Research Article

The arithmetic structure of tetrahedral groups of hyperbolic isometries

C. Maclachlana1 and A. W. Reida2

a1 Department of Mathematics, University of Aberdeen, The Edward Wright Building, Dunbar Street. Aberdeen, AB9 2TY.

a2 Department of Mathematics, The Ohio State University, 231 West 18th Avenue Columbus, Ohio, 43210-1174, U.S.A..

Introduction. Polyhedra in 3-dimensional hyperbolic space which give rise to discrete groups generated by reflections in their faces have been investigated in [14], [17], [29] and in the case of tetrahedra there are precisely nine compact non-congruent ones with dihedral angles integral submultiples of π [14]. These polyhedral groups give rise to hyperbolic 3-orbifolds and examples of these have been studied, for example, in [3], [15], [18], [24], [25].

(Received January 13 1989)

Key Words:

  • 22E40: TOPOLOGICAL GROUPS, LIE GROUPS; Lie groups; Discrete subgroups of Lie groups.