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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 .
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A computer screen showing a background wallpaper photo of the Palace of Versailles A wallpaper from fractal. A wallpaper or background (also known as a desktop background, desktop picture or desktop image on computers) is a digital image (photo, drawing etc.) used as a decorative background of a graphical user interface on the screen of a computer, smartphone or other electronic device.
A periodic tiling has a repeating pattern. Some special kinds include regular tilings with regular polygonal tiles all of the same shape, and semiregular tilings with regular tiles of more than one shape and with every corner identically arranged. The patterns formed by periodic tilings can be categorized into 17 wallpaper groups. A tiling that ...
Redecorate your rented apartment with peel and stick wallpaper and tiles.
The pattern represented by every finite patch of tiles in a Penrose tiling occurs infinitely many times throughout the tiling. They are quasicrystals: implemented as a physical structure a Penrose tiling will produce diffraction patterns with Bragg peaks and five-fold symmetry, revealing the repeated patterns and fixed orientations of its tiles ...
Following Grünbaum and Shephard (section 1.3), a tiling is said to be regular if the symmetry group of the tiling acts transitively on the flags of the tiling, where a flag is a triple consisting of a mutually incident vertex, edge and tile of the tiling. This means that, for every pair of flags, there is a symmetry operation mapping the first ...
The smallest wallpaper rectangle that can be tiled to form the whole pattern is known as the pattern repeat. Wallpaper printing techniques include surface printing , rotogravure , screen-printing , rotary printing press , and digital printing .
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