We present a microscopic triaxial quadrupole-octupole collective Hamiltonian (TQOCH) that unifies collective rotations, quadrupole-octupole vibrations, and their couplings to model low-lying nuclear states of both parities. The TQOCH's dynamics are governed by collective parameters derived from multidimensionally constrained covariant density functional theory. The model's validity is demonstrated through calculations of ${}^{152}\mathrm{Sm}$, including its deformation energy surfaces, excitation spectra, and transition probabilities. As a predictive tool, the TQOCH probes complex nuclear phenomena like shape coexistence and phase transitions, directly connecting their microscopic origins to spectroscopic observables.

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• Collective levels
• Electromagnetic transitions
• Nuclear shapes and moments
• 150 ≤ A ≤ 189
• Collective models
• Nuclear density functional theory