Rigid triaxiality has the SU(3) symmetry: ${}^{166}$Er as an example

The emergence of triaxiality in the low-lying collective bands of ${}^{166}$Er is systematically explored within the SU3-IBM. In this framework, SU(3) higher-order interactions are included, which enable the descriptions of various quadrupole deformations. The triaxiality of ${}^{166}$Er is described with a triaxiality angle $\gamma ={9.7}^{\circ }$. In addition, the calculated energy spectra, $B(E2)$ transition strengths, and quadrupole moments show excellent agreement with experimental data. These results provide further evidence supporting the SU(3) triaxial interpretation of ${}^{166}$Er and confirm its triaxial deformation rather than the prolate shape.