Infinite-order apeirogonal tiling


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.
Domains012

symmetry:

t

t

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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.