On Subgroups of Tetrahedron Groups

TL;DR

This paper introduces a framework leveraging color symmetry theory to identify subgroups within tetrahedron groups and tetrahedron Kleinian groups, advancing the understanding of their algebraic and geometric structures.

Contribution

It provides a novel method for analyzing subgroups of tetrahedron groups using color symmetry tools, which was not previously available.

Findings

Framework successfully identifies subgroups of tetrahedron groups.

Method applies to tetrahedron Kleinian groups.

Enhances understanding of geometric group structures.

Abstract

We present a framework to determine subgroups of tetrahedron groups and tetrahedron Kleinian groups, based on tools in color symmetry theory.