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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:
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.
Truncated order-7 square tiling; Truncated square tiling This page was last edited on 10 December 2018, at 13:15 (UTC). Text is available under the Creative Commons ...
T. Tetraheptagonal tiling; Tetrahexagonal tiling; Tetraoctagonal tiling; Tetrapentagonal tiling; Truncated infinite-order square tiling; Truncated infinite-order triangular tiling
Infinite-order truncated square tiling Poincaré disk model of the hyperbolic plane: Type: Hyperbolic uniform tiling: Vertex configuration: ∞.8.8 Schläfli symbol: t{4,∞} Wythoff symbol: 2 ∞ | 4 Coxeter diagram: Symmetry group [∞,4], (*∞42) Dual: apeirokis apeirogonal tiling: Properties: Vertex-transitive
The truncated square tiling is drawn over an equilateral chamfered square tiling. In geometry, the chamfered square tiling or semitruncated square tiling is a tiling of the Euclidean plane. It is a square tiling with each edge chamfered into new hexagonal faces. It can also be seen as the intersection of two truncated square tilings with offset ...
Truncated order-5 square tiling Poincaré disk model of the hyperbolic plane: Type: Hyperbolic uniform tiling: Vertex configuration: 8.8.5 Schläfli symbol: t{4,5} Wythoff symbol: 2 5 | 4 Coxeter diagram: Symmetry group [5,4], (*542) Dual: Order-4 pentakis pentagonal tiling: Properties: Vertex-transitive
Edges exist between a generator point and its image across a mirror. Up to 3 face types exist centered on the fundamental triangle corners. 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.