What is "tessellation"

Tessellation \Tes`sel*la"tion\, n. The act of tessellating; also, the mosaic work so formed.
--J. Forsyth.

"minute arrangement of parts or colors," 1650s, noun of action from Late Latin tessellatus (see tessellated).

n. 1 (context uncountable English) The property or fact of tessellate. 2 (context countable English) A tiling pattern with no gaps; the result of tessellating an area or plane. 3 (context uncountable English) A less common name for polygon tessellation.

1. n. the careful juxtaposition of shapes in a pattern; "a tessellation of hexagons"

2. the act of adorning with mosaic

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. 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.

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

In computer graphics, tessellation is used to manage datasets of polygons (sometimes called vertex sets) presenting objects in a scene and divide them into suitable structures for rendering. Especially for real-time rendering, data is tessellated into triangles, for example in OpenGL and Direct3D 11.