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.

You should be able to make 10 distinct cubes:

6 black, 0 white = 1 cube
5 black, 1 white = 1 cube
4 black, 2 white = 2 cubes (2 white side are either opposite or adjacent)
3 black, 3 white = 2 cubes (3 of same color are either "in a row" around the cube, or they all meet at one corner)
2 black, 4 white = 2 cubes (same as above)
1 black, 5 white = 1 cube
0 black, 6 white = 1 cube

Well that's a start...