2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/151922We show through selected examples, relevant to the physics of fullerene ions, that the presence of a Berry phase in dynamical Jahn-Teller systems does not guarantee the degeneracy of the ground state, contrary to what previously believed. Moreover, we introduce a new class of Jahn-Teller systems with no Berry phase, as a generalization of the basic icosahedral $H \otimes h$ case.8 pages, 1 ps figCondensed MatterChemical Physicstext