I'm looking for a way to calculate the probabilities of Archimedean Solids landing on a specific face if a person would roll one. Of course, not the regular polygons like cubes and dodecahedrons, but something with more than one type of face like the snub cube or truncated icosahedron. I am wondering of the edges and vertices would need to be calculated as well as face area, or if the area would be enough to get a good approximation of this. If area is the dominant parameter on this it would be interesting that size determines the probability in an ideal situation. Of course, in reality it wouldn't be ideal and drag forces (and weight of the object) would change these probabilities as well. If this has already been studied (and I'm guessing it likely has been), I'd be grateful for links to papers, or even the appropriate key words to search for on arXiv. Thanks!