The controlled assembly of anisotropic particles through shape induced interface deformations is shown to be a potential route for the fabrication of novel functional materials. In this article, the shape-induced interface deformation, capillary bridging, and directed self-assembly of cuboidal-shaped hematite particles at fluid fluid interfaces are reported. The multipolar nature of the interface distortions is directly visualized using high-resolution scanning electron microscopy and 3D optical surface profiling. The nature of the interface deformations around cuboidal particles vary from monopolar to octupolar types depending on their orientation and position with respect to the interface. The deformations are of either hexapolar or octupolar type in the face up orientation; quadrupolar or monopolar type in the edge-up orientation, and monopolar type in the vertex-up orientation. The particles adsorbed at the interface interact through the interface deformations, forming capillary bridges that lead to isolated assemblies of two or more particles. The arrangement of particles in any assembly is such that the condition for capillary attraction is satisfied, that is, in accordance with predictions based on the nature of interface deformations. At sufficient particle concentrations, these isolated structures interact to form a percolating network of cuboids. Furthermore, the difference in the nature of the assembly Structures formed at the air-water interface and in the bulk water phase indicates that the interfacial assembly of these particles is controlled by the capillary interactions.