The following is inspired by this question. From time to time I search the web for tables of polyhedra, but without much success. Part of the problem is that there are many non-equivalent questions that can be asked. For example:

- If $G$ is a planar graph where every edge is in a cycle, what extra conditions are needed so that $G$ realizable as a polyhedron?
- How many polyhedra with $e$ edges are there?
- If $G$ is a planar graph where every edge is in a cycle, what extra conditions are needed so that $G$ realizable as a polyhedron with regular faces?
- How many polyhedra with $e$ edges and regular faces are there?
- What are the obstructions to realizability?
- etc$\ldots$

Meta-question:Where are questions like these addressed?