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A 1957 print by M. C. Escher, Regular Division of the Plane VI, has this tiling as its underlying structure, with each square tile of a binary tiling (as seen in its quadtree form) subdivided into three isosceles right triangles. [16] It is one of several Escher prints based on the half-plane model of the hyperbolic plane. [17]
For example: 3 6; 3 6; 3 4.6, tells us there are 3 vertices with 2 different vertex types, so this tiling would be classed as a ‘3-uniform (2-vertex types)’ tiling. Broken down, 3 6 ; 3 6 (both of different transitivity class), or (3 6 ) 2 , tells us that there are 2 vertices (denoted by the superscript 2), each with 6 equilateral 3-sided ...
The smaller A-tile, denoted A S, is an obtuse Robinson triangle, while the larger A-tile, A L, is acute; in contrast, a smaller B-tile, denoted B S, is an acute Robinson triangle, while the larger B-tile, B L, is obtuse. Concretely, if A S has side lengths (1, 1, φ), then A L has side lengths (φ, φ, 1). B-tiles can be related to such A-tiles ...
In 1961, Wang conjectured that if a finite set of Wang tiles can tile the plane, then there also exists a periodic tiling, which, mathematically, is a tiling that is invariant under translations by vectors in a 2-dimensional lattice. This can be likened to the periodic tiling in a wallpaper pattern, where the overall pattern is a repetition of ...
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The Fibonacci tile almost tiles the plane. The juxtaposition of 4 tiles (see illustration) leaves at the center a free square whose area tends to zero as k tends to infinity. At the limit, the infinite Fibonacci tile tiles the plane. If the tile is enclosed in a square of side 1, then its area tends to =.
Tilera's primary product family was the Tile CPU. Tile is a multicore design, with the cores communicating via a new mesh architecture, called iMesh, intended to scale to hundreds of cores on a single chip.
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