k -Isocoronal tilings
In this article, a framework is presented that allows the systematic derivation of planar edge-to-edge k-isocoronal tilings from tile-s-transitive tilings, s k. A tiling T is k-isocoronal if its vertex coronae form k orbits or k transitivity classes under the action of its symmetry group. The vertex...
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| Format: | text |
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Archīum Ateneo
2019
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| Online Access: | https://archium.ateneo.edu/mathematics-faculty-pubs/48 https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1047&context=mathematics-faculty-pubs |
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| Institution: | Ateneo De Manila University |
| Summary: | In this article, a framework is presented that allows the systematic derivation of planar edge-to-edge k-isocoronal tilings from tile-s-transitive tilings, s k. A tiling T is k-isocoronal if its vertex coronae form k orbits or k transitivity classes under the action of its symmetry group. The vertex corona of a vertex x of T is used to refer to the tiles that are incident to x. The k-isocoronal tilings include the vertex-k-transitive tilings (k-isogonal) and k-uniform tilings. In a vertex-k- transitive tiling, the vertices form k transitivity classes under its symmetry group. If this tiling consists of regular polygons then it is k-uniform. This article also presents the classification of isocoronal tilings in the Euclidean plane. |
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