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Sachs triangulations and regular maps

✍ Scribed by Jozef Širáň; Martin Škovier; Heinz-Jurgen Voss

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
948 KB
Volume
134
Category
Article
ISSN
0012-365X

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✦ Synopsis

A Sachs triangulation of a closed surface S is a triangulation T admitting a vertex-labelling 3, in a group G subject to the following conditions: (Sl) For any facial triangle t of Twith vertices x, y and z, either n(x)L(y),l(z)= 1 or L(x)n(z)L(y)=l. (S2) For any g,kG, there exists at most one edge in T whose endpoints are labelled g and h.

In this paper we establish various sufficient conditions for a Sachs triangulation to be a regular (symmetrical) map. As an application of these results we construct, for each integer d 2 2, a 2d-valent reflexible symmetrical triangulation of genus 1 + d(d-3)/2.

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