Rolling of Coxeter polyhedra along mirrors

TL;DR

This paper explores the geometric structure of n-dimensional Coxeter polyhedra, demonstrating a canonical decomposition of their surfaces into parts that can be covered by lower-dimensional Coxeter domains.

Contribution

It introduces a canonical cutting of Coxeter polyhedra surfaces, enabling coverage by Coxeter (n-1)-dimensional domains, advancing understanding of their geometric properties.

Findings

Surface admits a canonical cutting

Each piece can be covered by Coxeter (n-1)-dimensional domain

Provides a new method for analyzing Coxeter polyhedra

Abstract

The topic of the paper are developments of $n$-dimensional Coxeter polyhedra. We show that the surface of such polyhedron admits a canonical cutting such that each piece can be covered by a Coxeter $(n-1)$-dimensional domain.