There are two uniform constructions of this tiling, one from [6,4] or (*642) symmetry, and secondly removing the mirror middle, [6,1+,4], gives a rectangular fundamental domain [∞,3,∞], (*3222).
sees the yellow squares as rectangles, with two color edges, with [6+,4] (6*2) symmetry.
This four color tiling is related to a semiregular infinite skew polyhedron with the same vertex figure in Euclidean 3-space with a prismatic honeycomb construction of .
Its fundamental domain is a Lambert quadrilateral, with 3 right angles.
Removing half of the blue mirrors doubles the domain again into *3322 symmetry.