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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.
This is a list of two-dimensional geometric shapes in Euclidean and other geometries. For mathematical objects in more dimensions, see list of mathematical shapes. For a broader scope, see list of shapes.
Kali, a free and open source software application for wallpaper, frieze and other patterns. Kali Archived 2020-11-21 at the Wayback Machine , free downloadable Kali for Windows and Mac Classic. Tess , a nagware tessellation program for multiple platforms, supports all wallpaper, frieze, and rosette groups, as well as Heesch tilings.