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

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.