Tegula is a program for displaying and exploring two-dimensional periodic tilings, based on the concept of Delaney-Dress symbols. Tegula was written by Daniel Huson and Rüdiger Zeller, using code by Klaus Westphal. Tegula is written in Java (12) and uses JavaFX.
Download the program here: https://github.com/husonlab/tegula/releases/latest.
View the user manual here: https://husonlab.github.io/tegula/.
We provide three databases of tilings, containing all periodic tilings with Dress complexity ≤ 18 and all euclidean and spherical tilings with Dress complexity ≤ 24. These were computed using genDSyms, available here: https://github.com/odf/julia-dsymbols.
We have computed 2.4 billion tilings in total, but that file is too big to put online.
Image credits: Daniel Huson
The underlying mathematics, algorithms and sofware are described in this paper:
Rüdiger Zeller, Olaf Delgado-Friedrichs, Daniel H. Huson, Tegula – exploring a galaxy of two-dimensional periodic tilings, Computer Aided Geometric Design, 90 (2021) https://doi.org/10.1016/j.cagd.2021.102027.