Doubly Semiequivelar Maps on Torus and Klein Bottle. (24th March 2020)

• Record Type: Journal Article
• Authors: Tiwari, Anand K.; Tripathi, Amit; Singh, Yogendra; Gupta, Punam
• Other Names: Shabbir Ghulam Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2020(2020)
• Publication Date: 2020-03-24
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2020/5674172
• Languages: English
• ISSNs: 2314-4629

Abstract

Abstract : A tiling of the Euclidean plane, by regular polygons, is called 2-uniform tiling if it has two orbits of vertices under the action of its symmetry group. There are 20 distinct 2-uniform tilings of the plane. Plane being the universal cover of torus and Klein bottle, it is natural to ask about the exploration of maps on these two surfaces corresponding to the 2-uniform tilings. We call such maps as doubly semiequivelar maps. In the present study, we compute and classify (up to isomorphism) doubly semiequivelar maps on torus and Klein bottle. This classification of semiequivelar maps is useful in classifying a category of symmetrical maps which have two orbits of vertices, named as 2-uniform maps.