Tessellations form a class of patterns in nature, for example in the arrays of hexagonal cells found in honeycombs.Ī rhombitrihexagonal tiling: tiled floor in the Archeological Museum of Seville, Spain, using square, triangle, and hexagon prototiles Tessellations are sometimes employed for decorative effect in quilting. Escher often made use of tessellations, both in ordinary Euclidean geometry and in hyperbolic geometry, for artistic effect. Historically, tessellations were used in Ancient Rome and in Islamic art such as in the Moroccan architecture and decorative geometric tiling of the Alhambra palace. Such tilings may be decorative patterns, or may have functions such as providing durable and water-resistant pavement, floor, or wall coverings. A tessellation of space, also known as a space filling or honeycomb, can be defined in the geometry of higher dimensions.Ī real physical tessellation is a tiling made of materials such as cemented ceramic squares or hexagons. An aperiodic tiling uses a small set of tile shapes that cannot form a repeating pattern. ![]() ![]() A tiling that lacks a repeating pattern is called "non-periodic". The patterns formed by periodic tilings can be categorized into 17 wallpaper groups. 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. In mathematics, tessellation can be generalized to higher dimensions and a variety of geometries.Ī periodic tiling has a repeating pattern. Send us feedback about these examples.An example of non‑periodicity due to another orientation of one tile out of an infinite number of identical tiles.Ī tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps. These examples are programmatically compiled from various online sources to illustrate current usage of the word 'tessellation.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Quanta Magazine, The squinting eyes, the jut of the chin, the precise tessellation of the lower lip and upper lip stay the same. Quanta Magazine, 11 July 2017 An example is the tessellation of a strange, multipronged shape called the Taylor-Socolar tile, discovered by the Australian amateur mathematician Joan Taylor in the 1990s, and analyzed in detail with Joshua Socolar of Duke University in 2010. 2020 As one journey - the classification of all convex polygon tessellations - ends, another is just beginning. Escher’s famous tessellations of a disk with fish or angels and devils that get smaller near the boundary. 2020 In the cases Wiles studied, the tiling might be something along the lines of M.C. Caroline Delbert, Popular Mechanics, 31 Aug. Brian Westover, PCMAG, 8 July 2022 Keller’s conjecture, a tessellation problem about the way certain shapes tile in certain spaces, has been solved for all but seven-dimensional space. ![]() 2016 Both exercise graphics and compute shaders, but one focuses on hardware tessellation and the other on the OpenGL application programming interface (API). Nathaniel Scharping, Discover Magazine, 19 Dec. ![]() 2022 The true impact of roads seems to be the gradual tessellation of once-cohesive landscapes. Nathaniel Scharping, Discover Magazine, 29 Nov. Recent Examples on the Web The path of the International Space Station, as mapped over a tessellation of Narukawa's world map.
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