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A Pythagorean tiling Street Musicians at the Door, Jacob Ochtervelt, 1665.As observed by Nelsen [1] the floor tiles in this painting are set in the Pythagorean tiling. A Pythagorean tiling or two squares tessellation is a tiling of a Euclidean plane by squares of two different sizes, in which each square touches four squares of the other size on its four sides.
There are different notations for expressing these uniform solutions, Wythoff symbol, Coxeter diagram, and Coxeter's t-notation. Simple tiles are generated by Möbius triangles with whole numbers p,q,r, while Schwarz triangles allow rational numbers p,q,r and allow star polygon faces, and have overlapping elements.
The pattern represented by every finite patch of tiles in a Penrose tiling occurs infinitely many times throughout the tiling. They are quasicrystals: implemented as a physical structure a Penrose tiling will produce diffraction patterns with Bragg peaks and five-fold symmetry, revealing the repeated patterns and fixed orientations of its tiles ...
A stoup from brown Slivenec marble in the church in Dobřichovice [4] Český Šternberk marble (šternberský mramor) from Český Šternberk, Benešov District: white; Pernštejn marble (pernštejnský mramor) from Nedvědice, Brno-Country District: white; Nehodiv marble (nehodivský mramor) from Nehodiv, Klatovy District: grey
The herringbone pattern has a symmetry of wallpaper group pgg, as long as the blocks are not of different color (i.e., considering the borders alone). Herringbone patterns can be found in wallpaper, mosaics, seating, cloth and clothing (herringbone cloth), shoe tread, security printing, herringbone gears, jewellery, sculpture, and elsewhere.
In information visualization and graphic design, Truchet tiles are square tiles decorated with patterns that are not rotationally symmetric. When placed in a square tiling of the plane, they can form varied patterns, and the orientation of each tile can be used to visualize information associated with the tile's position within the tiling.
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The tiles are colored according to their rotational orientation modulo 60 degrees. [1] (Smith, Myers, Kaplan, and Goodman-Strauss) Smith, Myers, Kaplan, and Goodman-Strauss) In plane geometry, the einstein problem asks about the existence of a single prototile that by itself forms an aperiodic set of prototiles ; that is, a shape that can ...