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Self-assembly of faceted nanoparticles is a promising route for fabricating nanomaterials; however, achieving low-dimensional assemblies of particles with tunable orientations is challenging. Here, we demonstrate that trapping surface-functionalized faceted nanoparticles at fluid–fluid interfaces is a viable approach for controlling particle orientation and facilitating their assembly into unique one- and two-dimensional superstructures. Using molecular dynamics simulations of polymer-grafted nanocubes in a polymer bilayer along with a particle-orientation classification method we developed, we show that the nanocubes can be induced into face-up, edge-up, or vertex-up orientations by tuning the graft density and differences in their miscibility with the two polymer layers. The orientational preference of the nanocubes is found to be governed by an interplay between the interfacial area occluded by the particle, the difference in interactions of the grafts with the two layers, and the stretching and intercalation of grafts at the interface. The resulting orientationally constrained nanocubes are then shown to assemble into a variety of unusual architectures, such as rectilinear strings, close-packed sheets, bilayer ribbons, and perforated sheets, which are difficult to obtain using other assembly methods. Our work thus demonstrates a versatile strategy for assembling freestanding arrays of faceted nanoparticles with possible applications in plasmonics, optics, catalysis, and membranes, where precise control over particle orientation and position is required.