Every bipartite mediangle graph is the tope graph of a finitary complex of oriented matroids, so it carries a contractible cell complex with simplicial oriented matroid cells.
Rotation groups virtually embed into right-angled rotation groups
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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).
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Cell structure of mediangle graphs
Every bipartite mediangle graph is the tope graph of a finitary complex of oriented matroids, so it carries a contractible cell complex with simplicial oriented matroid cells.