1)I have lots of black and white squares that can be joined together to make cubes. How many distinguishable cubes can I make?

2)Now I try it with triangles and regular octahedrons?

3)Now pentagons and regular dodecahedrons?

4)Triangles again but making regular icosahedrons!?

Note: Distinguishable means rotations are the same, but reflections are not.

Tristan - Thanks for saving me.  I was about to commence #4 using brute force. I was at the point of coloring three sides when your post arrived.

While I will let someone else find the flaw in my logic for #3 (94 vs 96), I worked through Charlie's answer for #2 and concur with his answer.

In both cases Polya's theory is 2 variations higher . . .