  From a viewpoint of oblate-prolate symmetry and its breaking, we adopt the
quadrupole collective Hamiltonian to study dynamics of triaxial deformation in
shape coexistence phenomena. It accommodates the axially symmetric rotor model,
the $\gamma$-unstable model, the rigid triaxial rotor model and an ideal
situation for the oblate-prolate shape coexistence as particular cases.
Numerical solutions of this model yield a number of interesting suggestions.
(1) The relative energy of the excited 0+ state can be a signature of the
potential shape along the $\gamma$ direction. (2) Specific E2 transition
probabilities are sensitive to the breaking of the oblate-prolate symmetry. (3)
Nuclear rotation may induce the localization of collective wave functions in
the ($\beta, \gamma$) deformation space.
