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Voronoi Hexagon Dish

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Voronoi Hexagon Dish
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Voronoi Hexagon Dish
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Voronoi Hexagon Dish _Designed by Kzhr ( http://www.thingiverse.com/thing:794204/#files ) _In mathematics, a Voronoi diagram is a partitioning of a plane into regions based on 'closeness' to points in a specific subset of the plane. That set of points (called seeds, sites, or generators) is specified beforehand, and for each seed there is a corresponding region consisting of all points closer to that seed than to any other. These regions are called Voronoi cells. The Voronoi diagram of a set of points is dual to its Delaunay triangulation.It is named after Georgy Voronoy, and is also called a Voronoi tessellation, a Voronoi decomposition, a Voronoi partition, or a Dirichlet tessellation (after Peter Gustav Lejeune Dirichlet). Voronoi diagrams have practical and theoretical applications to a large number of fields, mainly in science and technology but even including visual art. _In the simplest and most familiar case (shown in the first picture), we are given a finite set of points {p1, …, pn} in the Euclidean plane. In this case each site pk is simply a point and its corresponding Voronoi cell (also called Voronoi region or Dirichlet cell) Rk consisting of every point whose distance to pk is less than or equal to its distance to any other site. Each such cell is obtained from the intersection of half-spaces, and hence it is a convex polygon. The segments of the Voronoi diagram are all the points in the plane that are equidistant to the two nearest sites. The Voronoi vertices (nodes) are the points equidistant to three (or more) sites. _Voronoi diagrams are also related to other geometric structures such as the medial axis (which has found applications in image segmentation, optical character recognition, and other computational applications), straight skeleton, and zone diagrams. Besides points, such diagrams use lines and polygons as seeds. By augmenting the diagram with line segments that connect to nearest points on the seeds, a planar subdivision of the environment is obtained.This structure can be used as a navigation mesh for path-finding through large spaces. The navigation mesh has been generalized to support 3D multi-layered environments, such as an airport or a multi-storey building. _ Voronoi diagrams find widespread applications in areas such as computer graphics, epidemiology, geophysics, and meteorology. _In geometry, a hexagon is a polygon with six edges and six vertices. A regular hexagon has Schläfli symbol {6}. The total of the internal angles of any hexagon is 720°.From bees' honeycombs to the Giant's Causeway, hexagonal patterns are prevalent in nature due to their efficiency. In a hexagonal grid each line is as short as it can possibly be if a large area is to be filled with the fewest number of hexagons. This means that honeycombs require less wax to construct and gain lots of strength under compression. _A regular hexagon is defined as a hexagon that is both equilateral and equiangular. It is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle). The common length of the sides equals the radius of the circumscribed circle. All internal angles are 120 degrees. A regular hexagon has 6 rotational symmetries (rotational symmetry of order six) and 6 reflection symmetries (six lines of symmetry), making up the dihedral group D6. The longest diagonals of a regular hexagon, connecting diametrically opposite vertices, are twice the length of one side. From this it can be seen that a triangle with a vertex at the center of the regular hexagon and sharing one side with the hexagon is equilateral, and that the regular hexagon can be partitioned into six equilateral triangles.
Additional Information

Additional Information

SKU 10001433
Length [mm] 195.21
Width [mm] 174.49
Height [mm] 52.45
Volume [cm³] 54.06
Area [cm²] 503.56
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