  Hartree-Fock-Bogolyubov solutions corresponding to the tetrahedral
deformation are found in six tetrahedrally doubly-magic nuclei. Values of the
beta32 deformation, depths of the tetrahedral minima, and their energies
relative to the co-existing quadrupole minima are determined for several
versions of the Skyrme force. Reduction of the tetrahedral deformation energies
by pairing correlations is quantitatively analysed. In light nuclei, shallow
tetrahedral minima are found to be the lowest in energy, while in heavy nuclei,
the minima are deeper but appear at a few MeV of excitation.
