Infinite-order square tiling

Infinite-order square tiling

Poincaré disk model of the hyperbolic plane
TypeHyperbolic regular tiling
Vertex figure4
Schläfli symbol{4,}
Wythoff symbol | 4 2
Coxeter diagram
Symmetry group[,4], (*42)
DualOrder-4 apeirogonal tiling
PropertiesVertex-transitive, edge-transitive, face-transitive

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.

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.

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

See also

Wikimedia Commons has media related to Infinite-order square tiling.

References

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