By considering a transition-metal ion in the field of some symmetrically placed ions, we illustrate the consequences of a continuous change of the structure of the ligands on the energies of the 3d electrons of the transition-metal atom. Both a rigorous mathematical derivation and an analysis based on group theory are presented. For six ions surrounding the transition-metal atom, a continuoustransition is observed, whereas for four ions, a continuoustransition results. Although the two systems possess many similarities, interesting differences are found as well. Finally, we demonstrate that when including orbital interactions between the ligands and the transition-metal atom, quantitative differences occur.