The Icosahedron

The image in the upper left corner depicts an icosahedron, which is a polyhedron with twenty identical faces, each an equilateral triangle, in which five faces meet at each vertex. There is a large icosahedron in the Mathematics Suite (room 102) of De La Roche Hall, located atop the Resources bookcase.

This icosahedron was given to the Department of Mathematics in 1996 by Professor Richard Neal, currently the co-chair of the MAA Committee on Undergraduate Student Activities and Chapters. Dr. Neal sends monthly problems to interested departments of mathematics, which may use them for student problem-solving contests. This free service is called The Problem-Solving Competition. Bonas mathematics major Philip J. Darcy (class of `96) sent Dr. Neal a problem and solution to be used in The Problem-Solving Competition, for which Dr. Neal gave our department the icosahedron. The icosahedron is made of white pine and was originally unpainted. In 2004, Dr. Maureen Cox and Dr. Chris Hill painted it using the five colors yellow, orange, green, blue, and teal. The icosahedron is painted so that each face has one color, faces that share an edge have different colors, and each vertex is surrounded by all five colors.

A polyhedron whose faces are identical regular polygons with the same number of faces meeting at each vertex is called a Platonic solid. The ancient Greeks proved that there are only five Platonic solids: the tetrahedron (four faces, each an equilateral triangle), the cube (six faces, each a square), the octahedron (eight faces, each an equilateral triangle), the dodecahedron (twelve faces, each a regular pentagon), and the icosahedron (twenty faces, each an equilateral triangle).