I have a polyhedron and want to determine whether it is combinatorially equivalent to another polyhedron. I know how many faces comprise each polyhedron and for each face, I know all of its vertices, and for each vertex, I know its location.
For example, if I had a pentahedron, I would want to figure out whether it was a triangular prism or a square pyramid. I can easily do this for pentahedral, but do not know how to do it for arbitrary polyhedra.
Additionally, if two polyhedra are the the same shape, I want to map the vertices from one to the other.
Can anyone point me to an algorithm to accomplish these things?