  A continuum elastic model of fullerenes is presented by utilizing the analogy
between the closed carbon cages and elastic shells. We derive expressions for
the curvature related strain energies Ep of the pentagonal protrusions. We
propose to explain the observed sphericity of the carbon onions shells as
opposed to the predicted protrusions around the pentagonal defects on the basis
of our continuum elastic model of fullerenes. In our model the energy inherent
in the pentagonal protrusions Ep is due to the stretching and bending of the
shell and shown to be a function of the structural parameters. It also defines
the upper limit on the size of the free-standing fullerenes. Using Ep and the
topological arguments, we show that the pentagonal protrusions will be smoothed
out, resulting in spherical shells of the carbon onions denoted as
C60@C240@C540@C960@C1500 ,... .
