On Uniform Edge-n-colorings of Tilings
Document Type
Article
Publication Date
2024
Abstract
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.
Recommended Citation
Abila, A.K., De Las Peñas, M.L.A.N. and Tomenes. On uniform edge-n-colorings of tilings. Acta Cryst. A80 (2024) 367-378. https://doi.org/10.1107/S2053273324005643
