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 \(-2\) .