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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:
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
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.
Truncated order-5 square tiling; Truncated order-6 dodecahedral honeycomb; Truncated order-6 hexagonal tiling; Truncated order-6 hexagonal tiling honeycomb; Truncated order-6 octagonal tiling; Truncated order-6 pentagonal tiling; Truncated order-6 square tiling; Truncated order-6 tetrahedral honeycomb; Truncated order-7 heptagonal tiling ...
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. In these images fundamental domains are alternately colored black and cyan, and mirrors exist on the boundaries between colors.
Truncated order-6 square tiling; Truncated order-7 square tiling; Truncated square tiling This page was last edited on 10 December 2018, at 13:15 (UTC). ...
In geometry, a polytope (e.g. a polygon or polyhedron) or a tiling is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure. This implies that each vertex is surrounded by the same kinds of face in the same or reverse order, and with the same angles between corresponding faces.