Chirality Group and Chirality Index of Coxeter Chiral Maps

Abstract

In this paper we compute the chirality group, the chirality index and the smallest regular coverings of the chiral Coxeter maps, the toroidal orientably regular maps described in Coxeter and Moser monograph [H.S.M.Coxeter and W.O.J.Moser,Generation and Relations Discrete Group(4th ed.),Springer-varlag,Berlin,1984]. We also compute the greatest regular maps covered by chiral Coxeter maps.