Volumes in Hyperbolic Space

TL;DR

This paper studies the volumes of large Coxeter hyperbolic polyhedra, identifying the minimal volume cases and analyzing pyramids with vertices at infinity to deepen understanding of hyperbolic geometry.

Contribution

It introduces new results on the minimal volume of large Coxeter hyperbolic polyhedra and explores volumes of hyperbolic pyramids with ideal vertices.

Findings

Determined the smallest possible volume for large Coxeter hyperbolic polyhedra.

Calculated volumes of pyramids with one vertex at infinity.

Provided insights into hyperbolic volume properties.

Abstract

This paper focuses on the investigation of volumes of large Coxeter hyperbolic polyhedron. First, the paper investigates the smallest possible volume for a large Coxeter hyperbolic polyhedron and then looks at the volume of pyramids with one vertex at infinity.