This may be of interest to only a few: Simplest Canonical Polyhedra of Each Symmetry Type (rotable in Java); in other words, canonical forms of the simplest topologies that allow the specified symmetries and none higher. Any convex polyhedron can be deformed into a “canonical” form whose edges are all tangent to a sphere; if a polyhedron is self-dual, it is canonical.
This collection could be considered a generalization of the set of all fair dice.