A simple unequal-sphere packing (USP) model, based on pure geometrical principles, was applied to study the centered-rectangular iodine c(p x root 3)R30 degrees adlayer on the Au(111) surface, well-known from surface X-ray structure (SXS), low energy electron diffraction (LEED), and scanning tunneling microscopy (STM) experiments. To reproduce the exact patterns observed in experiments, two selective conditions-minimum average adsorbate height and minimum adlayer roughness-were imposed. As a result, a series of adlayer patterns with c(p x root 3)R30 degrees symmetry (2.3 < p < 3), with precise structural details, including atomic registry and identification of the p-bisector as the most likely trajectory for the iodine adatom movement during the so-called uniaxial compression phenomenon, were identified. In addition, using the same model, the difference between the iodine adlayer arranged in hexagonal and centered-rectangular c(p x root 3)R30 degrees patterns, as in the case of Pt(111) and Au(111) surfaces, was investigated. Qualitative and quantitative comparison shows that iodine adatoms in these two arrangements differ significantly in atomic registry, distance from the substrate, and the adlayer corrugation. Our findings could be of special interest in the study of the nature of the iodine adatom bonding to different substrates (i.e., Au vs Pt).