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The tiles in the square tiling have only one shape, and it is common for other tilings to have only a finite number of shapes. These shapes are called prototiles, and a set of prototiles is said to admit a tiling or tile the plane if there is a tiling of the plane using only these shapes.
Diagram showing square tiles, on the diagonal, nailed at all four corners and grouted in mounds over the joins and nails. Namako wall or Namako-kabe (sometimes misspelled as Nameko) is a Japanese wall design widely used for vernacular houses, particularly on fireproof storehouses by the latter half of the Edo period. [1]
An example of uniform tiling in the Archeological Museum of Seville, Sevilla, Spain: rhombitrihexagonal tiling Regular tilings and their duals drawn by Max Brückner in Vielecke und Vielflache (1900) This table shows the 11 convex uniform tilings (regular and semiregular) of the Euclidean plane , and their dual tilings.
The familiar "brick wall" tiling is not edge-to-edge because the long side of each rectangular brick is shared with two bordering bricks. [18] A normal tiling is a tessellation for which every tile is topologically equivalent to a disk, the intersection of any two tiles is a connected set or the empty set, and all tiles are uniformly bounded ...
Zellij tiling was most typically used to pave floors and to cover the lower walls inside buildings. Zellij was also used on the exterior of minarets and on some entrance portals. [ 5 ] Geometric motifs predominated, with patterns of increasing complexity being formed during this period.
An example is the sphinx tiling, an aperiodic tiling formed by a pentagonal rep-tile. [20] The sphinx may also tile the plane periodically, by fitting two sphinx tiles together to form a parallelogram and then tiling the plane by translation of this parallelogram, [ 20 ] a pattern that can be extended to any non-convex pentagon that has two ...