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A tiling with rectangles is a tiling which uses rectangles as its parts. The domino tilings are tilings with rectangles of 1 × 2 side ratio. The tilings with straight polyominoes of shapes such as 1 × 3, 1 × 4 and tilings with polyominoes of shapes such as 2 × 3 fall also into this category.
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.
This is an accepted version of this page This is the latest accepted revision, reviewed on 27 February 2025. American multinational home improvement supplies retailing company The Home Depot, Inc. A Home Depot in Onalaska, Wisconsin Company type Public Traded as NYSE: HD DJIA component S&P 100 component S&P 500 component Industry Retail (home improvement) Founded February 6, 1978 ; 47 years ...
A rep-tile is labelled rep-n if the dissection uses n copies. Such a shape necessarily forms the prototile for a tiling of the plane, in many cases an aperiodic tiling. A rep-tile dissection using different sizes of the original shape is called an irregular rep-tile or irreptile. If the dissection uses n copies, the shape is said to be irrep-n ...
Tile, including ceramic tile and stone tile, is installed in much the same way as floor tiles or wall tiles through the use of mortar and grouting the tile gaps after they have been cemented down. The tiles that sit on the wall typically behind a countertop are called a backsplash .
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 ]
A rectangle tiled by squares, rectangles, or triangles is said to be a "squared", "rectangled", or "triangulated" (or "triangled") rectangle respectively. The tiled rectangle is perfect [17] [18] if the tiles are similar and finite in number and no two tiles are the same size. If two such tiles are the same size, the tiling is imperfect.
Following Grünbaum and Shephard (section 1.3), a tiling is said to be regular if the symmetry group of the tiling acts transitively on the flags of the tiling, where a flag is a triple consisting of a mutually incident vertex, edge and tile of the tiling. This means that, for every pair of flags, there is a symmetry operation mapping the first ...
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