Conway, Burgiel, and Goodman-Strauss call it a kisquadrille,[1] represented by a kis operation that adds a center point and triangles to replace the faces of a square tiling (quadrille).

It is also called the Union Jack lattice because of the resemblance to the UK flag of the triangles surrounding its degree-8 vertices.

[5] This tiling also forms the basis for a commonly used "pinwheel", "windmill", and "broken dishes" patterns in quilting.

There are many small index subgroups of p4m, [4,4] symmetry (*442 orbifold notation), that can be seen in relation to the Coxeter diagram, with nodes colored to correspond to reflection lines, and gyration points labeled numerically.

Rotational symmetry is shown by alternately white and blue colored areas with a single fundamental domain for each subgroup is filled in yellow.