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A wallpaper group (or plane symmetry group or plane crystallographic group) is a mathematical classification of a two-dimensional repetitive pattern, based on the symmetries in the pattern. Such patterns occur frequently in architecture and decorative art , especially in textiles , tiles , and wallpaper .
The 17 wallpaper groups, with finite fundamental domains, are given by International notation, orbifold notation, and Coxeter notation, classified by the 5 Bravais lattices in the plane: square, oblique (parallelogrammatic), hexagonal (equilateral triangular), rectangular (centered rhombic), and rhombic (centered rectangular).
Image title: This is the structure diagram of the walpaper group p1 I, the creator of this work, hereby release it into the public domain. This applies worldwide.
The following other wikis use this file: Usage on ca.wikipedia.org Notació de Coxeter; Usage on da.wikipedia.org Tapetgruppe; Usage on es.wikipedia.org
In mathematics, a layer group is a three-dimensional extension of a wallpaper group, with reflections in the third dimension. It is a space group with a two-dimensional lattice, meaning that it is symmetric over repeats in the two lattice directions.
Description: Cell structure diagram of the wallpaper group p1: Date: created 22. Jul. 2005, uploaded 26. Feb. 2006: Source: generated by self written XSLT available from the category overview
Description: Cell structure diagram of the wallpaper group p4g aka. p4gg: Date: 28 February 2006: Source: generated by self written XSLT available from the category overview: Author
In mathematics, a non-Euclidean crystallographic group, NEC group or N.E.C. group is a discrete group of isometries of the hyperbolic plane. These symmetry groups correspond to the wallpaper groups in euclidean geometry .