  Axial octupole and tetrahedral correlations in $^{80}$Zr and $^{98}$Zr have
been investigated using the generator coordinate method, applied to a basis
generated by Skyrme HF+BCS calculations. We focus on the possible presence of
states with tetrahedral symmetry and their stability with respect to octupole
vibrations. We show that pairing significantly reduces the stability of the
tetrahedral configuration and that a shallow mean-field tetrahedral minimum
coexists with an axial octupole minimum. The contributions to the correlation
energies coming from the tetrahedral degree of freedom and octupole axial
deformation are discussed.
