Tessellations were used by the Sumerians (about 4000 BC) in building wall decorations formed by patterns of clay tiles. History A temple mosaic from the ancient Sumerian city of Uruk IV (3400–3100 BC), showing a tessellation pattern in coloured tiles Tessellations form a class of patterns in nature, for example in the arrays of hexagonal cells found in honeycombs. 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. 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.

Tesselation images of a military tank