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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 symmetry groups are named here by three naming schemes: International notation, orbifold notation, and Coxeter notation. There are three kinds of symmetry groups of the plane: 2 families of rosette groups – 2D point groups; 7 frieze groups – 2D line groups; 17 wallpaper groups – 2D space groups.
Description: Cell structure diagram of the wallpaper group p3: Date: 22 July 2005: Source: generated by self written XSLT available from the category overview: Author: Martin von Gagern
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
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.
Image title: This is the structure diagram of the walpaper group p6m I, the creator of this work, hereby release it into the public domain. This applies worldwide.
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Example C has a different wallpaper group, called p4g or 4*2 . 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.