Order-5 apeirogonal tiling


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

Symmetry

The dual to this tiling represents the fundamental domains of 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 five faces per vertex, starting with the icosahedron, with Schläfli symbol, and Coxeter diagram, with n progressing to infinity.