Subtilings of Elnitsky Tilings for Finite Irreducible Coxeter Groups

TL;DR

This paper introduces new subtilings of Elnitsky tilings for specific Coxeter groups, expanding the understanding of their combinatorial structures and providing new tilings for types B and H3.

Contribution

It presents novel subtilings of Elnitsky tilings for Coxeter groups of type B and H3, including a D6-subtiling for H3, which were not previously known.

Findings

New Elnitsky subtilings for type B Coxeter groups.

A D6-subtiling for the non-crystallographic group H3.

Enhanced combinatorial understanding of Coxeter group tilings.

Abstract

Two new Elnitsky tilings for Coxeter groups of type $\mathrm{B}$ are displayed as certain subtilings. Additionally, a new tiling for the non-crystallographic Coxeter group of type $\mathrm{H}_3$ is obtained, described as a $\mathrm{D}_6$-subtiling.