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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.
![]() | This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. (March 2014) |
Infinite-order square tiling | |
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![]() Poincaré disk model of the hyperbolic plane | |
Type | Hyperbolic regular tiling |
Vertex configuration | 4∞ |
Schläfli symbol | {4,∞} |
Wythoff symbol | ∞ | 4 2 |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Symmetry group | [∞,4], (*∞42) |
Dual | Order-4 apeirogonal tiling |
Properties | Vertex-transitive, edge-transitive, face-transitive |
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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).
See also
Wikimedia Commons has media related to Infinite-order square tiling.
References
External links
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