"How to Play Platonic Billiards," by Barry Cipra. Science, 21 February 1997, page 1070.
Suppose you have a billiard table in the shape of a regular polygon, and you shoot a billiard ball from the midpoint of one side to the midpoint of the adjacent side. The ball will travel around the table, hitting the midpoint of each side and returning to its starting point. Now suppose that you are playing not on a flat billiard table, but inside a three-dimensional regular polyhedron. What path would the ball have to take to hit each side once and return to its starting point? This article looks at the work of mathematician Matthew Hudelson, who used a computer to solve this problem for octahedra (8 sides), dodecahedra (12 sides), and icosahedra (20 sides). His results may prove useful to physicists who use billiard ball models to model certain kinds of atomic behavior.
--- Allyn Jackson