Abstract
A generalized tetrahedron group is defined to be a group admitting a presentation [Formula: see text] where l, m, n, p, q, r ≥ 2, each Wi(a,b) is a cyclically reduced word involving both a and b. These groups appear in many contexts, not least as fundamental groups of certain hyperbolic orbifolds or as subgroups of generalized triangle groups. In this paper, we build on previous work to give a complete classification of all finite generalized tetrahedron groups.
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