The description of low-lying collective excitation spectra in atomic nuclei requires the inclusion of correlations beyond the mean field. These can be taken into account through configuration mixing of symmetry-projected mean-field states by means of the generator coordinate method (GCM). Ample studies have been carried out for the description of quadrupole collectivity, which requires the configuration mixing of angular-momentum (AMP) and particle-number (PNP) projected states. Likewise, several recent studies concentrated on the description of octupole collectivity, none, however, taking into account the full GCM of AMP, PNP, and parity projected (PP) mean-field states. I will discuss a first application of a beyond mean-field calculation including configuration-mixed AMP, PNP and PP states for 20Ne. Finally, the emergence of asymmetric fission will also be discussed within this framework.
