k–isotoxal Tilings from [p^n] Tilings

• Main Authors: Tomenes, Mark D, De Las Peñas, Ma. Louise Antonette N
• Format: text
• Published: Archīum Ateneo 2022
• Subjects: isotoxal; isotoxality; tilings; symmetry group; [p^n] tilings; Mathematics
• Online Access: https://archium.ateneo.edu/mathematics-faculty-pubs/182; https://www.tandfonline.com/doi/full/10.1080/17513472.2021.2011687
• Institution: Ateneo De Manila University

A tiling is k−isotoxal if its edges form k orbits or k transitivity classes under the action of its symmetry group. In this article, a method is presented that facilitates the systematic derivation of planar edge-to-edge k−isotoxal tilings from isohedral [pn] tilings. Two well-known subgroups of triangle groups will be used to create and determine classes of k−isotoxal tilings in the Euclidean, hyperbolic and spherical planes which will be described in terms of their symmetry groups and symbols. The symmetry properties of k−isotoxal tilings make these appropriate tools to create geometrically influenced artwork such as Escher-like patterns or aesthetically pleasing designs in the three classical geometries.