Edge-to-Edge Tilings with Vertex, Edge and Tile Transivity Properties
Date of Award
2021
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics
Department
Mathematics
First Advisor
Ma. Louise Antonette N. De Las Peñas, PhD
Abstract
Edge-to-edge tilings with vertex, edge and tile transitivity properties An (a, b, c) tiling T is an a-isogonal, b-isotoxal and c-isohedral tiling, that is, T forms, respectively, a orbits of vertices, b orbits of edges and c orbits of tiles under its symmetry group. This study gives a method of constructing an (a, b, c) tiling of the Euclidean (E 2 ), hyperbolic (H2 ) or spherical (S 2 ) plane. The method allows for a complete enumeration of the (a, 2, c) tilings of E 2 and S 2 as well as a listing of (a, 3, c) tilings of E 2 derived from tilings by regular polygons, which will be presented. Moreover, classes of (1 , b, c) tilings of E 2 , H2 and S 2 will be shown, particularly those derived from [p n ] tilings.
Recommended Citation
Tomenes, Mark, (2021). Edge-to-Edge Tilings with Vertex, Edge and Tile Transivity Properties. Archīum.ATENEO.
https://archium.ateneo.edu/theses-dissertations/539
