A Cayley graph is a pictorial representation of the structure of a group G with respect to a generating subset S. The vertices of the graph are the elements of G. (Mouse over a vertex to see the permutation.) Two vertices g and h are connected by an edge if there is a generator in S that multiplies g into h or vice versa. Here pairs of permutations {p, q} are used for S to construct polyhedra, symmetric graphs, and so on.