Small angle and wide angle X-ray methods have been used to study the structure 2-{2-(2-hydroxyethoxy)-ethoxy}ethyl-3,4,5-tris(p-octadecyl-oxybenzyloxy)-benzoate (H18-ABG-3EO-OH), which is one of a series of precursors used to synthesize polymers with highly tapered side chains that form self-assembling, columnar hexagonal (phi(h)) phases. This material is crystalline at room temperature, and undergoes crystalline-to-phi(h) and phi(h)-to-isotropic transitions in the region of 65-70 and 75-80 degrees C respectively, depending on the thermal history. Small angle X-ray data for oriented fibres drawn from the phi(h) phase and cooled to room temperature point to the presence of hexagonally packed columns with a diameter of 57 Angstrom. The corresponding wide angle data indicate that there is three dimensional order within the columns : we observe a six-point pattern probably due to packing of the C18 tails in a manner analogous to the hexagonal form of polyethylene. On annealing, there is a progressive increase in the internal order of the cylinders as the structure is converted to one analogous to the crystalline forms of the C12-tetraethoxy analog (HI2-ABG-4EO-OH) and the methacrylate polymer thereof (H12-ABG-4EO-PMA). These results suggest that the internal ordering now extends to the aromatic and tri-ethoxy units. Heating and cooling cycles from room temperature to successively higher temperatures show that these improvements in the internal order are accompanied by a progressive reduction in the diameter of the cylinders.