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.
Adding a tetrahedron to the problem, the number of sides to the number of variations looks like this:
Solid Sides Variations
Tetra: 4 4
Cube 6 10
Octa 8 21
Dodeca 12 116 (assuming I found them all)
While these numbers should have a relationship to factorials, they loosly approximate a cube function. I am estimating that a icosahedron, with 20 sides will have in the neighborhood of 500 possible variations. Though this may be a gross underestimation.
Posted by Leming
on 2006-03-04 20:20:21