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The arithmetic structure of tetrahedral groups of hyperbolic isometries

Part of:Lie groups

Published online by Cambridge University Press:  26 February 2010

C. Maclachlan and
A. W. Reid
C. Maclachlan
Affiliation:
Department of Mathematics, University of Aberdeen, The Edward Wright Building, Dunbar Street. Aberdeen, AB9 2TY.
A. W. Reid
Affiliation:
Department of Mathematics, The Ohio State University, 231 West 18th AvenueColumbus, Ohio, 43210-1174, U.S.A..
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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].

MSC classification

Secondary:22E40: Discrete subgroups of Lie groups

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Type
Research Article
Information
Mathematika , Volume 36 , Issue 2 , December 1989, pp. 221 - 240
Copyright
Copyright © University College London 1989

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