  Due to the ubiquitous presence of a Berry phase, in most cases of dynamical
Jahn-Teller systems the symmetry of the vibronic ground state is the same as
that of the original degenerate electronic state. As a single exception, the
linear H x h icosahedral model, relevant to the physics of C60 cations, is
determined by an additional free parameter, which can be continuously tuned to
eliminate the Berry phase from the low-energy closed paths: accordingly, the
ground state changes to a totally-symmetric nondegenerate state.
