There are two uniform constructions of this tiling, one from [8,4] or (*842) symmetry, and secondly removing the mirror middle, [8,1+,4], gives a rectangular fundamental domain [∞,4,∞], (*4222).
Its fundamental domain is a Lambert quadrilateral, with 3 right angles.
With edge-colorings there is a half symmetry form (4*4) orbifold notation.
The octagons can be considered as truncated squares, t{4} with two types of edges.
In the limit, where the rectangles degenerate into edges, an order-8 square tiling results, constructed as a snub tetraoctagonal tiling, .