The orientation of hexagonal cylinders self-assembled from fan-shaped dendrimers is strongly affected by surface anchoring. Planar ordering of the cylinders is obtained on a water surface, while the cylinder assemblies align homeotropically on carbon substrates. To understand self-assembling mechanism of the planar ordering, we investigate the surface texture of Langmuir-Blodgett monolayers and multilayers of an asymmetric fan-shaped second generation dendrimer containing a CO2C3H7 core group of the cylinder and dodecyl (C12H25) alkyl tails at the air-water interface. Surface pressure-area (pi-A) isotherm and Brewster angle microscopy (BAM) measurements show that the molecule forms a stable monolayer on a water surface with two phase transitions (gaseous phase --> expanded phase --> condensed phase). The electron diffraction (ED) patterns, transmission electron microscopy (TEM) images, and atomic force microscopy (AFM) images of the condensed monolayers clearly reveal that the molecule forms edge-on-oriented monolayers with hexagonal packing on the water surface, suggesting fractional cylindrical configuration at the air-water interface. Upon further compression, the condensed monolayer is transformed into a multilayer, and the interfacial structure becomes planar morphology. These results demonstrate the origin of planar alignment of self-assembled dendrimers on water surface.