The Bi3n+1Ti7Fe3n-3,O9n+11 materials are built of (001)(p) plane parallel perovskite blocks with a thickness of n (Ti,Fe)O-6 octahedra, separated by periodic translational interfaces. The interfaces are based on anatase-like chains of edge -sharing (Ti,Fe)O-6 octahedra. Together with the octahedra of the perovskite blocks, they create S-shaped tunnels stabilized by lone pair Bi3+ cations. In this work, the structure of the n = 4-6 Bi3n+1Ti7Fe3n-3,O9n+11 homologues is analyzed in detail using advanced transmission electron microscopy, powder X-ray diffraction, and Mossbauer spectroscopy. The connectivity of the anatase-like chains to the perovskite blocks results in,a 3ap periodicity along the interfaces, so that they can be located either on top of each other or with shifts of +/- a(p) along [100](p). The ordered arrangement of the interfaces gives rise to orthorhombic Immm and monoclinic A2/m polymorphs with the unit cell parameters a = 3a(p), b = b(p), c = 2(n + 1)c(p) and a = 3a(p), b = b(p), c = 2(n + 1)c(p) - a(p), respectively. While the n = 3 compound is orthorhombic, the monoclinic modification is more favorable in higher homologues. The Bi3n+1Ti7Fe3n-3,O9n+11 structures demonstrate intricate patterns of atomic displacements in the perovskite blocks, which are supported by the stereochemical activity of the Bi3+ cations. These patterns are coupled to the cationic coordination of the oxygen atoms in the (Ti,Fe)O-2 layers at the border of the perovskite blocks. The coupling is strong in the 1/ = 3, 4 homologues, but gradually reduces with the increasing thickness of the perovskite blocks, so that, in the n = 6 compound, the dominant mode of atomic displacements is aligned along the interface planes. The displacements in the adjacent perovskite blocks tend to order antiparallel, resulting in an overall antipolar structure. The Bi3n+1Ti7Fe3n-3,O9n+11 materials demonstrate an unusual diversity of structure defects. The n = 4-6 homologues are robust antiferromagnets below T-N = 135, 220, and 295 K, respectively. They show a high dielectric constant that weakly increases with temperature and is relatively insensitive to the Ti/Fe ratio.