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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.
Voronoi tessellations of regular lattices of points in two or three dimensions give rise to many familiar tessellations. A 2D lattice gives an irregular honeycomb tessellation, with equal hexagons with point symmetry; in the case of a regular triangular lattice it is regular; in the case of a rectangular lattice the hexagons reduce to ...
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 .
This is a list of tessellations. This list is incomplete; you can help by adding missing items. ... V3 3.4 2: d{3,6}:e Floret pentagonal tiling: V3 4.6 dsr{6,3}
Tessellations of euclidean and hyperbolic space may also be considered regular polytopes. Note that an 'n'-dimensional polytope actually tessellates a space of one dimension less. For example, the (three-dimensional) platonic solids tessellate the 'two'-dimensional 'surface' of the sphere.
This is a list of two-dimensional geometric shapes in Euclidean and other geometries. For mathematical objects in more dimensions, see list of mathematical shapes. For a broader scope, see list of shapes.
The original form of Penrose tiling used tiles of four different shapes, but this was later reduced to only two shapes: either two different rhombi, or two different quadrilaterals called kites and darts. The Penrose tilings are obtained by constraining the ways in which these shapes are allowed to fit together in a way that avoids periodic tiling.
Therefore, the second problem is that this nomenclature is not unique for each tessellation. In order to solve those problems, GomJau-Hogg’s notation [ 3 ] is a slightly modified version of the research and notation presented in 2012, [ 2 ] about the generation and nomenclature of tessellations and double-layer grids.