  The departure from perfect spherical symmetry in the case of fullerenes, C60
being the sole exception, induces instabilities due to the stresses generated
by the pentagonal protrusions in the sigma-bonded surfaces. By assuming sigma
and pi separability and treating pi electrons as a degenerate Fermi gas in the
two shells around the central sigma structure, the resulting degeneracy
pressures can further enhance the sigma-surface initiated instabilities for
non-icosahedral structures especially for those smaller than C60 as well as the
icosahedral fullerenes that are larger than C60, with large protrusions. Under
certain circumstances the net degeneracy pressure across the sigma surface
might have structure-stabilizing effect. The role of the pi electron degeneracy
in a broad range of fullerenes from C20 to C1500 and its effects on fullerene
stability is investigated.

Mesoscale and Nanoscale Physics