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Dual semi-regular Article Face configuration Schläfli symbol Image Apeirogonal deltohedron: V3 3.∞ : dsr{2,∞} Apeirogonal bipyramid: V4 2.∞ : dt{2,∞} Cairo pentagonal tiling
Tessellated designs often appear on textiles, whether woven, stitched in, or printed. Tessellation patterns have been used to design interlocking motifs of patch shapes in quilts. [75] [76] Tessellations are also a main genre in origami (paper folding), where pleats are used to connect molecules, such as twist folds, together in a repeating ...
This list may not reflect recent changes. Tessellation * List of tessellations; 0–9. 3-4-3-12 tiling; 3-4-6-12 tiling; 33344-33434 tiling; A. Algebra and Tiling;
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.
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 .
Tessellations are patterns formed by repeating tiles all over a flat surface. There are 17 wallpaper groups of tilings. [78] While common in art and design, exactly repeating tilings are less easy to find in living things. The cells in the paper nests of social wasps, and the wax cells in honeycomb built by honey bees are well-known examples.
The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X . (Section 2–3 Circle packings, plane tessellations, and networks , pp. 34–40).
H. S. M. Coxeter, M. S. Longuet-Higgins, and J. C. P. Miller, in the 1954 paper 'Uniform polyhedra', Table 8: Uniform Tessellations, use the first three expansions and enumerate a total of 38 uniform tilings. If a tiling made of 2 apeirogons is also counted, the total can be considered 39 uniform tilings.