The infinite-order apeirogonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {∞,∞}, which means it has countably infinitely many apeirogons around all its ideal vertices.
Symmetry This tiling represents the fundamental domains of *∞ symmetry.
Uniform colorings This tiling can also be alternately colored in the [(∞,∞,∞)] symmetry from 3 generator positions. Domains012symmetry:[(∞,∞,∞)] t{(∞,∞,∞)}t{(∞,∞,∞)}t{(∞,∞,∞)}
Related polyhedra and tiling The union of this tiling and its dual can be seen as orthogonal red and blue lines here, and combined define the lines of a *2∞2∞ fundamental domain.
a{∞,∞} or = ∪
See also
Tilings of regular polygons List of uniform planar tilings List of regular polytopes
References John Horton 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