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An extension of the Consistent-Q formalism for the Interacting Boson Modelthat includes the cubic QxQxQ term is proposed. The potential energy surfacefor the cubic quadrupole interaction is explicitly calculated within thecoherent state formalism using the complete chi-dependent expression for thequadrupole operator. The Q-cubic term is found to depend on the asymmetrydeformation parameter gamma as a linear combination of cos(3gamma) andcos^2(3\gamma) terms, thereby allowing for triaxiality. The phase diagram ofthe model in the large N limit is explored, it is described the order of thephase transition surfaces that define the phase diagram, and moreover, thepossible nuclear equilibrium shapes are established. It is found that, contraryto 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 mostcases, the onset of triaxiality might go unnoticed.

Phase diagram for a Cubic Consistent-Q Interacting Boson Model Hamiltonian: signs of triaxiality