Polyhedrons and PBIBDs from hyperbolic manifolds

Abstract

By taking quotients of a certain tiling of hyperbolic plane / space by certain group actions, we obtain geometric polyhedra / cellulations with interesting symmetries and incidence structure.

arXiv commentv2: Lemma 2.3(4) corrected, and as a result, $\Omega (n^{3/2})$ combinatorially different triangulated 3-manifolds on n vertices are constructed. in Geometriae Dedicata 2015, online