A triangulation of S^2 yields a right-angled Coxeter group whose defining graph is the one-skeleton of that triangulation. In this case, the Coxeter group is the orbifold-fundamental group of a reflection orbifold which is finitely covered by a 3-manifold. We investigate the relationship between acute triangulations of S^2 and the geometry of the associated right-angled Coxeter group. We will also discuss Dehn surgery and torus decompositions in this setting.

This is joint work in progress with Sam Kim.