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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 the 1850s, during the Victorian era prior to Morris, most English wallpaper was inspired by the geometric and historical designs of Augustus Welby Pugin, who had created the neo-Gothic interiors of Westminster Palace, and Owen Jones, notable for his abstract geometric patterns. Wallpaper design was also strongly influenced by imitations of ...
Ceron Geometric Wallpaper Wayfair boasts no shortage of home decor options—and that includes a bevy of Instagrammable wallpapers, like this tile-esque one that costs less than a dollar per ...
The patterns formed by periodic tilings can be categorized into 17 wallpaper groups. A tiling that lacks a repeating pattern is called "non-periodic". An aperiodic tiling uses a small set of tile shapes that cannot form a repeating pattern (an aperiodic set of prototiles).
In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition. Such a transformation is an invertible mapping of the ambient space which takes the object to itself, and which preserves all the relevant structure of the object.
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