Abstract
A Sachs triangulation of a closed surface S is a triangulation T admitting a vertex-labelling λ in a group G subject to the following conditions: (S1) For any facial triangle t of T with vertices x, y and z, either λ( x)λ( y)λ( z) = 1 or λ( x)λ( z)λ( y) = 1. (S2) For any g, hϵ G, 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, a 2 d-valent reflexible symmetrical triangulation of genus 1 + d( d - 3)/2.
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