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If there are k orbits of vertices, a tiling is known as k-uniform or k-isogonal; if there are t orbits of tiles, as t-isohedral; if there are e orbits of edges, as e-isotoxal. k-uniform tilings with the same vertex figures can be further identified by their wallpaper group symmetry.
A rhombitrihexagonal tiling: tiled floor in the Archeological Museum of Seville, Spain, using square, triangle, and hexagon prototiles. Tessellation in two dimensions, also called planar tiling, is a topic in geometry that studies how shapes, known as tiles, can be arranged to fill a plane without any gaps, according to a given set of rules ...
Wall tile; Wallpaper; Wallpaper paste; Wallpaper tax; William Morris wallpaper designs; Z. Zellij This page was last edited on 21 June 2015, at 15:57 (UTC). ...
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 a single non-repeating large design carried over a set of sheets. The smallest wallpaper rectangle that can be tiled to form the whole pattern is known as the pattern repeat.
Example of an Egyptian design with wallpaper group p4m. 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 ...
In 1961, Wang conjectured that if a finite set of Wang tiles can tile the plane, then there also exists a periodic tiling, which, mathematically, is a tiling that is invariant under translations by vectors in a 2-dimensional lattice. This can be likened to the periodic tiling in a wallpaper pattern, where the overall pattern is a repetition of ...
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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.