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From Wikipedia, the free encyclopedia
In 2-dimensional hyperbolic geometry, the infinite-order hexagonal tiling is a regular tiling. It has Schläfli symbol of {6,∞}. All vertices are ideal, located at "infinity", seen on the boundary of the Poincaré hyperbolic disk projection.
Infinite-order hexagonal tiling | |
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![]() Poincaré disk model of the hyperbolic plane | |
Type | Hyperbolic regular tiling |
Vertex configuration | 6∞ |
Schläfli symbol | {6,∞} |
Wythoff symbol | ∞ | 6 2 |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Symmetry group | [∞,6], (*∞62) |
Dual | Order-6 apeirogonal tiling |
Properties | Vertex-transitive, edge-transitive, face-transitive |
There is a half symmetry form, , seen with alternating colors:
This tiling is topologically related as a part of sequence of regular polyhedra and tilings with vertex figure (6n).
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