From the hyperbolic 24-cell to the cuboctahedron

Abstract

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.

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

References in corpus (1)

• Introduction to Arithmetic Groups

Cited by in corpus (6)

• Geometric transition from hyperbolic to anti-de Sitter structures in dimension four
• Hyperbolic Dehn filling in dimension four
• New hyperbolic 4-manifolds of low volume
• Character varieties of a transitioning Coxeter 4-orbifold
• Counting cusped hyperbolic 3-manifolds that bound geometrically
• A small cusped hyperbolic 4-manifold