  The triaxial nature of low-lying rotational bands of $^{166}$Er is presented
from the viewpoint of the Bohr Hamiltonian and from that of many-fermion
calculations by the Monte Carlo shell model and the constrained Hartree-Fock
method with projections. A recently proposed novel picture of those bands
suggests definite triaxial shapes of those bands, in contrast to the
traditional view with the prolate ground-state band and the
$\gamma$-vibrational excited band. Excitation level energies and E2 transitions
can be described well by the Bohr Hamiltonian and by the many-fermion
approaches, where rather rigid triaxiality plays vital roles, although certain
fluctuations occur in shell-model wave functions. Based on the potential energy
surfaces with the projections, we show how the triaxial rigidity appears and
what the softness of the triaxiality implies. The excitation to the so-called
double $\gamma$-phonon state is discussed briefly.
