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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.
Dual semi-regular Article Face configuration Schläfli symbol Image Apeirogonal deltohedron: V3 3.∞ : dsr{2,∞} Apeirogonal bipyramid: V4 2.∞ : dt{2,∞} Cairo pentagonal tiling
Natural patterns include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes. [1] Early Greek philosophers studied pattern, with Plato, Pythagoras and Empedocles attempting to explain order in nature. The modern understanding of visible patterns developed gradually over time.
Convex uniform honeycomb – The 28 uniform 3-dimensional tessellations, a parallel construction to the convex uniform Euclidean plane tilings. Euclidean tilings by convex regular polygons; List of tessellations; Percolation threshold; Uniform tilings in hyperbolic plane
Pages in category "Tessellation" The following 43 pages are in this category, out of 43 total. This list may not reflect recent changes. ...
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.
Regular Division of the Plane III, woodcut, 1957 - 1958.. Regular Division of the Plane is a series of drawings by the Dutch artist M. C. Escher which began in 1936. These images are based on the principle of tessellation, irregular shapes or combinations of shapes that interlock completely to cover a surface or plane.
The tesseract can make a regular tessellation of 4-dimensional hyperbolic space, with 5 tesseracts around each face, with Schläfli symbol {4,3,3,5}, called an order-5 tesseractic honeycomb. The Ammann–Beenker tiling is an aperiodic tiling in 2 dimensions obtained by cut-and-project on the tesseractic honeycomb along an eightfold rotational ...