  We consider properties of critical points in the interacting boson model,
corresponding to flat-bottomed potentials as encountered in a second-order
phase transition between spherical and deformed $\gamma$-unstable nuclei. We
show that intrinsic states with an effective $\beta$-deformation reproduce the
dynamics of the underlying non-rigid shapes. The effective deformation can be
determined from the the global minimum of the energy surface after projection
onto the appropriate symmetry. States of fixed $N$ and good O(5) symmetry
projected from these intrinsic states provide good analytic estimates to the
exact eigenstates, energies and quadrupole transition rates at the critical
point.
