X-ray methods have been used to analyze the supramolecular tubular structures in the hexagonal solid state and columnar hexagonal liquid crystalline (phi(h)) phases of a polymethacrylate with tapered side groups : specifically, poly{2-{2-[2-(2-(methacryloyloxy)ethoxy)ethoxy]ethoxy}ethyl 3,4,5-tris((p-(dodecyloxy)-benzyl)oxy)benzoate}, abbreviated as 12-ABG-4EO-PMA. Oriented fibers were drawn from the (phi(h) liquid crystalline phase at similar to 60 degrees C and annealed for several days at 4 degrees C. The X-ray pattern for these fibers recorded at room temperature (25 degrees C) contained eight equatorial reflections that are orders predicted for a hexagonal unit cell with a = b = 60.4 Angstrom. The similarity of the data to those for unoriented specimens in the phi(h) phase suggests that both phases contain the same type of supramolecular cylindrical moieties. In addition, wide-angle maxims are observed on the equator and two layer lines that suggest formation of a three-dimensionally-ordered structure at room temperature. These data give the first available information on the supramolecular structure within the columns. The layer line spacings define a repeat of c = 5.03 Angstrom along the column axis, containing eight monomeric units based on the observed density. Strong off-meridional maxims at d = 4.30 and 3.84 Angstrom on the first layer line suggest that the "planes" of the aromatic moieties are tilted rather than perpendicular to the cylinder axis. Possible "pine tree" models are discussed in which the tapered side groups are stacked in 8-fold layers or form 8-fold helices within the columns. Increasing the temperature to 60 degrees C leads to a reduction in the cylinder diameter to 58.0 Angstrom. Stacking correlations remain along the fiber axis direction, but otherwise the internal structure of the cylinder is much more disordered than at room temperature. On cooling, the three-dimensional order is restored.