  Conventionally, the Ih symmetry of fullerene C60 is accepted which is
supported by numerous calculations. However, this conclusion results from the
consideration of the molecule electron system, of its odd electrons in
particular, in a close-shell approximation without taking the electron spin
into account. Passing to the open-shell approximation has lead to both the
energy and the symmetry lowering up to Ci. Seemingly contradicting to a
high-symmetry pattern of experimental recording, particularly concerning the
molecule electronic spectra, the finding is considered in the current paper
from the continuous symmetry viewpoint. Exploiting both continuous symmetry
measure and continuous symmetry content, was shown that formal Ci symmetry of
the molecule is by 99.99% Ih. A similar continuous symmetry analysis of the
fullerene monoderivatives gives a reasonable explanation of a large variety of
their optical spectra patterns within the framework of the same C1 formal
symmetry exhibiting a strong stability of the C60 skeleton.
