Atomic Nuclei with Tetrahedral and Octahedral Symmetries

We present possible manifestations of octahedral and tetrahedral symmetries in nuclei. These symmetries are associated with the O h and T d double point groups. Both of them have very characteristic finger-prints in terms of the nucleonic level properties unique in the Fermionic universe. The tetrahedral symmetry leads to the four-fold degeneracies in the nucleonic spectra; it does not preserve the parity. The octahedral symmetry leads to the four-fold degeneracies in the nucleonic spectra as well but it does preserve the parity.