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 five faces per vertex, starting with the icosahedron, with Schläfli symbol {n,5}, and Coxeter diagram , with n progressing to infinity.
See also
Tilings of regular polygons List of uniform planar tilings List of regular polytopes
References John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, (Chapter 19, The Hyperbolic Archimedean Tessellations)
External links
Hyperbolic and Spherical Tiling Gallery KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings Hyperbolic Planar Tessellations, Don Hatch