Faithful permutation representations of toroidal regular maps

In this paper, we list all possible degrees of a faithful transitive permutation representation of the group of symmetries of a regular map of types {4,4}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{4,4\}$$\end{document} and {3,6}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{3,6\}$$\end{document}, and we give examples of graphs, called CPR graphs, representing some of these permutation representations.