# 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}     