Warning: reading this text requires having read *the article that introduces the signature and weight of tilings*.
In a wallpaper group (or wallpaper group), the same pattern repeats indefinitely in two dimensions to tile the entire plane. Behind this apparent variety lies a group that transforms a basic pattern into all the others. Evgraf Fedorov proved that there are exactly seventeen such groups. This is easily demonstrated once one knows the plane-tiling theorem.

Wallpaper with symbol o.

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