Volume 9, issue 2 (2009)

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Volume estimates for equiangular hyperbolic Coxeter polyhedra

Christopher K Atkinson

Algebraic & Geometric Topology 9 (2009) 1225–1254
Abstract

An equiangular hyperbolic Coxeter polyhedron is a hyperbolic polyhedron where all dihedral angles are equal to πn for some fixed n , n 2. It is a consequence of Andreev’s theorem that either n = 3 and the polyhedron has all ideal vertices or that n = 2. Volume estimates are given for all equiangular hyperbolic Coxeter polyhedra.

Keywords
hyperbolic geometry, Coxeter polyhedra, $3$-orbifolds
Mathematical Subject Classification 2000
Primary: 57M50
Secondary: 30F40
References
Publication
Received: 26 June 2008
Revised: 6 May 2009
Accepted: 11 May 2009
Published: 13 June 2009
Authors
Christopher K Atkinson
Department of Mathematics, Statistics and Computer Science
University of Illinois at Chicago
851 S Morgan St
Chicago, IL 60607
http://www.math.uic.edu/~atkinson