Enumeration of Semi-Equivelar Maps on the Torus

Semi-equivelar maps are generalizations of equivelar maps. There are eight non-isomorphic types of semi-equivelar maps on the torus. These are of the types $\{3^{3},4^{2}\}$, $\{3^{2},4,3,4\}$, $\{3, 6, 3, 6\}$, $\{3^{4},6\}$, $\{4,8^{2}\}$, $\{3,12^{2}\}$, $\{4,6,12\}$, $\{3, 4, 6, 4\}$. In this article we attempt to classify these maps.