jats:titleAbstract</jats:title> jats:pA model for vibrational and rotational excitations of an intrinsic tetrahedral structure of the Oxygen-16 nucleus has been investigated, building on classic work of Wheeler, Dennison and Robson. Tetrahedral A- and F-phonons are treated harmonically, but the E-phonon dynamics is extended to dynamics on an E-manifold of configurations of four α-particles. This allows for tunnelling between the tetrahedral configuration and its dual, through a square configuration, and lifts the parity doubling that would otherwise occur. Unlike in earlier models, including the algebraic cluster model, the E-phonon frequency is taken to be about half the F-phonon frequency, which in turn is about half the A-phonon frequency. As a result, the first-excited 0jats:sup+</jats:sup> state is a 2-phonon, E-manifold excitation, whereas the lowest 2jats:sup+</jats:sup> and 2jats:sup−</jats:sup> states are 1-phonon, E-manifold excitations. Coriolis contributions to the rotational energy of states with F-phonons are significant. Altogether, rotational bands are constructed based on vibrational states with up to four phonons, and with spin/parity up to 9jats:sup−</jats:sup>. Nearly all the observed states of Oxygen-16 are accommodated, up to 20 MeV and partly beyond. Predictions for some so far unobserved states, especially those of unnatural parity, are made.</jats:p>