  The interpretation of nuclear observables in the laboratory frame in terms of
the intrinsic deformation parameters beta and gamma is a classical theme in
nuclear structure. Here we use the quadrupole invariants (Kumar), calculated
within the framework of the configuration-interaction shell model, to clarify
the meaning and limitations of nuclear shapes. We introduce a novel method that
enables us to calculate accurately higher-order invariants and, therefore, the
fluctuations in both beta and gamma. We find that the shape parameter beta
often has a non-negligible degree of softness, and that the angle gamma is
usually characterized by large fluctuations, rendering its effective value not
meaningful. Contrary to common belief, we conclude that doubly magic nuclei are
not spherical because the notion of a well-defined shape does not apply to
them.
