  The possibility of the existence of stable tetrahedral deformations at spin
zero is investigated using the Skyrme-HFBCS approach and the generator
coordinate method (GCM). The study is limited to nuclei in which the
tetrahedral mode has been predicted to be favored on the basis of non
self-consistent models. Our results indicate that a clear identification of
tetrahedral deformations is unlikely as they are strongly mixed with the axial
octupole mode. However, the excitation energies related to the tetrahedral mode
are systematically lower than those of the axial octupole mode in all the
nuclei included in this study.
