Archimedean toroidal maps and their edge covers
Arnab Kundu, Dipendu Maity- Applied Mathematics
- General Mathematics
Abstract
The automorphism group of a map on a surface acts naturally on its flags (triples of incident vertices, edges, and faces). We will study the action of the automorphism group of a map on its edges. A map is semi-equivelar if all of its vertices have the same type of face-cycles. A semi-equivelar toroidal map refers to a semi-equivelar map embedded on a torus. If a map has k edge orbits under its automorphism group, it is referred to as a k-edge orbital or k-orbital. Specifically, it is referred to as an edge-transitive map if