-'A Tessellation (or Tiling) is when you cover a surface with a pattern of flat shapes so that there are no overlaps or gaps.'
-'Tessellation is the process of creating a two-dimensional plane
using the repetition of a geometric shape with no overlaps and no gaps.
Generalizations to higher dimensions are also possible. Tessellations
frequently appeared in the art of M. C. Escher, who was inspired by studying the Moorish use of symmetry in the Alhambra tiles during a visit in 1922. Tessellations are seen throughout art history, from ancient architecture to modern art.
In Latin, tessella is a small cubical piece of clay, stone or glass used to make mosaics.The word "tessella" means "small square" (from "tessera", square, which in its turn is from the Greek word for "four"). It corresponds with the everyday term tiling which refers to applications of tessellations, often made of glazed clay.'
-'In 1619 Johannes Kepler
did one of the first documented studies of tessellations when he wrote
about the regular and semiregular tessellation, which are coverings of a
plane with regular polygons. Some two hundred years later in 1891, the
Russian crystallographer Yevgraf Fyodorov
proved that every periodic tiling of the plane features one of
seventeen different groups of isometries. Fedorov's work marked the
unofficial beginning of the mathematical study of tessellations. Other
prominent contributors include Shubnikov and Belov (1951); and Heinrich Heesch and Otto Kienzle (1963).'
-'A regular tessellation is a highly symmetric tessellation made up of congruent regular polygons. Only three regular tessellations exist: those made up of equilateral triangles, squares, or hexagons. A semiregular tessellation
uses a variety of regular polygons; there are eight of these. The
arrangement of polygons at every vertex point is identical. An edge-to-edge tessellation
is even less regular: the only requirement is that adjacent tiles only
share full sides, i.e. no tile shares a partial side with any other
tile. Other types of tessellations exist, depending on types of figures
and types of pattern. There are regular versus irregular, periodic
versus nonperiodic, symmetric versus asymmetric, and fractal tessellations, as well as other classifications.'
-'Penrose tilings using two different polygons are the most famous example of tessellations that create aperiodic patterns. They belong to a general class of aperiodic tilings that can be constructed out of self-replicating sets of polygons by using recursion.'
-'A monohedral tiling is a tessellation in which all tiles are congruent. Spiral monohedral tilings include the Voderberg tiling discovered by Hans Voderberg in 1936, whose unit tile is a nonconvex enneagon; and the Hirschhorn tiling discovered by Michael Hirschhorn in the 1970s, whose unit tile is an irregular pentagon.'
-'Basaltic lava flows often display columnar jointing as a result of contraction
forces causing cracks as the lava cools. The extensive crack networks
that develop often produce hexagonal columns of lava. One example of
such an array of columns is the Giant's Causeway in Northern Ireland.
The Tessellated pavement in Tasmania is a rare sedimentary rock formation where the rock has fractured into rectangular blocks.
Within botany, the term "tessellate" describes a checkered pattern, for example on a flower petal, tree bark, or fruit.'
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