Order-3 apeirogonal tiling

Order-3 apeirogonal tiling
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

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.

The order-2 apeirogonal tiling represents an infinite dihedron in the Euclidean plane as {∞,2}.