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It is a chiral pattern, meaning that it is impossible to superpose it on top of its mirror image using only translations and rotations. A uniform tiling is a tiling in which each tile is a regular polygon and in which every vertex can be mapped to every other vertex by a symmetry of the tiling. Usually, uniform tilings additionally are required ...
A p4g pattern can be looked upon as a checkerboard pattern of copies of a square tile with 4-fold rotational symmetry, and its mirror image. Alternatively it can be looked upon (by shifting half a tile) as a checkerboard pattern of copies of a horizontally and vertically symmetric tile and its 90° rotated version.
Special cases are right triangles (p q 2). Uniform solutions are constructed by a single generator point with 7 positions within the fundamental triangle, the 3 corners, along the 3 edges, and the triangle interior. All vertices exist at the generator, or a reflected copy of it. Edges exist between a generator point and its image across a mirror.
Truchet tiles are square tiles decorated with patterns so they do not have rotational symmetry; in 1704, Sébastien Truchet used a square tile split into two triangles of contrasting colours. These can tile the plane either periodically or randomly. [46] [47] An einstein tile is a single shape that forces aperiodic tiling. The first such tile ...
The program tiles the pattern image horizontally to cover an area whose size is identical to the depth map. Conceptually, at every pixel in the output image, the program looks up the grayscale value of the equivalent pixel in the depth map image, and uses this value to determine the amount of horizontal shift required for the pixel.
Star polygon tiles can be included. Apeirogons, {∞}, can be used as tiling faces. Zigzags (apeirogons alternating between two angles) can also be used. The restriction that tiles meet edge-to-edge can be relaxed, allowing additional tilings such as the Pythagorean tiling. Symmetry group triangles with retrogrades include:
A vectorized version of File:Celtic_spiral_tile_pattern.png: Author: User:Hyacinth, converted to SVG by Bartledan : Other versions: Original PNG image: Image:Celtic spiral tile pattern.png For other Celtic "key" patterns, see File:Celtic key Cross.svg and File:Celtic key Cross 2.svg
Tiled printing is a method that computer programs use to enable users to print images larger than a standard page. This method was popularized by a program called The Rasterbator. A tiled printing program overlays a grid on the printed image in which each cell (or tile) is the size of a printed page, and then prints each tile. A person can then ...