Expansion of centered triangulations (Q1328389)

We use a construction of A. Bouchet for covering triangulations by means of nowhere-zero dual flows, but slightly modified, to prove that whenever \(G\) is a simple graph, which is not a star, two-cell embedded in a surface \(S\), and \(m\) is a nonnegative integer not divisible by 2, 3, or 5, there is a covering two-cell embedding of \(G_{(m)}\) in a surface \(\widetilde S\), orientable if and only if \(S\) is orientable, such that each face of the embedding of \(G\) and the faces above it in the embedding of \(G_{(m)}\) have the same length.