Semi-equivelar maps

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Abstract

Semi-Equivelar maps are generalizations of maps on the surface of Archimedean Solids to surfaces other than $2$ -Sphere. We classify some semi-equivelar maps on surface of Euler characteristic $-1$ and show that none of these are vertex transitive. We establish existence of $12$ -covered triangulations for this surface. We further construct double cover of these maps to show existence of semi-equivelar maps on the surface of double torus. We also construct several semi-equivelar maps on the surfaces of Euler characteristics $-8$ and $-10$ and on non-orientable surface of Euler characteristics $-2$ .