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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
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 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:
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). ...
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.
In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane. It has Schläfli symbol of {4,4}, meaning it has 4 squares around every vertex. Conway called it a quadrille. The internal angle of the square is 90 degrees so four squares at a point make a full 360
John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 19, The Hyperbolic Archimedean Tessellations) "Chapter 10: Regular honeycombs in hyperbolic space".
The truncated square tiling honeycomb, t{4,4,3}, has cube and truncated square tiling facets, with a triangular pyramid vertex figure. It is the same as the cantitruncated order-4 square tiling honeycomb , tr{4,4,4}, .