Volume estimates for equiangular hyperbolic Coxeter polyhedra

Atkinson, Christopher K

doi:10.2140/agt.2009.9.1225

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ISSN (electronic): 1472-2739

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Volume estimates for equiangular hyperbolic Coxeter polyhedra

Christopher K Atkinson

Algebraic & Geometric Topology 9 (2009) 1225–1254

DOI: 10.2140/agt.2009.9.1225

Abstract

An equiangular hyperbolic Coxeter polyhedron is a hyperbolic polyhedron where all dihedral angles are equal to $π ∕ n$ for some fixed $n \in ℤ$ , $n \geq 2$ . 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

Volume 9, issue 2 (2009)