[en] This paper provides an algebraic description of collective nuclear motion. One of its most attractive features is the existence of three dynamic symmetries corresponding to subgroup chains of U(6) which contain the rotation group O(3). The U(5), SU(3) and O(6) dynamic symmetries correspond in the geometric collective model to the spherical vibrator, the axially symmetric rotor and the gamma-soft rotor respectively. It is the object of this paper to examine some properties of the O(6) dynamic symmetry and their manifestations in the region around A = 130. The authors also investigate the connexion to the rigid triaxial rotor and examine the gamma softness in the light of a very different model, viz. the cranking model