Gallery of Polyhedral Types

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 vi and vj of P if and only if there is an edge between the corresponding vertices vi' and vj' of P'.

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:

  1. All edges are tangent to a sphere.
  2. 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: Saturday, 30-Sep-2017 21:42:01 CEST _