Such tilings may be decorative patterns, or may have functions such as providing durable and water -resistant pavement, floor or wall coverings.

In the geometry of higher dimensions, a space -filling or honeycomb is also called a tessellation of space.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, tessellations can be generalized to higher dimensions and a variety of geometries.Ī periodic tiling has a repeating pattern. 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.

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