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Tiles are most often made from plastic or resin that approximates the feel of stone or ivory, similar to most modern commercial domino sets. Numbers are recessed into the surface and painted black. Some "deluxe" sets include a raised, brass tack head in the center. This addition to the sets assists in mixing up or shuffling tiles, as the tack ...
A self-tiling tile set, or setiset, of order n is a set of n shapes or pieces, usually planar, each of which can be tiled with smaller replicas of the complete set of n shapes. That is, the n shapes can be assembled in n different ways so as to create larger copies of themselves, where the increase in scale is the same in each case.
A tiling that cannot be constructed from a single primitive cell is called nonperiodic. If a given set of tiles allows only nonperiodic tilings, then this set of tiles is called aperiodic. [3] The tilings obtained from an aperiodic set of tiles are often called aperiodic tilings, though strictly speaking it is the tiles themselves that are ...
[8] [9] This first such set, used by Berger in his proof of undecidability, required 20,426 Wang tiles. Berger later reduced his set to 104, and Hans Läuchli subsequently found an aperiodic set requiring only 40 Wang tiles. [10] A smaller set, of six aperiodic tiles (based on Wang tiles), was discovered by Raphael M. Robinson in 1971. [11]
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.
Girih tiles are a set of five tiles that were used in the creation of Islamic geometric patterns using strapwork for decoration of buildings in Islamic architecture. They have been used since about the year 1200 and their arrangements found significant improvement starting with the Darb-i Imam shrine in Isfahan in Iran built in 1453.
The Socolar–Taylor tile was proposed in 2010 as a solution to the einstein problem, but this tile is not a connected set. In 1996, Petra Gummelt constructed a decorated decagonal tile and showed that when two kinds of overlaps between pairs of tiles are allowed, the tiles can cover the plane, but only non-periodically. [6]
For instance, a 1993 archaeological dig in Merseyside in England uncovered over 300 kg (660 lb) of tile and kiln remains. Some of the tegulae were stamped with the "LXXVV" insigniae of the Legio XX Valeria Victrix. [2] [3] Romans also often recycled broken tiles by incorporating them into mortar. Tiles of marble were first used around the year ...