Polyhedron Coloring

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 aCube and 144 ways to color an Icosahedron. Given four colors, there are two distinct ways to color aTetrahedron and 4 ways to color a Dodecahedron. Given five colors, there are four ways to color anIcosahedron.

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.

• Whisker Plot
• Whitehead Double
• Whitehead Link
• Whitehead Manifold
• Whitehead's Theorem
• Whitney-Graustein Theorem
• Whitney-Mikhlin Extension Constants
• Whitney Singularity
• Whitney Sum
• Whitney Umbrella
• Whittaker Differential Equation
• Whittaker Function
• Whole Number
• Width (Partial Order)
• Width (Size)
• Wiedersehen Manifold
• Wieferich Prime
• Wielandt's Theorem
• Wiener Filter
• Wiener Function
• Wiener-Khintchine Theorem
• Wiener Measure
• Wiener Space
• Wigner 3j-Symbol
• Wigner 6j-Symbol