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