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k ‐Isocoronal tilings
Author(s) -
Taganap Eduard,
De Las Peñas Ma. Louise Antonette
Publication year - 2019
Publication title -
acta crystallographica section a
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.742
H-Index - 83
ISSN - 2053-2733
DOI - 10.1107/s2053273318013992
Subject(s) - substitution tiling , combinatorics , vertex (graph theory) , transitive relation , mathematics , hexagonal tiling , euclidean geometry , penrose tiling , quasicrystal , geometry , graph , grid
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 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 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.