The Symmetry Groups of the Regular Tessellations of S^2 and S^3

The construction of the symmetry groups is described for the regular complexes that tessellate S^2 and S^3. For S^3 these groups are four-dimensional point groups, and they are described in this paper both in terms of their presentations and as subgroups of products of the binary polyhedral groups. The second description is used to obtain the irreducible representations of the symmetry groups; the character tables are also given.