Abstract
Certain Jahn-Teller systems, in which the frequencies and couplings of participating modes are suitably constrained, possess a hidden symmetry corresponding to invariance under a rotation in two, three, four or five dimensions. The authors illustrate the physical significance of such symmetries by giving a concrete realisation of an invariance under rotation in two dimensions for a tetragonal system. This may be exhibited conveniently using a (two-dimensional) perspex model on an overhead projector. The model also affords a simple illustration of the use of spatial and time-reversal symmetries in generating selection rules on the ion-vibration coupling.