Four series of hyperbolic space groups with simplicial domains, and their supergroups

Abstract

Hyperbolic space groups are isometry groups, acting discontinuously on the hyperbolic 3-space with compact fundamental domain. One possibility to classify them is to look for fundamental domains of these groups. Here are considered supergroups for four series of groups with simplicial fundamental domains. Considered simplices, denoted in [9] by T19, T46, T59, belong to family F12, while T31 belongs to F27.