EXPANSION OF CENTERED TRIANGULATIONS

We use a construction of A. Bouchet for covering triangulations by mea ns of nowhere-zero dual flows, but slightly modified, to prove that wh enever G is a simple graph, which is not a star, two-cell embedded in a surface S, and m is a non-negative integer not divisible by 2, 3, or 5, there is a covering two-cell embedding of G(m) in a surface S, ori entable if and only if S is orientable, such that each face of the emb edding of G and the faces above it in the embedding of G(m) have the s ame length. (C) 1994 Academic Press, Inc.