Point symmetries in the nuclear SU(3) partner groups model

The algebraic approach which allows for simulation of symmetries of a nucleus with respect to the laboratory and intrinsic frames is presented. The formalism is based on the partner groups (a group and the corresponding intrinsic group) idea. An illustrative example is related to the successful SU(3) Elliot nuclear model. An example of schematic Hamiltonian is chosen to have tetrahedral or octahedral symmetry.