A classification of semi-equivelar maps on the surface of Euler characteristic $$-1$$ - 1

Debashis Bhowmik () and Ashish Kumar Upadhyay ()
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Debashis Bhowmik: Indian Institute of Technology Patna
Ashish Kumar Upadhyay: Indian Institute of Technology Patna

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 1, 289-296

Abstract: Abstract Semi Equivelar maps are generalizations of Archimedean solids to surfaces other than 2-sphere. Semi Equivelar Maps were introduced by Upadhyay et. al. in 2014. They also studied semi equivelar maps on the surface of Euler characteristics $$\chi = -1$$ χ = - 1 . In this article we classify all the semi equivelar maps on this surface with upto 12 vertices. We show that there are exactly four such maps. We also prove that there are at least 10 semi equivelar maps on this surface. We compute their Automorphism groups and show that none of these maps are vertex transitive.

Keywords: Vertex transitive maps; Archimedean solids; Semi-Equivelar Maps; Automorphism group; 52B70; 52C20; 57M20; 57N05 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13226-021-00074-z

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