Investigation of the nuclear shapes allows us correctly estimate the hights of fission bariers, yrast line, moments of inertia, spins and parity, electromagnetic transtion coeficient and collective properties for example the shape of strenght function of the Giant Dipole Resonance or life-times in ground states or excited states. The octupole deformation considers the nuclear mass asymetry. In early fifties last century a hipothesis that the octupole vibration can be source of the negative parity rotational bands has arised. Our large scale calculation of the total energy with the microscopic-macroscopic method in multidimentional deformation space allows us observe the evolution of the different nuclear shapes. One of the non-axial octupole deformation parameters is called 'tetrahedral'. It can be approximate by tetrahedron and it has 48 symmetry transitions. It is wonderful case of the point-group symmetry and we can connect nuclear shape with the group theory. We investigated all even-even nuclei from Z=16 up to Z=136 which allow us to define new magic numbers and discover new stability islands.

Fig. 1 Example of the Octupole shape (left) and Tetrahedral shape (right).