Francisco Lara-Dammer
"The Icosahedral Group"
Digital Print, 20"x24", 2005
Francisco Lara-Dammer, Indiana University (CRCC)
This work is centered on a collection consisting of about 30 highly distinct colored Cayley diagrams of A5, the famous alternating group on five elements, also known as the icosahedral group, best known for its key role in Galois' proof of the unsolvability of the quintic by radicals. Fifteen golden rectangles can be symmetrically embedded inside a regular icosahedron, three at a time forming an orthogonal triad, thus making five "golden triads". Each of the 60 rotations of the icosahedron shuffles the five golden triads in an even permutation. Since each Cayley diagram involves a different set of generators - some having period 2, some having period 3, some having period 5 - each diagram divulges a different aspect of the group's structure. Some diagrams have an overall triangular aspect, others are globally pentagonal, and others exhibit other shapes.
email: flaradam@cs.indiana.edu