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The truncated square tiling is used in an optical illusion with truncated vertices divides and colored alternately, seeming to twist the grid.. The truncated square tiling is topologically related as a part of sequence of uniform polyhedra and tilings with vertex figures 4.2n.2n, extending into the hyperbolic plane:
Right triangle domains can have as few as 1 face type, making regular forms, while general triangles have at least 2 triangle types, leading at best to a quasiregular tiling. There are different notations for expressing these uniform solutions, Wythoff symbol , Coxeter diagram , and Coxeter's t-notation.
An example of uniform tiling in the Archeological Museum of Seville, Sevilla, Spain: rhombitrihexagonal tiling Regular tilings and their duals drawn by Max Brückner in Vielecke und Vielflache (1900) This table shows the 11 convex uniform tilings (regular and semiregular) of the Euclidean plane , and their dual tilings.
§2.1 Uniform tiling, Archimedean tiling, elongated triangular tiling, snub square tiling, truncated square tiling, truncated hexagonal tiling, trihexagonal tiling, snub trihexagonal tiling, rhombitrihexagonal tiling, §2.2 list of k-uniform tilings, demiregular tiling, 3-4-3-12 tiling, 3-4-6-12 tiling, 33344-33434 tiling, §2.3 k-isotoxal ...
In geometry, the truncated order-5 square tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t 0,1 {4,5}. Related polyhedra and tiling
In geometry, the truncated infinite-order square tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t{4,∞}. Uniform color.
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