Toroidal maps of modular quotient groups Original Research Article

Genus-one modular quotient groups have been studied in various guises, from the toroidal maps of Brahana and Coxeter, to the symmetric trivalent graphs of Coxeter, Miller, Bouwer, and Chernoff, to the level-six groups of Newman. We develop relations among the parameters of these objects as a means of describing the correspondence between these alternate descriptions.