Define a valid ``coloring'' to occur when no two faces with a common Edge share the same color. Given two colors, there is a single way to color an Octahedron. Given three colors, there is one way to color a Cube and 144 ways to color an Icosahedron. Given four colors, there are two distinct ways to color a Tetrahedron and 4 ways to color a Dodecahedron. Given five colors, there are four ways to color an Icosahedron.

**References**

Ball, W. W. R. and Coxeter, H. S. M. *Mathematical Recreations and Essays, 13th ed.* New York: Dover, 238-242, 1987.

Cundy, H. and Rollett, A. *Mathematical Models, 3rd ed.* Stradbroke, England: Tarquin Pub., pp. 82-83, 1989.

© 1996-9

1999-05-25