k–isotoxal Tilings from [p^n] Tilings
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.
Tomenes, M. D., & De Las Peñas, Ma. L. A. N. (2022). K–isotoxal tilings from [p^n] tilings. Journal of Mathematics and the Arts, 15(3–4), 245–260. https://doi.org/10.1080/17513472.2021.2011687