Hyperbolic realizations of tilings by Zhuk simplices

Abstract

One possibility to classify hyperbolic sapce groups is to look for their fundamental domains. For simplicial domains are combinatorialy classified face pairing identifications, but the space of realization is not known. In this paper two series of fundamental simplices are investigated, which have three equivalence classes for edges and two for vertices. Three edges in the first class belong to the same face and vertices of that face are in the same class. Those simplices are hyperbolic, mainly with outer vertices. If so, then truncated simplex tilings are also investigated and classified with their metric data and other conditions.