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.

Installers for Tegula can be found here: https://software-ab.informatik.uni-tuebingen.de/download/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.

A paper describing the underlying math, algorithms and the software is in preparation.

Image credits: Daniel Huson