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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).
Thus these 10 groups give rise to 17 wallpaper groups, and the four groups with n = 1 and 2, give also rise to 7 frieze groups. For each of the wallpaper groups p1, p2, p3, p4, p6, the image under p of all isometry groups (i.e. the "projections" onto E(2) / T or O(2) ) are all equal to the corresponding C n; also two frieze groups correspond to ...
He then derives the 7 frieze groups and the 17 wallpaper groups. In the second part, chapters 8–10, the dichromatic (black-and-white, two-colored) patterns are introduced and the 17 dichromatic line groups and the 46 black-and-white dichromatic plane groups are derived.
The surjective mapping from a layer group to a wallpaper group (plane group) can be obtained by disregarding symmetry elements along the stacking direction, typically denoted as the z-axis, and aligning the remaining elements with those of the plane groups. [3]
A wallpaper group is a mathematical concept used to classify repetitive designs on two-dimensional surfaces, such as floors and walls, based on the symmetries in the pattern. Such patterns occur frequently in architecture and decorative art. The mathematical study of such patterns reveals that exactly 17 different types of pattern can occur.
The subject of wallpaper groups is a mathematical subject, namely: realizing abstract groups as certain groups of motions in the plane. The images are essential to understanding this subject, and it would be inappropriate to hide them.
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