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The Cairo tiling has been used as a decorative pattern in many recent architectural designs; for instance, the city center of Hørsholm, Denmark, is paved with this pattern, and the Centar Zamet, a sports hall in Croatia, uses it both for its exterior walls and its paving tiles. [16]
Example of an Egyptian design with wallpaper group p4m. 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 ...
The pattern represented by every finite patch of tiles in a Penrose tiling occurs infinitely many times throughout the tiling. They are quasicrystals: implemented as a physical structure a Penrose tiling will produce diffraction patterns with Bragg peaks and five-fold symmetry, revealing the repeated patterns and fixed orientations of its tiles ...
A Pythagorean tiling Street Musicians at the Door, Jacob Ochtervelt, 1665.As observed by Nelsen [1] the floor tiles in this painting are set in the Pythagorean tiling. A Pythagorean tiling or two squares tessellation is a tiling of a Euclidean plane by squares of two different sizes, in which each square touches four squares of the other size on its four sides.
Modern tile art serves many purposes. The general definition of tile art includes many mediums and many different designs achieved by various techniques and media. For example, tile art may be used to decorate one's home, but must also be practical as a wall or flooring element, as the tiles in an interior design could be replaced by tile art. [6]
In 1961, Wang conjectured that if a finite set of Wang tiles can tile the plane, then there also exists a periodic tiling, which, mathematically, is a tiling that is invariant under translations by vectors in a 2-dimensional lattice. This can be likened to the periodic tiling in a wallpaper pattern, where the overall pattern is a repetition of ...