k -Isocoronal tilings

• Main Authors: Taganap, Eduard C, De Las Peñas, Ma. Louise Antonette N
• Format: text
• Published: Archīum Ateneo 2019
• Subjects: k-isocoronal tilings; vertex-k- transitive tilings; k-uniform tilings; isocoronal tilings; uniform tilings; Geometry and Topology; Mathematics
• Online Access: https://archium.ateneo.edu/mathematics-faculty-pubs/48; https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1047&context=mathematics-faculty-pubs
• Institution: Ateneo De Manila University

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.