Polyhedral water clusters (PWCs) are cage-like (H2O)(n) clusters where every 0 participates in exactly three H bonds. For a database of 83 PWCs, 8 <= n <= 20, geometry was optimized and zero point energy (ZPE) was calculated at the B3LYP/6-311++G** level. ZPE correlates negatively with electronic energy (E-0): each increase of 1 kcal/mol in E-0 corresponds to a decrease of about 0.11 kcal/mol in ZPE. For each n, a set of four connectivity parameters accounts for 98% or more of the variance in ZPE. Linear regression of ZPE against n and this set gives an RMS error of 0.13 kcal/mol. The contributions to ZPE from stretch modes only (ZPEs) and from torsional modes only (ZPE(T)) also correlate strongly with E-0 and with each other.