The ability to prepare nanostructured and/or nanocomposite materials on a large scale by simple and controllable routes still remains a challenge in chemistry and material science. By employing well-established synthetic strategies, nanoparticles with different sizes, shapes and compositions can be readily produced. The high tendency for self-aggregation and selforganization of these nanosized building blocks, which are surface-stabilized by organic molecules, into superstructures has been used to create 2D and 3D assemblies. [1][2][3][4][5][6][7][8][9] In the last decade, a series of 3D colloidal superlattices composed of different nanoparticles (Ag, Au, PbS, PbSe, CeO 2 , FePt, CoPt 3 , Fe 3 O 4 , PbSe/Au, Fe 2 O 3 /PbSe, PbSe/Pd, CdSe/PbSe, etc.) has been reported. [10][11][12][13][14][15][16][17][18][19][20] Particularly, PbS-organic nanoparticles of different shapes (including cubes, octahedra, truncated octahedra, rhombicuboctahedra, etc.) can be easily synthesized on a large scale, and attracted much attention [15,16,21,22] because of a variety of possible applications. [23][24][25][26][27] Therefore, this kind of system provides a chance to study diverse packing arrangements (e.g., fcc, bcc, etc.) and specific orientational ordering of nanoparticles. [11,13,15,16,28,29] Experimental observations [16,[29][30][31][32][33][34] suggest that nanoparticles within a colloidal crystal tend to arrange in such a way that the optimal packing efficiency is achieved (principle of maximum space filling [35] ). In a relatively common case of truncated octahedrally shaped nanoparticles, the available experimental data [4,5,16,[29][30][31][32][33]36] allow to rationalize the formation of a particular type of the superlattice array (depending on the degree of coverage of nanocrystals by organic molecules) by considering four phenomenological models: A) Rigid, anisotropically shaped space-filling nanoparticles (inorganic part) without or with a tiny shell of organic molecules; B) Hard spheres with a comparatively large anisotropic core (inorganic part) covered by a relatively thin shell of organic molecules; C) Hard spheres with a comparatively small anisotropic core (inorganic part) and a thick shell of organic molecules; D) Soft and easily deformable spheres with a small anisotropic core (inorganic part) and an even thicker shell of organic molecules.For each case (A-D) the type of superlattice packing (translational order [37] ) and orientational ordering of nanoparticles within the superlattice array is significantly different. In the simplest case (A), the more or less pure, inorganic, truncated octahedrally shaped nanoparticles assemble into a bcc superlattice [33] with 100 % packing efficiency and strong orientational relationship (crystallographic directions of nanocrystals are coaxial with those of the superlattice). [35,37] In case of models B and C, by increasing the degree of coverage of anisotropic (inorganic) nanoparticles by organic molecules, their faces are continuously smoothed, thereby introducing a certa...