This paper describes the two-dimensional self-assembly of hexagonal plates at the interface between perfluorodecalin and water. The plates were prepared with five different permutations of hydrophobic and hydrophilic faces. The shapes and amplitudes of the menisci that form on the faces of the plates determine the magnitude of the lateral capillary forces through which they interact. The amplitudes of the menisci also influence-through their out-of-plane components-the position and orientation of the plate relative to the plane of the liquid-liquid interface. In these experiments, the plates were made of poly(dimethylsiloxane) (PDMS) (rho = 1.05 g/cm(3)) containing aluminum oxide (rho = 4.00 g/cm(3)); this dopant adjusted the density of the plates, the extent to which they sank into the liquid-liquid interface, and thus the structure of their menisci. The plates studied had densities of 1.05 to 1.86 g/cm(3). This work complements previous papers (Bowden, N.; Choi I. S.; Grzybowski, B. A.; Whitesides, G. M. J. Am. Chem. Soc. 1999, 121, 5373. Bowden, N.; Oliver, S. R. J.; Whitesides, G. M. J. Phys. Chem. B 2000, 104, 2714.) that examined the assembly of hexagonal plates with densities at the extremes of the range studied. By following the structures of the aggregates formed at intermediate densities, it is possible to observe the way in which the self-assembling system transitions from an aggregate of one structure to that of another. The results from these studies are relevant to the design of micrometer-sized plates capable of self-assembly.