An extension of the Consistent-Q formalism for the Interacting Boson Model that includes the
cubic (^Q ^Q ^Q)(0) term is proposed. The potential energy surface for the cubic quadrupole interac-
tion is explicitly calculated within the coherent state formalism using the complete ( x-dependent)
expression for the quadrupole operator. The Q-cubic term is found to depend on the asymmetry
deformation parameter
as a linear combination of cos (3
) and cos2 (3
) 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 de ne 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.
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