This site is dedicated to the exploration of Cayley graphs and closely related subjects such as symmetric graphs and regular maps. The prehistory of Cayley graphs and regular maps includes the discovery of the Platonic and Archimedean solids, Kepler's discovery of what we now call higher genus maps, Hamilton's presentation of the Icosahedral group and Klein's platonic tessellation of the surface of genus 3.
Groups may be represented in a variety of interesting and powerful ways, such as permutation representations, matrix representations and by group presentation. They may also be represented as the automorphism group of geometric objects such as polyhedron, graphs or regular maps. A great advantage of this form of representation is, as A.T. White has pointed out, "that many results of the general theory can be readily visualized or modeled, so that students are constantly reassured that what they are doing has meaning and is more than a formal manipulation of symbols".