The Journal of the Indian Mathematical Society

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


Affiliations
1 Department of Science and Mathematics, Indian Institute of Information Technology Guwahati, Assam-781 015, India
2 Department of Mathematics, Indian Institute of Technology Patna, Patna 801 106, India
     

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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.

Keywords

Covering Maps, Isogonal Maps, Symmetric Group.
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  • 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, India
Debashis Bhowmik
Department of Mathematics, Indian Institute of Technology Patna, Patna 801 106, India
Dipendu Maity
Department of Science and Mathematics, Indian Institute of Information Technology Guwahati, Assam-781 015, India

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.

Keywords


Covering Maps, Isogonal Maps, Symmetric Group.

References





DOI: https://doi.org/10.18311/jims%2F2023%2F29802