In geometry, the infinite-order square tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {4,âÂÂ}. 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 *âÂÂâÂÂâÂÂâ symmetry. The dual to this tiling defines the fundamental domains of (*2<sup>âÂÂ</sup>) orbifold symmetry.
This tiling is topologically related as a part of sequence of regular polyhedra and tilings with vertex figure (4<sup>n</sup>).