The Regular Maps on a Surface of Genus Three

Author:

Sherk F. A.

Abstract

A considerable volume of research on the theory of regular maps is now in existence. Systematic enumerations of regular maps on the surfaces of genus 1 and 2 were begun by Brahana (1; 2) and completed by Coxeter (6; 7, p. 141). In addition Coxeter enumerated the regular maps on the simplest non-orientable surfaces (7, pp. 116, 139), and constructed tables of some interesting families of regular maps (3; 7, p. 140).Most of the regular maps on a surface of genus 3 have appeared in these papers, but no systematic enumeration of them seems to have been attempted. The ultimate goal of this paper is a complete list of these regular maps. However, the families of maps {j.p,q}and {j.p,j.q} which are defined in § 4 and listed in Tables I and II are of considerable interest in themselves. Also of some importance is the complete list of regular maps of type {p,3} with six or fewer faces (§ 5 and Table III).

Publisher

Canadian Mathematical Society

Subject

General Mathematics

Cited by 29 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Surface embeddings of the Klein and the Möbius–Kantor graphs;Acta Crystallographica Section A Foundations and Advances;2018-03-27

2. Non-abelian almost totally branched coverings over the platonic maps;European Journal of Combinatorics;2016-01

3. Regular Maps;Springer Monographs in Mathematics;2016

4. Historical and Introductory Background;Springer Monographs in Mathematics;2016

5. Branched cyclic regular coverings over platonic maps;European Journal of Combinatorics;2014-02

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