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Infinite-order triangular tiling
From Wikipedia, the free encyclopedia
In geometry, the infinite-order triangular tiling is a regular tiling of the hyperbolic plane with a Schläfli symbol of {3,∞}. All vertices are ideal, located at "infinity" and seen on the boundary of the Poincaré hyperbolic disk projection.
Infinite-order triangular tiling | |
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![]() Poincaré disk model of the hyperbolic plane | |
Type | Hyperbolic regular tiling |
Vertex configuration | 3∞ |
Schläfli symbol | {3,∞} |
Wythoff symbol | ∞ | 3 2 |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Symmetry group | [∞,3], (*∞32) |
Dual | Order-3 apeirogonal tiling |
Properties | Vertex-transitive, edge-transitive, face-transitive |
![](http://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/H3_33inf_UHS_plane_at_infinity.png/640px-H3_33inf_UHS_plane_at_infinity.png)