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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).
Solid geometry, including table of major three-dimensional shapes; Box-drawing character; Cuisenaire rods (learning aid) Geometric shape; Geometric Shapes (Unicode block) Glossary of shapes with metaphorical names; List of symbols; Pattern Blocks (learning aid)
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). A tessellation of space, also known as a space filling or honeycomb, can be defined in the geometry of higher dimensions.
A pattern is a regularity in the world, in human-made design, [1] or in abstract ideas. As such, the elements of a pattern repeat in a predictable manner. A geometric pattern is a kind of pattern formed of geometric shapes and typically repeated like a wallpaper design. Any of the senses may directly observe patterns.
Name Images Chinese characters Border Gong (工; work) and bats Decorative Floral and twines Grass pattern Tang caowen [4] Twined branches Chanzhiwen [4] Curves Pommel pattern Guri (屈輪) / Pommel scroll [21] Geometric Diagonal Diagonal straight lines Lishui: Diagonal wavy lines Semicricles Horizontal semi-circles Woshui Curvilinear Swirl [4 ...
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The name hexafoil is sometimes also used to refer to a different geometric design that is used as a traditional element of Gothic architecture, [21] created by overlapping six circular arcs to form a flower-like image. [22] [23] The hexafoil design is modeled after the six petal lily, for its symbolism of purity and relation to the Trinity. [24]