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In geometry, the infinite-order square tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {4,∞}. All vertices are ideal, located at "infinity", seen on the boundary of the Poincaré hyperbolic disk projection.
Contents
Uniform colorings
There is a half symmetry form, , seen with alternating colors:
Symmetry
This tiling represents the mirror lines of *∞∞∞∞ symmetry. The dual to this tiling defines the fundamental domains of (*2∞) orbifold symmetry.
Related polyhedra and tiling
This tiling is topologically related as a part of sequence of regular polyhedra and tilings with vertex figure (4n).
References
Infinite-order square tiling Wikipedia(Text) CC BY-SA