs:
- a list,

Description

Provides the list of all smooth 3-polytopes with up to 16 lattice points based on the classification by Anders Lundman.

i1 : L=listSmooth3D();

A. Lundman claims that 99 of the listed polytopes are Cayley. This can readily be tested.

i2 : #L

o2 = 103

i3 : tally apply(L,isCayley)

o3 = Tally{false => 4}
           true => 99

o3 : Tally

See also

listSmooth2D -- gives the list of all smooth 2-polytopes with up to 12 lattice points
isCayley -- checks if a polytope is Cayley

For the programmer

The object listSmooth3D is a function closure.