Rotation groups, mediangle graphs, and periagroups: A unified point of view on Coxeter groups and graph products of groups

Abstract

In this article, we introduce rotation groups as a common generalisation of Coxeter groups and graph products of groups. We characterise these groups algebraically by presentations (periagroups), and we propose a combinatorial geometry (mediangle graphs) to study them. As an application, we give natural and unified proofs for several results that hold for both Coxeter groups and graph products of groups.