  The first example of an empirically manifested quasi dynamical symmetry
trajectory in the interior of the symmetry triangle of the Interacting Boson
Approximation model is identified for large boson numbers. Along this curve,
extending from SU(3) to near the critical line of the first order phase
transition, spectra exhibit nearly the same degeneracies that characterize the
low energy levels of SU(3). This trajectory also lies close to the
Alhassid-Whelan arc of regularity, the unique interior region of regular
behavior connecting the SU(3) and U(5) vertices, thus offering a possible
symmetry-based interpretation of that narrow zone of regularity amidst regions
of more chaotic spectra.
