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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 ...
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.
Pages in category "Regular tessellations" The following 12 pages are in this category, out of 12 total. This list may not reflect recent changes. 0–9.
A Pythagorean tiling Street Musicians at the Door, Jacob Ochtervelt, 1665.As observed by Nelsen [1] the floor tiles in this painting are set in the Pythagorean tiling. A Pythagorean tiling or two squares tessellation is a tiling of a Euclidean plane by squares of two different sizes, in which each square touches four squares of the other size on its four sides.
In the 1987 book, Tilings and patterns, Branko Grünbaum calls the vertex-uniform tilings Archimedean, in parallel to the Archimedean solids. Their dual tilings are called Laves tilings in honor of crystallographer Fritz Laves. [1] [2] They're also called Shubnikov–Laves tilings after Aleksei Shubnikov. [3]
Ada Dietz (1882 – 1981) was an American weaver best known for her 1949 monograph Algebraic Expressions in Handwoven Textiles, which defines weaving patterns based on the expansion of multivariate polynomials. [9] J. C. P. Miller used the Rule 90 cellular automaton to design tapestries depicting both trees and abstract patterns of triangles. [10]
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 ...
A tessellation of the above prototile meeting the Conway criterion. In the mathematical theory of tessellations , the Conway criterion , named for the English mathematician John Horton Conway , is a sufficient rule for when a prototile will tile the plane.
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