20 results found for: “tile_spacers”.

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A 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. In...

Last Update: 2024-01-17T04:21:23Z Word Count : 5974 Synonim Tessellation

Einstein problem

anisohedral tiles all tile space periodically. In 1988, Peter Schmitt discovered a single aperiodic prototile in three-dimensional Euclidean space. While no...

Last Update: 2024-01-23T22:37:21Z Word Count : 1128 Synonim Einstein problem

Space Shuttle thermal protection system

loss of Space Shuttle Columbia.) The TPS was a system of different protection types, not just silica tiles. They are in two basic categories: tile TPS and...

Last Update: 2023-12-06T13:42:22Z Word Count : 4074 Synonim Space Shuttle thermal protection system


In another sense, a tile is a construction tile or similar object, such as rectangular counters used in playing games (see tile-based game). The word...

Last Update: 2024-02-07T03:44:04Z Word Count : 3984 Synonim Tile

Mahjong tiles

Mahjong tiles (Chinese: 麻將牌 or 麻雀牌; pinyin: májiàngpái; Cantonese Jyutping: maa4zoek3paai2; Japanese: 麻雀牌; rōmaji: mājanpai) are tiles of Chinese origin...

Last Update: 2024-02-15T02:05:09Z Word Count : 4558 Synonim Mahjong tiles


associated to it. First we consider the space-tiling property. The zonotope Z {\displaystyle Z} is said to tile R d {\displaystyle \mathbb {R} ^{d}} if...

Last Update: 2024-01-25T17:19:35Z Word Count : 2422 Synonim Zonohedron


that can tile space as the tetrahedral-octahedral honeycomb. However, several irregular tetrahedra are known, of which copies can tile space, for instance...

Last Update: 2024-02-02T09:21:12Z Word Count : 8508 Synonim Tetrahedron

Shim (spacer)

for better fit, or provide a level surface. Shims may also be used as spacers to fill gaps between parts subject to wear. Many materials make suitable...

Last Update: 2022-12-29T12:53:33Z Word Count : 524 Synonim Shim (spacer)

Dehn invariant

("dissected") into another, and whether a polyhedron or its dissections can tile space. It is named after Max Dehn, who used it to solve Hilbert's third problem...

Last Update: 2023-09-19T15:02:42Z Word Count : 5615 Synonim Dehn invariant

Tetrapentagonal tiling

In geometry, the tetrapentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t1{4,5} or r{4,5}. A half symmetry [1+,4...

Last Update: 2023-12-12T21:57:43Z Word Count : 171 Synonim Tetrapentagonal tiling

French drain

French drain (also called a weeping tile, trench drain, filter drain, blind drain, rubble drain, rock drain, drain tile, perimeter drain, land drain, French...

Last Update: 2023-10-31T13:27:10Z Word Count : 1279 Synonim French drain

Socolar–Taylor tile

Socolar–Taylor tile is a single non-connected tile which is aperiodic on the Euclidean plane, meaning that it admits only non-periodic tilings of the plane...

Last Update: 2023-12-27T09:03:43Z Word Count : 395 Synonim Socolar–Taylor tile

Penrose tiling

Penrose tiling is an example of an aperiodic tiling. Here, a tiling is a covering of the plane by non-overlapping polygons or other shapes, and a tiling is...

Last Update: 2023-11-21T20:33:07Z Word Count : 5763 Synonim Penrose tiling

Space Shuttle Columbia disaster

the insulating foam broke off from the Space Shuttle external tank and struck the thermal protection system tiles on the orbiter's left wing. Similar foam...

Last Update: 2024-02-20T04:41:40Z Word Count : 10585 Synonim Space Shuttle Columbia disaster

Hexagonal tiling

In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which exactly three hexagons meet at each vertex...

Last Update: 2023-11-26T10:17:41Z Word Count : 1286 Synonim Hexagonal tiling

Tiled rendering

Tiled rendering is the process of subdividing a computer graphics image by a regular grid in optical space and rendering each section of the grid, or tile...

Last Update: 2024-01-23T08:38:06Z Word Count : 1805 Synonim Tiled rendering

Weaire–Phelan structure

found that this structure was a better solution of the Kelvin problem of tiling space by equal volume cells of minimum surface area than the previous best-known...

Last Update: 2024-02-08T04:08:36Z Word Count : 1574 Synonim Weaire–Phelan structure

Toynbee tiles

The Toynbee tiles, also called Toynbee plaques, are messages of unknown origin found embedded in asphalt of streets in about two dozen major cities in...

Last Update: 2023-11-10T17:41:18Z Word Count : 2853 Synonim Toynbee tiles

Dropped ceiling

ceiling tiles and is a staple of modern construction and architecture in both residential and commercial applications. Dropped ceilings and ceiling tiles were...

Last Update: 2024-02-14T18:05:25Z Word Count : 3095 Synonim Dropped ceiling

Guastavino tile

The Guastavino tile arch system is a version of Catalan vault introduced to the United States in 1885 by Spanish architect and builder Rafael Guastavino...

Last Update: 2023-08-17T08:32:54Z Word Count : 1124 Synonim Guastavino tile

Main result


A 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. In mathematics, tessellation can be generalized to higher dimensions and a variety of geometries. 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 lacks a repeating pattern is called "non-periodic". An aperiodic tiling uses a small set of tile shapes that cannot form a repeating pattern (an aperiodic set of prototiles). A tessellation of space, also known as a space filling or honeycomb, can be defined in the geometry of higher dimensions. A real physical tessellation is a tiling made of materials such as cemented ceramic squares or hexagons. Such tilings may be decorative patterns, or may have functions such as providing durable and water-resistant pavement, floor, or wall coverings. 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. In the twentieth century, the work of M. C. Escher often made use of tessellations, both in ordinary Euclidean geometry and in hyperbolic geometry, for artistic effect. Tessellations are sometimes employed for decorative effect in quilting. Tessellations form a class of patterns in nature, for example in the arrays of hexagonal cells found in honeycombs.

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