On Uniform Edge-n-colorings of Tilings
An edge-n-coloring of a uniform tiling is uniform if for any two vertices of there is a symmetry of that preserves the colors of the edges and maps one vertex onto the other. This paper gives a method based on group theory and color symmetry theory to arrive at uniform edge-n-colorings of uniform...
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| Main Authors: | , , |
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| Format: | text |
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Archīum Ateneo
2024
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| Subjects: | |
| Online Access: | https://archium.ateneo.edu/mathematics-faculty-pubs/284 https://doi.org/10.1107/S2053273324005643 |
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| Institution: | Ateneo De Manila University |
| Summary: | An edge-n-coloring of a uniform tiling is uniform if for any two vertices of there is a symmetry of that preserves the colors of the edges and maps one vertex onto the other. This paper gives a method based on group theory and color symmetry theory to arrive at uniform edge-n-colorings of uniform tilings. The method is applied to give a complete enumeration of uniform edge-n-colorings of the uniform tilings of the Euclidean plane, for which the results point to a total of 114 colorings, n = 1, 2, 3, 4, 5. Examples of uniform edge-n-colorings of tilings in the hyperbolic plane and two-dimensional sphere are also presented. |
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