  A solution of the Bohr Hamiltonian appropriate for triaxial shapes, involving
a Davidson potential in beta and a steep harmonic oscillator in gamma, centered
around gamma=30 degrees, is developed. Analytical expressions for spectra and
B(E2) transition rates ranging from a triaxial vibrator to the rigid triaxial
rotator are obtained and compared to experiment. Using a variational procedure
it is pointed out that the Z(5) solution, in which an infinite square well
potential in beta is used, corresponds to the critical point of the shape phase
transition from a triaxial vibrator to the rigid triaxial rotator.
