A modification is made to the chemical shift-chemical shift, CS-CS, correlation spectroscopy method for measuring shift tensors. This new approach incorporates, in an iterative fashion, the redundancy of information available in the spectrum from congruent nuclei in the unit cell. The redundancy reduces the number of 2D spectra required to determine the full chemical shift tensor. The iterative procedure requires reasonably good starting shift values that may be derived from quantum chemical calculation of nuclear shielding parameters. These theoretical tensor estimates provide approximate spectral patterns used in assigning the experimental peaks. With this technique the 18 unique C-13 tensors in a triphenylene unit cell, which describe 72 spectral peaks, were measured with a precision of 0.52 ppm in the tensor components with use of only three 2D spectra instead of the six normally used in the CS-CS method. The chemical shift tensor analysis indicates that, to relieve intramolecular strain, the molecule deforms from planarity, and the molecular symmetry is left with only a single vertical plane. Shift tensors also reflect the major Kekule structures of triphenylene. Further, chemical shift modeling as a function of molecular geometry was used to probe variations between neutron and X-ray diffraction data.