When comparing two convex polyhedra, how can one determine if they are geometrically similar. Is there any algorithm to determine if one is the distorted or truncated version of the other? Vertex, edge and face analysis is often misleading. For instance the following polyhedra are visually similar while their p_vectors are completely different. Are the following polyhedra considered geometrically similar(notice the small edges in the 2nd figure)?
I appreciate any reading material that may give me more insights about these problems.