Two convex polyhedra *P* and *P'* are *isomorphic* if
there is a one-to-one correspondence between the vertices of *P*
and the vertices of *P'* such that there is and edge between two
vertices *v _{i}* and

A *polyhedral type* is a class of isomorphic polyhedra.

The applet shows, for each polyhedral type, the unique polyhedron (up to scale and orientation) which satisfies the following:

- All edges are tangent to a sphere.
- The center of gravity of the points where the edges touch the sphere is the center of the sphere.

This unique representation of polyhedral types is the topic of [8].

The enumeration of polyhedral types was done by the
`plantri`

program written by Gunnar Brinkmann and
Brendan McKay.

`polymake`

is a tool to study the combinatorics
and the geometry of convex polytopes and polyhedra. It is also
capable of dealing with simplicial complexes, matroids,
polyhedral fans, graphs, tropical objects, ...

Boris Springborn | |

Last modified: Friday, 24-Jun-2011 17:46:14 CEST | _ |