Given an arbitrary convex polyhedron that we are using as a die, is it possible to know the probability of it landing on each face? I am assuming that these probabilities depend on the shape of each polyhedron.
I am aware that the problem is physical in nature and that the randomness of a dice throw is produced by chaotic equations of motion and non-conservative influences on the system and etc... I was thinking about whether there was an interesting framework to abstract the problem away from physics and into mathematics.