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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 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
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.
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.
Truncated order-6 square tiling with *443 symmetry mirror lines. The dual tiling represents the fundamental domains of the *443 orbifold symmetry. There are two reflective subgroup kaleidoscopic constructed from [(4,4,3)] by removing one or two of three mirrors.
Truncated order-4 octagonal tiling with *882 mirror lines. The dual of the tiling represents the fundamental domains of (*882) orbifold symmetry. From [8,8] symmetry, there are 15 small index subgroup by mirror removal and alternation operators. Mirrors can be removed if its branch orders are all even, and cuts neighboring branch orders in half.
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