(Unfortunately I don't know the proper terminology for what I'm looking for, so bear with me.)
I want to identify which of the vertices, edges, and faces of a polyhedron are 'unique' and which are 'similar.' To explain what I mean by that, let's say I have a square antiprism: I would say that all 8 vertices are the same, the 8 triangular faces are all similar and separate from the two squares, and there are two types of edges: the 8 which form the squares' perimeters, and the 8 others. Meanwhile, for the platonic solids, there is only one 'subset' among each of the three categories: all of the edges of a cube are indistinguishable from one another; same for its vertices and faces.
So my question is: is there a standard way to use the properties of each of a shape's components (a face's area, an edge's length, etc.) to group them together such that the members of each group is mutually indistinguishable?
I really hope that makes sense and it's clear what I'm asking. Thanks for the help!