A simple unequal-sphere packing model is applied to study the iodine ͑3 ϫ 3͒ adlayer on the Pt͑111͒ surface. By using a newly introduced parameter, defined as the average adsorbate height, three characteristic adlattices, ͑3 ϫ 3͒-sym, ͑3 ϫ 3͒-asym, and ͑3 ϫ 3͒-lin, have been selected and characterized in great detail, including the exact adatom registry. The ͑3 ϫ 3͒-sym iodine adlattice, observed in many experimental studies, appears to be, on average, the closest one to the substrate surface. A special contour plot of average adsorbate height vs X and Y positions of the ͑3 ϫ 3͒ iodine unit cell indicates the existence of two local minima, which are related to preferential formation of ͑3 ϫ 3͒-sym and ͑3 ϫ 3͒-asym iodine adlattices. Our model gives good agreement with experimental findings, and explains the mechanism of preferential appearance of ͑3 ϫ 3͒-sym and ͑3 ϫ 3͒-asym structures.