From the hyperbolic 24-cell to the cuboctahedron

Details From the hyperbolic 24-cell to the cuboctahedron From the hyperbolic 24-cell to the cuboctahedron

2008-05-28

arxiv.org/abs/0805.4537v1

Mathematics

Geometric Topology

The article has 78 pages and 37 figures. Many of the figures use color in an essential way. If possible, use a color printer

Scientific paper

We describe a family of 4-dimensional hyperbolic orbifolds, constructed by deforming an infinite volume orbifold obtained from the ideal, hyperbolic 24-cell by removing two walls. This family provides an infinite number of infinitesimally rigid, infinite covolume, geometrically finite discrete subgroups of the isometry group of hyperbolic 4-space. It also leads to finite covolume Coxeter groups which are the homomorphic image of the group of reflections in the hyperbolic 24-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 4-dimensional, but infinite volume, analog of 3-dimensional hyperbolic Dehn filling.

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