Cell structure of bipartite mediangle graphs

Genevois introduced and investigated mediangle graphs as a common generalization of median graphs (1-sekeleta of CAT(0) cube complexes) and Coxeter graphs (Cayley graphs of Coxeter systems) and studied groups acting on them. He asked if mediangle graphs can be endowed with the structure of a contractible cell complex. We answer this in the affirmative by proving that bipartite mediangle graphs are tope graphs of finitary Complexes of Oriented Matroids (COMs). We also show that the oriented matroids (OMs) constituting the cells of COMs arising from bipartite mediangle graphs are exactly the simplicial OMs.