In geometry, the infinite-order square tiling is a regular tiling of the hyperbolic plane.
All vertices are ideal, located at "infinity", seen on the boundary of the Poincaré hyperbolic disk projection.
There is a half symmetry form, , seen with alternating colors: This tiling represents the mirror lines of *∞∞∞∞ symmetry.
The dual to this tiling defines the fundamental domains of (*2∞) orbifold symmetry.
This tiling is topologically related as a part of sequence of regular polyhedra and tilings with vertex figure (4n).