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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).
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.
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
Cell structure diagram of the wallpaper group p4m aka. p4mm: Date: 22 July 2005: Source: generated by self written XSLT available from the category overview: Author: Martin von Gagern: Permission (Reusing this file) Released into the public domain by Martin von Gagern: Other versions: square SVG rectangualar PNG square PNG
The fact that A and B have the same wallpaper group means that they have the same symmetries, regardless of details of the designs, whereas C has a different set of symmetries despite any superficial similarities. A complete list of all seventeen possible wallpaper groups can be found below. Symmetries of patterns
The following other wikis use this file: Usage on da.wikipedia.org Tapetgruppe; Usage on es.wikipedia.org Grupo del papel pintado; Usage on ja.wikipedia.org