Particles adsorbed at a fluid-fluid interface induce capillary deformations that determine their orientations and generate mutual capillary interactions which drive them to assemble into 2D ordered structures. We numerically calculate, by energy minimization, the capillary deformations induced by adsorbed cubes for various Young's contact angles. First, we show that capillarity is crucial not only for quantitative, but also for qualitative predictions of equilibrium configurations of a single cube. For a Young's contact angle close to 90°, we show that a single-adsorbed cube generates a hexapolar interface deformation with three rises and three depressions. Thanks to the threefold symmetry of this hexapole, strongly directional capillary interactions drive the cubes to self-assemble into hexagonal or graphenelike honeycomb lattices. By a simple free-energy model, we predict a density-temperature phase diagram in which both the honeycomb and hexagonal lattice phases are present as stable states. DOI: 10.1103/PhysRevLett.116.258001 Over a century ago, it had already been observed that submm sized particles strongly adsorb at fluid-fluid interfaces [1,2]. Indeed, a fluid-fluid interface of area A and surface tension γ has a free energy cost γA, and particles can reduce A by adsorbing at the interface. The bonding potential is usually strong enough to allow stable monolayers of particles. Since a pioneering study by Pieranski [3], a lot of interest has been devoted to these quasi-2D systems, which have many applications, e.g., emulsions [4][5][6][7][8][9], coatings [10,11], optics [12], and new material development [13]. Because of the contact angle constraint imposed by Young's Law, an adsorbed particle in general induces deformations in the shape of the fluid-fluid interface. These so-called capillary deformations are responsible for capillary interactions between the adsorbed particles [14,15], which regulate the particle self-assembly at the interface [16][17][18]. These interactions can be tuned by varying, e.g., the particle shape and chemistry [10,[19][20][21], or the curvature of the fluidfluid interface [22][23][24]. Very recent experiments [25][26][27] have shown that adsorbed nanocubes with truncated corners can assemble into graphenelike honeycomb and hexagonal lattices. The origin of these structures is unknown, although ligand adsorption and van der Waals forces between specific facets of the truncated cubes have been suggested [25]. In this Letter, however, we show that generic cubes with homogeneous surface properties generate hexapolar capillary deformations which are largely responsible for the observed structures. Cubes of other materials or dimensions could, therefore, form similar structures.A primary step for understanding adsorbedparticle systems is the study of an isolated particle at a macroscopically flat fluid-fluid interface. Important issues are the equilibrium configuration of the particle at the interface [28][29][30][31] and the adsorption energy [32-34] which depend on the particl...