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The Regular Maps on a Surface of Genus Three

Published online by Cambridge University Press:  20 November 2018

F. A. Sherk
F. A. Sherk*
Affiliation:
University of Toronto
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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).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 11 , 1959 , pp. 452 - 480
Copyright
Copyright © Canadian Mathematical Society 1959

References

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