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 v_i and v_j of P if and only if there is an edge between the corresponding vertices v_i' and v_j' 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, ...