Infinite-order apeirogonal tiling

In geometry, 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.

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.
 * Infinite-order_apeirogonal_tiling_and_dual.png
 * a{∞,∞} or =  ∪