Four series of hyperbolic space groups with simplicial domains, and their supergroups (Q2867537)

On the base of her former investigations, the author constructs and describes new infinite series of hyperbolic space groups with truncated simplices (trunc-simplices) as compact fundamental domains. The method is based on the famous Poincaré theorem. The four starting series with simplicial domains are \(T_{19}\), \(T_{46}\), \(T_{59}\), \(T_{31}\), taken from the earlier paper of the reviewer and his colleagues \textit{I. Prok} and \textit{J. Szirmai}, [Math. Appl. 581, 321--363 (2006; Zbl 1103.52017)]. This investigations seem to be fruitful for future researches as well.