  We study the origin of the regular features obtained in numerical studies of
the IBM with random interactions, in particular the dominance of L=0 ground
states and the occurrence of vibrational and rotational band structures. It is
shown that the geometric shapes associated with IBM Hamiltonians play a crucial
role in understanding these regular properties. Different regions of the
parameter space are associated with definite geometric shapes, such as
spherical and deformed shapes and a condensate of quadrupole bosons.
