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Tessellations are patterns covering a plane by fitting together replicas of a basic shape. In geometrical terms, a tessellation is the pattern resulting from the arrangement of regular polygons to cover a plane without any gaps or overlapping. These patterns are usually repeating. There are three different types of tessellations.
The first type of tessellation is the regular tessellation. A regular tessellation has three or four or five or more equal sides and angles. A regular tessellation is made up entirely of congruent regular polygons all meeting vertex to vertex. There are only three regular tessellations in the Euclidean plane triangles, squares, and hexagons.
The second type of tessellations is semi-regular tessellations. They are made up with two or more types of the regular polygon, which are fitted together, and the arrangement of polygons at every vertex point is identical. There are eight semi-regular tessellations, which comprise different combinations of equilateral triangles, squares, hexagons, octagons, and dodecagons.
Non-regular tessellations are the third type of tessellations. Non-regular tessellations are those in which there is no restriction on the order of the polygons around vertices. There are an infinite number of these tessellations. There are also tessellations that do not share common edges and vertices.
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Tessellations can be found in many forms, from tiling on a floor to a piece of artwork. Tessellations can be found in natural objects such as a honeycomb or the scales of a snakes skin. An excellent example of tessellations in artwork would be the dutch artist M.C. Escher. Tessellations can be found any time, any place.
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