  We discuss symmetries of the spherical shell model that make contact with the
geometric collective model of Bohr and Mottelson. The most celebrated symmetry
of this kind is SU(3), which is the basis of Elliott's model of rotation. It
corresponds to a deformed mean field induced by a quadrupole interaction in a
single major oscillator shell N and can be generalized to include several major
shells. As such, Elliott's SU(3) model establishes the link between the
spherical shell model and the (quadrupole component of the) geometric
collective model. We introduce the analogue symmetry induced by an octupole
interaction in two major oscillator shells N-1 and N, leading to an
octupole-deformed solution of the spherical shell model. We show that in the
limit of large oscillator shells (large N) the algebraic octupole interaction
tends to that of the geometric collective model.
