The three smallest compact arithmetic hyperbolic 5-orbifolds

TL;DR

This paper identifies the three smallest compact arithmetic hyperbolic 5-orbifolds, determines their fundamental groups as hyperbolic Coxeter groups, and provides two methods for computing their volumes.

Contribution

It uniquely classifies the smallest such orbifolds and links their fundamental groups to Coxeter groups, offering new volume computation methods.

Findings

Identified the three smallest compact arithmetic hyperbolic 5-orbifolds.

Established their fundamental groups as hyperbolic Coxeter groups.

Provided two distinct volume calculation methods.

Abstract

We determine the three hyperbolic 5-orbifolds of smallest volume among compact arithmetic orbifolds, and we identify their fundamental groups with hyperbolic Coxeter groups. This gives two different ways to compute the volume of these orbifolds.