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.

This tiling represents the fundamental domains of *∞^∞ symmetry.

This tiling can also be alternately colored in the [(∞,∞,∞)] symmetry from 3 generator positions.

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.