We all know how easy it is to spin a coin on a table top. With a good twist, it might spin for 20 seconds or so before wobbling flat. E.g., YouTube video. Let's view a coin as a convex polyhedron.
Q. What characteristics of a convex polyhedron make it "spinnable"?
I realize this is not a precise question, but still it might have reasonable answers, for necessary and possibly sufficient conditions for sustaining a stable spin. For example, I would say the regular tetrahedron is not spinnable, either on its base (too large a friction surface on the plane/table top), nor on one of its vertices (too unstable). But perhaps the regular icosahedron is spinnable? Maybe those with experience with polyhedral game-dice could formulate conjectures.
mathsgear
Perhaps every cross-section orthogonal to the spin axis should be centrally symmetric?
The question can be generalized from "convex polyhedron" to "convex body."