It has been noticed that a given nuclear phase may be associated to a certain symmetry. Hence, its properties may be described with the help of the irreducible representation of the respective symmetry group. Thus, the gamma unstable nuclei can be described by the O(6) symmetry [WIJE56], the symmetric rotor by the SU(3) symmetry and the spherical vibrator by the U(5) symmetry. The gamma triaxial nuclei are characterized by the invariance symmetry group D2 [DF58] of the rigid triaxial rotorTriaxial rotor Hamiltonian. Thus, even in the 50s of the last century, the symmetry properties were greatly appreciated.