Covalent chemical bonding beyond the two-center two-electron (2c-2e) bond is well-known for (inter)halogenic compounds, in particular, electron-rich multicenter (or hypervalent) bonding of the three-center four-electron (3c-4e) type to explain both their structure and stability. In the present work, we examine different solid-state polyiodides by combining both local orbital wave function and projected force constant analysis in order to numerically quantify the influence of multicenter (hypervalent) bonding based on periodic density functional theory (DFT) calculations. After linking our findings to established qualitative theories on multicenter bonding, particularly, Alcock's "secondary" bonding, we relate the bonding behavior in polyiodides to industrially relevant phase-change materials of the Ge-Sb-Te class, finding further evidence for the same underlying cause as regards chemical bonding in both material classes.