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A wallpaper group (or plane symmetry group or plane crystallographic group) is a mathematical classification of a two-dimensional repetitive pattern, based on the symmetries in the pattern. Such patterns occur frequently in architecture and decorative art , especially in textiles , tiles , and wallpaper .
Wallpaper is used in interior decoration to cover the interior walls of domestic and public buildings. It is usually sold in rolls and is applied onto a wall using wallpaper paste . Wallpapers can come plain as "lining paper" to help cover uneven surfaces and minor wall defects, "textured", plain with a regular repeating pattern design, or with ...
Girih patterns are very likely to be all over the walls of some Islamic architectures. The decorating lines connect to each other and form a continuous network across the entire tiling with edges combine. In addition, girih patterns vary a lot on the surface, with different geometric shapes including decagons, hexagons, bowties and rhombuses ...
For example, the decoration of the 15th-century mosque in Yazd, Persia is based on a circle, divided into six by six circles drawn around it, all touching at its centre and each touching its two neighbours' centres to form a regular hexagon. On this basis is constructed a six-pointed star surrounded by six smaller irregular hexagons to form a ...
k-uniform tilings with the same vertex figures can be further identified by their wallpaper group symmetry. 1-uniform tilings include 3 regular tilings, and 8 semiregular ones, with 2 or more types of regular polygon faces. There are 20 2-uniform tilings, 61 3-uniform tilings, 151 4-uniform tilings, 332 5-uniform tilings and 673 6-uniform tilings.
Ingrain wallpaper was invented by German pharmacist Hugo Erfurt in 1864; marketed by the company his grandfather founded, it was first used as a decoration for shop windows, but began seeing use as a wallpaper from the 1920s on as well. Ingrain wallpaper is the most commonly used type of wallpaper in Germany.