  It is a theorem due to F. Haglund and D. Wise that reflection groups (aka
Coxeter groups) virtually embed into right-angled reflection groups (aka
right-angled Coxeter groups). In this article, we generalise this observation
to rotation groups, which can be thought of as a common generalisation of
Coxeter groups and graph products of groups. More precisely, we prove that
rotation groups (aka periagroups) virtually embed into right-angled rotation
groups (aka graph products of groups).
