  The triaxiality of odd-mass nuclei is investigated by coupling a
quasiparticle to an even-even core through the core-quasiparticle coupling
model. Both soft and rigid triaxial cores are considered. The "soft core" is
described by the collective model with rotation-vibrational motion, while the
"rigid core" is described by the triaxial rotor model, which is a limiting case
of the collective model with only rotational motion. We show that the presence
of the odd quasiparticle modifies the collective quadrupole dynamics of the
core to appear more "rigid".
