The stability of the 8-fold orientational order quasipattern is studied both analytically and numerically. Close to the intensity threshold, the sequence, that minimizes the free energy, displays structures built up with four, two and one modes, successively, as the linear refractive index decreases. Differently, when increasing the intensity above the threshold, the 8-fold orientational order
... [Show full abstract] quasipattern bifurcates to a three mode quasiperiodic pattern, followed by a robust rhombic pattern. A multiconical emission process is invoked to explain the occurrence of the rhombuses.