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Slate tile covers this entire structure in Germany. Tile is a thin modular stone unit, commonly 12 inches (300 mm) square and 3 ⁄ 8 inch (9.5 mm) deep. Other popular sizes are 15 inches (380 mm) square, 18 inches (460 mm) square, and 24 inches (610 mm) square; these will usually be deeper than the 12-inch square.
It is also called a plan which is a measured plane typically projected at the floor height of 4 ft (1.2 m), as opposed to an elevation which is a measured plane projected from the side of a building, along its height, or a section or cross section where a building is cut along an axis to reveal the interior structure.
There are various tile patterns, such as herringbone, staggered, offset, grid, stacked, pinwheel, parquet de Versailles, basket weave, tiles Art, diagonal, chevron, and encaustic which can range in size, shape, thickness, and color. [2] Different cultures and nations also make their own tiles that reflect art and culture of respective times.
Quarry tile is a building material, usually 1 ⁄ 2 to 3 ⁄ 4 inch (13 to 19 mm) thick, made by either the extrusion process or more commonly by press forming and firing natural clay or shales. [ 1 ] [ 2 ] Quarry tile is manufactured from clay in a manner similar to bricks . [ 3 ]
Keller's conjecture was shown to be true in dimensions at most six by Perron (1940a, 1940b).The disproof of Keller's conjecture, for sufficiently high dimensions, has progressed through a sequence of reductions that transform it from a problem in the geometry of tilings into a problem in group theory and, from there, into a problem in graph theory.
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