  Medium and high-spin states in $^{133}$Ce were investigated using the
$^{116}$Cd($^{22}$Ne, $5n$) reaction and the Gammasphere array. The level
scheme was extended up to an excitation energy of $\sim22.8$ MeV and spin 93/2
. Eleven bands of quadrupole transitions and two new dipole bands are
identified. The connections to low-lying states of the previously known,
high-spin triaxial bands were firmly established, thus fixing the excitation
energy and, in many cases, the spin parity of the levels. Based on comparisons
with cranked Nilsson-Strutinsky calculations and tilted axis cranking covariant
density functional theory, it is shown that all observed bands are
characterized by pronounced triaxiality. Competing multiquasiparticle
configurations are found to contribute to a rich variety of collective
phenomena in this nucleus.
