Doubly Semiequivelar Maps on Torus and Klein Bottle
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 ex...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/5674172 |
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| author | Anand K. Tiwari Amit Tripathi Yogendra Singh Punam Gupta |
| author_facet | Anand K. Tiwari Amit Tripathi Yogendra Singh Punam Gupta |
| author_sort | Anand K. Tiwari |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-4c823319564e416c9fc2ef87d7572b46 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-4c823319564e416c9fc2ef87d7572b462025-02-03T06:45:46ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/56741725674172Doubly Semiequivelar Maps on Torus and Klein BottleAnand K. Tiwari0Amit Tripathi1Yogendra Singh2Punam Gupta3Department of Applied Science, Indian Institute of Information Technology, Allahabad 211 015, IndiaDepartment of Applied Science & Humanities, Rajkiya Engineering College, Banda 210201, IndiaDepartment of Applied Science, Indian Institute of Information Technology, Allahabad 211 015, IndiaDepartment of Mathematics & Statistics, Dr. Hari Singh Gour Vishwavidyalaya, Sagar 470 003, IndiaA 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.http://dx.doi.org/10.1155/2020/5674172 |
| spellingShingle | Anand K. Tiwari Amit Tripathi Yogendra Singh Punam Gupta Doubly Semiequivelar Maps on Torus and Klein Bottle Journal of Mathematics |
| title | Doubly Semiequivelar Maps on Torus and Klein Bottle |
| title_full | Doubly Semiequivelar Maps on Torus and Klein Bottle |
| title_fullStr | Doubly Semiequivelar Maps on Torus and Klein Bottle |
| title_full_unstemmed | Doubly Semiequivelar Maps on Torus and Klein Bottle |
| title_short | Doubly Semiequivelar Maps on Torus and Klein Bottle |
| title_sort | doubly semiequivelar maps on torus and klein bottle |
| url | http://dx.doi.org/10.1155/2020/5674172 |
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