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A reinterpretation of the complete energy spectrum of the Oxygen-16 nucleusup to 20 MeV, and partly beyond, is proposed. The underlying intrinsic shape ofthe nucleus is tetrahedral, as in the na\"ive alpha-particle model and othercluster models, and A, E and F vibrational phonons are included. The A- andF-phonons are treated in the harmonic approximation, but the E-vibrations areextended into a two-dimensional E-manifold of D2-symmetric, four-alpha-particleconfigurations, following earlier work. This allows for the underlyingtetrahedral configuration to deform through a square configuration into thedual tetrahedron, so there is tunnelling between the tetrahedron and its dual,with the associated breaking of parity doubling. However, E-manifold states canstill be interpreted in terms of E-phonons. Rotational excitations of thevibrational states are analysed as in the classic work of Dennison, Robson andothers, with centrifugal corrections to the rotational energy spectrumincluded. States with F-phonons require Coriolis corrections too. Thefirst-excited $0^+$ state at 6.05 MeV is modelled as a state with twoE-phonons; this allows a good fit of the lowest $2^+$ and $2^-$ states asexcitations with one E-phonon. The Coriolis parameter $\zeta$ is chosenpositive to ensure the right splitting of the $3^+$ and $3^-$ states near 11MeV. Altogether, about 80 states with isospin zero are predicted below 20 MeV,and these match rather well the more than 60 experimentally tabulated states.Several high-spin states are predicted, up to spin 9 and energy 30 MeV, andthese match some of the high-spin, natural parity states in this energy rangethat have been observed. The model proposed here is mainly phenomenological butit receives some input from analysis of Skyrmions with baryon number 16.

Oxygen-16 Spectrum from Tetrahedral Vibrations and their Rotational Excitations