Determination Of All Regular Maps Of Small Genus

Complete lists are given of all reflexible orientable regular maps of genus 2 to 15, all non-orientable regular maps of genus 4 to 30, and all (orientable) rotary but chiral (irreflexible) maps of genus 2 to 15 inclusive. On each list the maps are classified according to genus and type (viz. fp; qg where every face is incident with p edges and every vertex is incident with q edges). The complete lists were determined with the help of a parallel program which finds all normal subgroups of low index in a finitely-presented group. 1991 Mathematics Subject Classification: 05C25, 57M15 1. Introduction A map is a 2-cell embedding of a connected graph (or multigraph) into a closed surface without boundary. Such a map M is composed of a vertex-set V = V (M ), an edge-set E = E(M ), and a set of faces which we will denote by F = F (M ). The map is called orientable or non-orientable according to whether the underlying surface (on which the graph is embedded) is orientable or non-orientable. The..