Geometry & Topology
- Geom. Topol.
- Volume 14, Number 3 (2010), 1383-1477.
From the hyperbolic $24$–cell to the cuboctahedron
We describe a family of –dimensional hyperbolic orbifolds, constructed by deforming an infinite volume orbifold obtained from the ideal, hyperbolic –cell by removing two walls. This family provides an infinite number of infinitesimally rigid, infinite covolume, geometrically finite discrete subgroups of . It also leads to finite covolume Coxeter groups which are the homomorphic image of the group of reflections in the hyperbolic –cell. The examples are constructed very explicitly, both from an algebraic and a geometric point of view. The method used can be viewed as a –dimensional, but infinite volume, analog of –dimensional hyperbolic Dehn filling.
Geom. Topol., Volume 14, Number 3 (2010), 1383-1477.
Received: 25 August 2008
Revised: 18 May 2010
Accepted: 22 March 2010
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]
Secondary: 20F55: Reflection and Coxeter groups [See also 22E40, 51F15] 20H10: Fuchsian groups and their generalizations [See also 11F06, 22E40, 30F35, 32Nxx] 51M99: None of the above, but in this section
Kerckhoff, Steven P; Storm, Peter A. From the hyperbolic $24$–cell to the cuboctahedron. Geom. Topol. 14 (2010), no. 3, 1383--1477. doi:10.2140/gt.2010.14.1383. https://projecteuclid.org/euclid.gt/1513732229