  Exact solutions of the Bohr Hamiltonian with a five-dimensional square well
potential, in isolation or coupled to a fermion by the five-dimensional
spin-orbit interaction, are considered as examples of a new class of dynamical
symmetry or Bose-Fermi dynamical symmetry. The solutions provide baselines for
experimental studies of even-even [E(5)] and odd-mass [E(5|4)] nuclei near the
critical point of the spherical to deformed gamma-unstable phase transition.
