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One approach is to color the vertices (with two colors, e.g., black and white) and require that adjacent tiles have matching vertices. [32] Another is to use a pattern of circular arcs (as shown above left in green and red) to constrain the placement of tiles: when two tiles share an edge in a tiling, the patterns must match at these edges. [21]
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.
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 geometry, a tiling is a partition of the plane (or any other geometric setting) into closed sets (called tiles), without gaps or overlaps (other than the boundaries of the tiles). [1] A tiling is considered periodic if there exist translations in two independent directions which map the tiling onto itself.
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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.
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The pattern corresponds to each of the following: symmetrically staggered rows of identical doubly symmetric objects; a checkerboard pattern of two alternating rectangular tiles, of which each, by itself, is doubly symmetric; a checkerboard pattern of alternatingly a 2-fold rotationally symmetric rectangular tile and its mirror image