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Patterns based on the 17 wallpaper groups. From Grotesque Geometry by Andrew Crompton   Web Link: http://www.cromp.com/tess/home.html


There are seventeen possibilities, which were first classified by Eugraf Federov in 1881;  but it appears that they were all known, and employed for decorative purposes, by the ancient Egyptians. The most spectacular renderings of them  are to be found in the Moorish decorations on the Alhambra. When one departs from these regular designs, which all have a lattice-like structure that is  invariant after moving along vertical or horizontal directions, the number of possible designs grows dramatically. In fact, any one of the patterns can then be combined with the others in an infinite number of different permutations.  

Text from ‘The Artful Universe’ by John Barrow