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In geometry, the order-5 apeirogonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {∞,5}.
Contents
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.
References
Order-5 apeirogonal tiling Wikipedia(Text) CC BY-SA