Coxeter Decompositions of Bounded Hyperbolic Pyramids and Triangular Prisms

TL;DR

This paper classifies Coxeter decompositions of bounded convex pyramids and triangular prisms in hyperbolic 3-space, extending previous work on hyperbolic simplices to more complex polyhedral shapes.

Contribution

It introduces a classification of Coxeter decompositions for specific polyhedra in hyperbolic space, building on earlier methods used for simplices.

Findings

Complete classification of Coxeter decompositions for pyramids and prisms in H^3

Extension of existing methods to new polyhedral shapes

Provides a framework for analyzing hyperbolic polyhedral decompositions

Abstract

Coxeter decompositions of hyperbolic simplices where studied in math.MG/0212010 and math.MG/0210067. In this paper we use the methods of these works to classify Coxeter decompositions of bounded convex pyramids and triangular prisms in the hyperbolic space H^3.