# Order-5 apeirogonal tiling

Order-5 apeirogonal tiling

Poincaré disk model of the hyperbolic plane
Type Hyperbolic regular tiling
Vertex configuration 5
Schläfli symbol {∞,5}
Wythoff symbol 5 | ∞ 2
Coxeter diagram
Symmetry group [∞,5], (*∞52)
Dual Infinite-order pentagonal tiling
Properties Vertex-transitive, edge-transitive, face-transitive edge-transitive

In geometry, the order-5 apeirogonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {∞,5}.

## Symmetry

The dual to this tiling represents the fundamental domains of [∞,5*] symmetry, orbifold notation *∞∞∞∞∞ symmetry, a pentagonal domain with five ideal vertices.

The order-5 apeirogonal tiling can be uniformly colored with 5 colored apeirogons around each vertex, and coxeter diagram: , except ultraparallel branches on the diagonals.

## Related polyhedra and tiling

This tiling is also topologically related as a part of sequence of regular polyhedra and tilings with four faces per vertex, starting with the octahedron, with Schläfli symbol {n,5}, and Coxeter diagram , with n progressing to infinity.

Spherical Hyperbolic tilings

{2,5}

{3,5}

{4,5}

{5,5}

{6,5}

{7,5}

{8,5}
...
{∞,5}