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A Family of Regular Maps of Type {6, 6}

Published online by Cambridge University Press:  20 November 2018

F.A. Sherk
F.A. Sherk*
Affiliation:
University of Toronto
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In (4), pp. 25−27, Coxeter divided the regular maps on a surface of genus 1 into three infinite families. They are:

  1. (i) Maps of type {4, 4}.

  2. (ii) Maps of type {6, 3}.

  3. (iii) Maps of type {3, 6} (the duals of (ii)).

We consider the family (iii). By adjoining an element to the group of any map in (iii) we shall derive the group of a regular map of type {6, 6}. Thus we produce a 1−1 correspondence between the members of the family (iii) and of the new family. Corresponding members in the two families have certain properties in common, the most interesting of which is the property of reflexibility. Our results are summarized in Theorems 1 and 2.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 5 , Issue 1 , January 1962 , pp. 13 - 20
Copyright
Copyright © Canadian Mathematical Society 1962

References

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