  We report on the results of the calculations of the low energy excitation
patterns for three Zirconium isotopes, viz. $^{80}$Zr$_{40}$, $^{96}$Zr$_{56}$
and $^{110}$Zr$_{70}$, reported by other authors to be doubly-magic tetrahedral
nuclei (with tetrahedral magic numbers $Z$=40 and $N$=40, 56 and 70). We employ
the realistic Gogny effective interactions using three variants of their
parametrisation and the particle-number, parity and the angular-momentum
projection techniques. We confirm quantitatively that the resulting spectra
directly follow the pattern expected from the group theory considerations for
the tetrahedral symmetric quantum objects. We also find out that, for all the
nuclei studied, the correlation energy obtained after the angular momentum
projection is very large for the tetrahedral deformation as well as other
octupole deformations. The lowering of the energies of the resulting
configurations is considerable, i.e. by about 10 MeV or even more, once again
confirming the significance of the angular-momentum projections techniques in
the mean-field nuclear structure calculations.
