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In 1956, Mohawk Carpet Mills merged with Alexander Smith, Inc. to become Mohasco Corporation, a company large enough to appear on the first Fortune 500 rankings. Mohasco faced competition from new tufted carpet operations in Georgia, which used synthetic fibers such as nylon and polyester rather than the traditional wool used in woven carpets.
In geometry, many uniform tilings on sphere, euclidean plane, and hyperbolic plane can be made by Wythoff construction within a fundamental triangle, (p q r), defined by internal angles as π/p, π/q, and π/r.
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 ...
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.
In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane. It has Schläfli symbol of {4,4}, meaning it has 4 squares around every vertex. Conway called it a quadrille. The internal angle of the square is 90 degrees so four squares at a point make a full 360
Robinson proves these tiles must form this structure inductively; in effect, the tiles must form blocks which themselves fit together as larger versions of the original tiles, and so on. This idea – of finding sets of tiles that can only admit hierarchical structures – has been used in the construction of most known aperiodic sets of tiles ...
The common carpet or white-banded toothed carpet (Epirrhoe alternata) is a moth of the family Geometridae. The species was first described by Otto Friedrich Müller in 1764. It is found throughout the Palearctic and the Near East. In North America it ranges across the northern tier of the United States plus every province and territory of Canada.
Each tile will cover exactly one black square. Vertical tiles where the top square covers a black square, is colored in one color, and the other vertical tiles in a second. Similarly for horizontal tiles. Knuth has also defined Aztec diamonds of order n + 1/2. [4] They are identical with the polyominoes associated with the centered square numbers.
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