# Infinite-order apeirogonal tiling

Infinite-order apeirogonal tiling

Poincaré disk model of the hyperbolic plane
Type Hyperbolic regular tiling
Vertex configuration
Schläfli symbol {∞,∞}
Wythoff symbol ∞ | ∞ 2
∞ ∞ | ∞
Coxeter diagram
Symmetry group [∞,∞], (*∞∞2)
[(∞,∞,∞)], (*∞∞∞)
Dual self-dual
Properties Vertex-transitive, edge-transitive, face-transitive

In geometry, the infinite-order apeirogonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {∞,∞}, which means it has an infinite number of apeirogons around all its ideal vertices.

## Symmetry

This tiling represents the fundamental domains of *∞ symmetry.

## Uniform colorings

This tiling can also be alternately colored in the [(∞,∞,∞)] symmetry from 3 generator positions.

Domains 0 1 2

symmetry:
[(∞,∞,∞)]

t0{(∞,∞,∞)}

t1{(∞,∞,∞)}

t2{(∞,∞,∞)}

## Related polyhedra and tiling

The union of this tiling and its dual can be seen as orthogonal red and blue lines here, and combined define the lines of a *2∞2∞ fundamental domain.

a{∞,∞} or       =