A careful transmission electron microscopy (TEM) investigation of an incommensurately modulated member of the (Bi1-xSrx)Fe3+O3-x/2□x/2, 0.2≤x≤0.67, solid solution has been carried out. High resolution (HR) TEM imaging is used to show the presence of at least 6-fold twinning on a rather fine (∼5 nm) scale. The (3+1)-d superspace group symmetry is suggested to be Pmmm (0, frac(1, 2), γ) or one of the non-centrosymmetric sub-groups thereof, namely P 2 mm (0, frac(1, 2), γ), Pm 2 m (0, frac(1, 2), γ), Pmm 2 (0, frac(1, 2), γ) and P 222 (0, frac(1, 2), γ). A superspace construction is then used to propose the nature of the local compositional ordering and, hence, of the oxygen-deficient slab that intergrows with the perovskite slab to produce the observed solid solution phase. The proposed compositional superspace atomic surfaces can be used to produce model structures at any composition within the solid solution range. © 2009 Elsevier Inc. All rights reserved.