  The rapid increase of computational power over the last several years has
allowed detailed microscopic investigations of the structure of many nuclei in
terms of Relativistic Mean Field theories as well as in the framework of the
no-core Shell Model. In heavy deformed nuclei, in which microscopic
calculations remain a challenge, algebraic models based on the SU(3) symmetry
offer specific predictions, parameter-independent in several cases, directly
comparable to experimental data. Two different approximate models for heavy
deformed nuclei based on the SU(3) symmetry, the pseudo-SU(3) and the
proxy-SU(3) schemes will be discussed and the compatibility between their
predictions for the nuclear deformation parameters will be shown. In
particular, the dominance of prolate over oblate shapes in the ground states of
even-even nuclei and the prolate to oblate shape phase transition occurring in
heavy rare earths will be considered.
