Minimum Colors for an Icosahedron

[Oliviam12]

How could you mathematically solve for the minimum amount of colors needed for each face of an icosahedron or any regular polyhedron to not touch? (E.g. a tetrahedron pyramid would need four unique colors.)

 

[Newtime]

"There is no obvious extension of the coloring problem to three-dimensional solid regions."
-taken from http://en.wikipedia.org/wiki/Four_color_theorem.

So it looks like it's guess and check mostly, and even then, you'd have a pretty tough time proving your solution is indeed minimal. It is an interesting problem though.

 

[CRGreathouse]

If I'm reading this right, what you want is the chromatic number of the dodecahedral (!) graph, which is 3.