The details and difficulties underlying the calculation of the symmetry coordinates of an icosahedral molecule are explained in detail and applied to an icosahedral cage. The force field chosen is conceptually very simple and depends on a simple stretching force constantk1which is found to be 144 N m-1for the cage of boron atoms in [B12H12]2-and two bending constants which are -42 N m-1for adjacent bonds (60° bond angle) and +33 N m-1for non-adjacent bonds (108° bond angle). The frequencies of the forbidden fundamentals are predicted with an error which is not expected to exceed ±50 cm-1and which compare favourably with previous predictions.