Karl Jones at 15:34, 26 May 2016

2016-05-26T15:34:51Z

Karl Jones: Created page with "A '''tessellation''' of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. == Description == In..."

2016-05-26T15:32:00Z

Created page with "A '''tessellation''' of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. == Description == In..."

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A '''tessellation''' of a flat surface is the tiling of a [[plane]] using one or more [[geometric shapes]], called tiles, with no overlaps and no gaps.

== Description ==

In [[mathematics]], tessellations 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. In the geometry of higher dimensions, a space-filling or [[honeycomb]] is also called a tessellation of space.

== Real-world examples ==

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 decorative 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.

== Examples in nature ==

Tessellations form a class of patterns in nature, for example in the arrays of hexagonal cells found in [[Honeycomb|honeycombs]].

== See also ==

* [[Geometry]]
* [[Mathematics]]
* [[Patterns]]

== External links ==

* [https://en.wikipedia.org/wiki/Tessellation Tessellation] @ Wikipedia

[[Category:Geometry]]
[[Category:Mathematics]]
[[Category:Patterns]]

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-A '''tessellation''' of a flat surface is the tiling of a [[plane]] using one or more [[geometric shapes]], called tiles, with no overlaps and no gaps.
+[[File:1280px-2005-06-25 Tiles together.jpg|thumb|[[Pythagorean tiling]]]]A '''tessellation''' of a flat surface is the tiling of a [[plane]] using one or more [[geometric shapes]], called tiles, with no overlaps and no gaps.
 == Description ==
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 * [[Mathematics]]
 * [[Patterns]]
+* [[Pythagorean tiling]]
 == External links ==

Tessellation - Revision history

Karl Jones at 15:34, 26 May 2016

Karl Jones: Created page with "A '''tessellation''' of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. == Description == In..."