  In this article, we introduce rotation groups as a common generalisation of
Coxeter groups and graph products of groups (including right-angled Artin
groups). We characterise algebraically these groups 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.
