  The two-fluid Interacting Vector Boson Model (IVBM) with the U(6) as a
dynamical group possesses a rich algebraic structure of physical interesting
subgroups that define its distinct exactly solvable dynamical limits. The
classical images corresponding to different dynamical symmetries are obtained
by means of the coherent state method. The phase structure of the IVBM is
investigated and the following basic phase shapes, connected to a specific
geometric configurations of the ground state, are determined: spherical,
$U_{p}(3)\otimes U_{n}(3)$, $\gamma-$unstable, O(6), and axially deformed
shape, $SU(3)\otimes U_{T}(2)$. The ground state quantum phase transitions
between different phase shapes, corresponding to the different dynamical
symmetries and mixed symmetry case, are investigated.
