Determination of all Regular Maps of Small Genus

Abstract

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 {p, q} 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. © 2001 Academic Press.