  The possible existence of stable axial octupole and tetrahedral deformations
is investigated in $^{80}$Zr and $^{98}$Zr. HFBCS calculations with parity
projection have been performed for various parametrizations of the Skyrme
energy functional. The correlation and excitation energies of negative parity
states associated with shape fluctuations have been obtained using the
generator coordinate method (GCM). The results indicate that in these nuclei
both the axial octupole and tetrahedral deformations are of dynamic character
and possess similar characteristics. Various Skyrme forces give consistent
results as a function of these two octupole degrees of freedom both at the
mean-field level as well as for configuration mixing calculations.
