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Infinite-order square tiling

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Infinite-order square tiling
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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.

Infinite-order square tiling
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Poincaré disk model of the hyperbolic plane
TypeHyperbolic regular tiling
Vertex configuration4
Schläfli symbol{4,}
Wythoff symbol | 4 2
Coxeter diagram
Symmetry group[,4], (*42)
DualOrder-4 apeirogonal tiling
PropertiesVertex-transitive, edge-transitive, face-transitive
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Uniform colorings

There is a half symmetry form, , seen with alternating colors:

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Symmetry

This tiling represents the mirror lines of *∞∞∞∞ symmetry. The dual to this tiling defines the fundamental domains of (*2) orbifold symmetry.

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This tiling is topologically related as a part of sequence of regular polyhedra and tilings with vertex figure (4n).

More information Spherical, Euclidean ...
More information Dual figures, Alternations ...

See also

References

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