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A 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. In mathematics, tessellation can be generalized to higher dimensions and a variety of geometries. A periodic tiling has a repeating pattern.
Let be a metric space with distance function .Let be a set of indices and let () be a tuple (indexed collection) of nonempty subsets (the sites) in the space .The Voronoi cell, or Voronoi region, , associated with the site is the set of all points in whose distance to is not greater than their distance to the other sites , where is any index different from .
Download as PDF; Printable version; In other projects Wikidata item; Appearance. move to sidebar hide This ... This is a list of tessellations.
These notes sections are interesting and entertaining, as they discuss the efforts of the previous workers in the field and detail the good (and bad) approaches to the topic. The notes also identify unsolved problems, point out areas of potential application, and provide connections to other disciplines in mathematics, science, and the arts.
In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which exactly three hexagons meet at each vertex. It has Schläfli symbol of {6,3} or t {3,6} (as a truncated triangular tiling).
A Pythagorean tiling Street Musicians at the Door, Jacob Ochtervelt, 1665.As observed by Nelsen [1] the floor tiles in this painting are set in the Pythagorean tiling. A Pythagorean tiling or two squares tessellation is a tiling of a Euclidean plane by squares of two different sizes, in which each square touches four squares of the other size on its four sides.
A power diagram of four circles. In computational geometry, a power diagram, also called a Laguerre–Voronoi diagram, Dirichlet cell complex, radical Voronoi tesselation or a sectional Dirichlet tesselation, is a partition of the Euclidean plane into polygonal cells defined from a set of circles.
(In addition, the adjacency graph of the tiles induces another Euclidean graph.) If there are finitely many prototiles in the tessellation, and the tessellation is periodic, then the resulting Euclidean graph will be periodic. Going in the reverse direction, the prototiles of a tessellation whose 1-skeleton is (topologically equivalent to) the ...