Periodic tilings play a role in the decorative arts, in construction and in crystal structures. Combinatorial tiling theory allows the systematic generation, visualization and exploration of such tilings of the plane, sphere and hyperbolic plane, using advanced algorithms and software. Here we present a “galaxy” of tilings that consists of the set of all 2.4 billion different types of periodic tilings that have Dress complexity up to 24. We make these available in a database and provide a new program called Tegula that can be used to search and visualize such tilings.

中文翻译：

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特古拉——探索二维周期性平铺的星系

周期性瓷砖在装饰艺术、建筑和水晶结构中发挥着重要作用。组合平铺理论允许使用先进的算法和软件系统地生成、可视化和探索平面、球面和双曲平面的此类平铺。在这里，我们展示了一个由所有 24 亿种不同类型的周期性切片组成的切片“星系”，这些周期性切片的 Dress 复杂度高达 24。我们在数据库中提供了这些，并提供了一个名为 Tegula 的新程序，可用于搜索和可视化此类平铺。