  An extension of the Consistent-Q formalism for the Interacting Boson Model
that includes the cubic QxQxQ term is proposed. The potential energy surface
for the cubic quadrupole interaction is explicitly calculated within the
coherent state formalism using the complete chi-dependent expression for the
quadrupole operator. The Q-cubic term is found to depend on the asymmetry
deformation parameter gamma as a linear combination of cos(3gamma) and
cos^2(3\gamma) terms, thereby allowing for triaxiality. The phase diagram of
the model in the large N limit is explored, it is described the order of the
phase transition surfaces that define the phase diagram, and moreover, the
possible nuclear equilibrium shapes are established. It is found that, contrary
to expectations, there is only a very tiny region of triaxiality in the model,
and that the transition from prolate to oblate shapes is so fast that, in most
cases, the onset of triaxiality might go unnoticed.
