To understand what tools are really suitable to identify and classify the iodine-iodine non-covalent interactions in solid organic polyiodides, we have examined the anisotropy of the electron density within the iodine atomic basin along and across the iodine-iodine halogen bond using the Laplacian of electron density, one-electron potential and electron localization function produced by Kohn-Sham calculations with periodic boundary conditions. The Laplacian of electron density exhibits the smallest anisotropy and yields a vague picture of the outermost electronic shells. The one-electron potential does not show such a deficiency and reveals that the valence electron shell for the halogen-bond acceptor iodine is always wider than that for the halogen-bond donor iodine along its σ-hole direction. We have concluded that the one-electron potential is the most suitable for classification of the iodine-iodine bonds and interactions in complicated cases, while the electron localization function allows to distinguish the diiodine molecule bonded with the monoiodide anion from the typical triiodide anion.