3-Isogonal Planar Tilings are not 3-Isogonal on the Torus

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Authors

  • Marbarisha M. Kharkongor
     Department of Science and Mathematics, Indian Institute of Information Technology Guwahati, Assam-781 015 ,IN
  • Debashis Bhowmik
     Department of Mathematics, Indian Institute of Technology Patna, Patna 801 106 ,IN
  • Dipendu Maity
     Department of Science and Mathematics, Indian Institute of Information Technology Guwahati, Assam-781 015 ,IN

DOI:

https://doi.org/10.18311/jims/2023/29802

Keywords:

Covering Maps, Isogonal Maps, Symmetric Group.
52C20, 52B70, 51M20, 57M60

Abstract

A 3-isogonal tiling is an edge-to-edge tiling by regular polygons having 3 distinct transitivity classes of vertices. We know that there are sixty-one distinct 3-isogonal tilings on the plane. In this article, we discuss and determine the bounds of the vertex orbits of the plane’s 3-isogonal lattices on the torus and will show that these bounds are sharp.

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Published

2023-07-12

How to Cite

Kharkongor, M. M., Bhowmik, D., & Maity, D. (2023). 3-Isogonal Planar Tilings are not 3-Isogonal on the Torus. The Journal of the Indian Mathematical Society, 90(3-4), 375–386. https://doi.org/10.18311/jims/2023/29802

Issue

Volume 90, Issue 3-4, July-December 2023

Section

Articles

License

Copyright (c) 2023 Marbarisha M. Kharkongor, Debashis Bhowmik, Dipendu Maity

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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Europe PMC
Received 2022-03-15
Accepted 2022-07-28
Published 2023-07-12

 

References

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