  We investigate the prolate-to-oblate shape phase transitions in the
neutron-rich Pt, Os and Ir nuclei in the mass $A\approx 190$ region. The
Hamiltonian of the interacting boson-fermion model, used to describe the
odd-mass $^{185-199}$Pt, $^{185-193}$Os and $^{185-195}$Ir isotopes, is
partially constructed by using as a microscopic input the results of
constrained self-consistent mean-field calculations within the
Hartree-Fock-Bogoliubov method with the Gogny force. The remaining few
parameters are adjusted to experimental data in the odd systems. In this way
the calculations reasonably describe the spectroscopic properties of the
odd-mass systems considered. Several calculated observables for the odd-mass
nuclei, especially the low-energy excitation spectra and the effective
deformation parameters, point to a prolate-oblate shape transition as a
function of the neutron number for all the isotopic chains considered and
similar to the one already observed in the neighboring even-even systems.
