 It represents a semiregular honeycomb as defined by all regular cells, although from the Wythoff construction, rectified square tiling r{4,4}, becomes the regular square tiling {4,4}.A lower symmetry form, index 6, of this honeycomb can be constructed with [(4,4,4,3*] symmetry, represented by a trigonal trapezohedron fundamental domain, and Coxeter diagram .Another lower symmetry constructions exists with symmetry [(4,4,(4,3)*)], index 48 and an ideal regular octahedral fundamental domain.