Doubly semi-equivelar maps on the plane and the torus

Abstract

A map is called 2-semi equivelar if it has exactly two distinct cyclic arrangement of faces at its vertices. A 2-semi-equivelar map is called 2-uniform if it has precisely 2 orbits of vertices under its symmetric group. Doubly semi-equivelar maps are a subclass of 2-semi equivelar maps that are used to determine 2-uniform maps. In this article, we determine doubly semi-equivelar maps of curvature 0 on the plane and torus exhaustively. Further, we present a classification of doubly semi-equivelar maps on the torus and illustrate this for those doubly semi-equivelar maps which comprise face-sequence pairs and