Semi-equivelar maps on the surface of Euler characteristic $-1$

Semi-Equivelar maps are generalizations of Archimedean solids to surfaces other than the 2-sphere. In an earlier work a complete classification of semi-equivelar map of type $(3^5, 4)$ on the surface of Euler characteristic $-1$ was given. Vertex transitive semi-equivelar maps on the double torus have been classified. In this article we study these types of maps on the surface of Euler characteristic $-1$. We classify them and show that none of them is vertex transitive.