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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:
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.
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
The 3.12.12 vertex figure alone generates a truncated hexagonal tiling, while the 3.4.3.12 only exists in this 2-uniform tiling. There are 2 3-uniform tilings that contain both of these vertex figures among one more. It has square symmetry, p4m, [4,4], (*442). It is also called a demiregular tiling by some authors.
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.
The omnitruncated order-4 square tiling honeycomb, t 0,1,2,3 {4,4,4}, has truncated square tiling and octagonal prism facets, with a digonal disphenoid vertex figure. Alternated order-4 square tiling honeycomb
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