Order-3 apeirogonal tiling
In geometry, the order-3 apeirogonal tiling is a regular tiling of the hyperbolic plane. It is represented by the Schläfli symbol {∞,3}, having three regular apeirogons around each vertex. Each apeirogon is inscribed in a horocycle.
| Order-3 apeirogonal tiling | |
|---|---|
Poincaré disk model of the hyperbolic plane | |
| Type | Hyperbolic regular tiling |
| Vertex configuration | ∞3 |
| Schläfli symbol | {∞,3} t{∞,∞} t(∞,∞,∞) |
| Wythoff symbol | 3 | ∞ 2 2 ∞ | ∞ ∞ ∞ ∞ | |
| Coxeter diagram | |
| Symmetry group | [∞,3], (*∞32) [∞,∞], (*∞∞2) [(∞,∞,∞)], (*∞∞∞) |
| Dual | Infinite-order triangular tiling |
| Properties | Vertex-transitive, edge-transitive, face-transitive |
The order-2 apeirogonal tiling represents an infinite dihedron in the Euclidean plane as {∞,2}.
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