We have used grazing incidence X-ray diffraction and X-ray specular reflectivity to study the behavior of platelike hexaalkoxytriphenylene derivatives at the air-water interface. The data are consistent with a two-dimensional columnar mesophase, wherein the molecules are arranged "edge-on" to the water surface, with intercolumnar spacings of 13-19 Angstrom. We propose a molecular conformation in which hydrophobic tails lie parallel to the water surface so as to allow the hydrophilic oxygen atoms to directly contact the water surface. In equimolar mixtures of two disubstituted amphiphilic isomers of a triphenylene derivative, we see direct evidence for structural self-organization and intercolumnar order. We also present indirect evidence for orientational self-organization in symmetrically substituted triphenylene derivatives.