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: 2023-01-28T13:53:51Z Word Count : 5850 Synonim Tessellation

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: 2022-11-13T16:59:36Z Word Count : 4057 Synonim Space Shuttle thermal protection system

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: 2023-01-24T10:49:02Z Word Count : 4353 Synonim Mahjong tiles


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: 2023-01-30T08:11:03Z Word Count : 8444 Synonim Tetrahedron


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: 2022-12-15T14:24:42Z Word Count : 3547 Synonim Tile


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: 2022-12-24T15:20:32Z Word Count : 2422 Synonim Zonohedron

Tetrahedron packing

not tile space, and an upper bound below 100% (namely, 1 − (2.6...)·10−25) has been reported. Aristotle claimed that tetrahedra could fill space completely...

Last Update: 2022-11-08T15:34:56Z Word Count : 1002 Synonim Tetrahedron packing

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: 2023-01-30T06:24:36Z Word Count : 5416 Synonim Dehn invariant

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: 2022-12-25T06:05:23Z Word Count : 2951 Synonim Toynbee tiles

Penrose tiling

A 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 aperiodic...

Last Update: 2022-12-23T00:17:21Z Word Count : 5764 Synonim Penrose 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: 2023-01-04T11:13:26Z Word Count : 1718 Synonim Tiled rendering

Space Shuttle Columbia disaster

the insulative 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: 2023-02-02T00:58:59Z Word Count : 12086 Synonim Space Shuttle Columbia disaster

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: 2023-01-29T01:44:29Z Word Count : 3106 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: 2022-12-13T17:57:13Z Word Count : 1115 Synonim Guastavino tile

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: 2022-09-05T16:10:14Z Word Count : 1557 Synonim Weaire–Phelan structure

Wigner–Seitz cell

There are only five topologically distinct polyhedra which tile three-dimensional space, ℝ3. These are referred to as the parallelohedra. They are the...

Last Update: 2023-01-28T23:08:52Z Word Count : 1487 Synonim Wigner–Seitz cell

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: 2020-02-02T10:54:16Z Word Count : 171 Synonim Tetrapentagonal tiling

Tile drainage

Tile drainage is a form of agricultural drainage system that removes excess sub-surface water from fields to allow sufficient air space within the soil...

Last Update: 2022-11-01T11:38:20Z Word Count : 3585 Synonim Tile drainage

Einstein problem

tiles all tile space periodically. In 1988, Peter Schmitt discovered a single aperiodic prototile in 3-dimensional Euclidean space. While no tiling by...

Last Update: 2022-04-19T16:38:58Z Word Count : 636 Synonim Einstein problem

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. 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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