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.
(In reply to # 1-4, possible errors
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 . . .
Posted by Leming
on 2006-03-06 09:14:45