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The union of all edges of a Cairo tiling is the same as the union of two tilings of the plane by hexagons.Each hexagon of one tiling surrounds two vertices of the other tiling, and is divided by the hexagons of the other tiling into four of the pentagons in the Cairo tiling. [4]
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 .
In Latin, tessella is a small cubical piece of clay, stone, or glass used to make mosaics. [12] The word "tessella" means "small square" (from tessera, square, which in turn is from the Greek word τέσσερα for four). It corresponds to the everyday term tiling, which refers to applications of tessellations, often made of glazed clay.
This is a list of tessellations. This list is incomplete; you can help by adding missing items. (May 2021) Spherical ... 3 5 {3,5} Spherical dodecahedron: 5 3 {5,3}
The five-piece dissections used in the proofs by Al-Nayrizi and Thābit ibn Qurra (left) and by Henry Perigal (right). This tiling is called the Pythagorean tiling because it has been used as the basis of proofs of the Pythagorean theorem by the ninth-century Islamic mathematicians Al-Nayrizi and Thābit ibn Qurra, and by the 19th-century British amateur mathematician Henry Perigal.
Pages in category "Tessellation" The following 43 pages are in this category, out of 43 total. This list may not reflect recent changes. ...
In computer graphics, tessellation is the dividing of datasets of polygons (sometimes called vertex sets) presenting objects in a scene into suitable structures for rendering. Especially for real-time rendering , data is tessellated into triangles , for example in OpenGL 4.0 and Direct3D 11 .
In geometry, the icosahedral honeycomb is one of four compact, regular, space-filling tessellations (or honeycombs) in hyperbolic 3-space.With Schläfli symbol {3,5,3}, there are three icosahedra around each edge, and 12 icosahedra around each vertex, in a regular dodecahedral vertex figure.