# 2-semi equivelar maps on the torus and the Klein bottle with few vertices

Document Type : Original paper

Authors

1 Department of Applied Science, Indian Institute of Information Technology, Allahabad 211 015, India

2 Department of Mathematics and Statistics, Vignan's Foundation for Science, Technology & Research, Vadlamudi 522213, India

3 Department of Applied Science & Humanities, Rajkiya Engineering College, Banda 210201, India

Abstract

The $k$-semi equivelar maps, for $k \geq 2$, are generalizations of maps on the surfaces of Johnson solids to closed surfaces other than the 2-sphere. In the present study, we determine 2-semi equivelar maps of curvature 0 exhaustively on the torus and the Klein bottle. Furthermore, we classify (up to isomorphism) all these 2-semi equivelar maps on the surfaces with up to 12 vertices.

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Main Subjects

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