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In Latin, tessella is a small cubical piece of clay, stone or glass used to make mosaics. The word "tessella" means "small square" (from "tessera", square, which in its turn is from the Greek word for "four"). It corresponds with the everyday term tiling which refers to applications of tessellations, often made of glazed clay.



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In 1619 Johannes Kepler did one of the first documented studies of tessellations when he wrote about the regular and semiregular tessellation, which are coverings of a plane with regular polygons. Some two hundred years later in 1891, the Russian crystallographer Yevgraf Fyodorov proved that every periodic tiling of the plane features one of seventeen different groups of isometries. Fedorov's work marked the unofficial beginning of the mathematical study of tessellations. Other prominent contributors include Shubnikov and Belov (1951); and Heinrich Heesch and Otto Kienzle (1963).



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Tilings with translational symmetry can be categorized by wallpaper groups, of which 17 exist. All seventeen of these groups are represented in the Alhambra palace in Granada, Spain. Of the three regular tilings two are in the p6m wallpaper group and one is in p4m.





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