The concept of the equalization of atomic electronegativities accompanying molecule formation is applied to a study of the electronic structure of polyhedral clusters of main-group atoms such as Ge, Sn, Pb, TI, and Bi. Emphasis is placed upon charged clusters such as Sn9-,Pb:-(x =0+9), Sn+,Ge;-, Sn8-= Pb,T15-, Sn,Bii-, SnTei-, etc. The role of the relativistic spin-orbit splitting of an np shell into np,,, and np3,, subshells in modifying atomic and hence molecular electronegativities is discussed. Correlations are made between calculated charge distributions and observed'99 Sn NMR chemical shifts for clusters of a given size and charge. It is concluded that a useful picture of charge distributions in these clusters may be obtained from electronegativity equalization considerations.