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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
Examples The hexagonal prism is constructed from both the (6 2 2) and (3 2 2) families.: The truncated square tiling is constructed by two different symmetry positions in the (4 4 2) family.
The cantitruncated order-4 square tiling honeycomb, is the same as the truncated square tiling honeycomb, . It contains cube and truncated square tiling facets, with a mirrored sphenoid vertex figure. It is the same as the truncated square tiling honeycomb, .
In geometry, the truncated order-6 square tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t{4,6}. Uniform colorings.
Truncated order-6 square tiling; This page was last edited on 3 November 2014, at 05:48 (UTC). Text is available under the Creative Commons Attribution ...
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.