This is more of a curiosity to me, but I'm sure I don't have the mathematical skills to answer it. That said... I took a look at several other posts with questions that relate to this one, but I haven't seen this specifically addressed...

Given a uniform solid rhombicosidodecahedron, what are the odds of rolling each of the faces: triangle, square and pentagon?

I'm interested in a theoretical answer here, I'm not concerned with reality... like a roller trying to "cheat" the roll for a specific outcome. And I'm obviously not concerned with the die being "fair". So let's assume that the roll is truly random.

This is more of a curiosity to me, but I'm sure I don't have the mathematical skills to answer it. That said... I took a look at several other posts with questions that relate to this one, but I haven't seen this specifically addressed...

Given a uniform solid rhombicosidodecahedron, what are the odds of rolling each of the faces: triangle, square and pentagon?

I'm interested in a theoretical answer here, I'm not concerned with reality... like a roller trying to "cheat" the roll for a specific outcome. And I'm obviously not concerned with the die being "fair". So let's assume that the roll is truly random.