  A reinterpretation of the complete energy spectrum of the Oxygen-16 nucleus
up to 20 MeV, and partly beyond, is proposed. The underlying intrinsic shape of
the nucleus is tetrahedral, as in the na\"ive alpha-particle model and other
cluster models, and A, E and F vibrational phonons are included. The A- and
F-phonons are treated in the harmonic approximation, but the E-vibrations are
extended into a two-dimensional E-manifold of D2-symmetric, four-alpha-particle
configurations, following earlier work. This allows for the underlying
tetrahedral configuration to deform through a square configuration into the
dual tetrahedron, so there is tunnelling between the tetrahedron and its dual,
with the associated breaking of parity doubling. However, E-manifold states can
still be interpreted in terms of E-phonons. Rotational excitations of the
vibrational states are analysed as in the classic work of Dennison, Robson and
others, with centrifugal corrections to the rotational energy spectrum
included. States with F-phonons require Coriolis corrections too. The
first-excited $0^+$ state at 6.05 MeV is modelled as a state with two
E-phonons; this allows a good fit of the lowest $2^+$ and $2^-$ states as
excitations with one E-phonon. The Coriolis parameter $\zeta$ is chosen
positive to ensure the right splitting of the $3^+$ and $3^-$ states near 11
MeV. 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, and
these match some of the high-spin, natural parity states in this energy range
that have been observed. The model proposed here is mainly phenomenological but
it receives some input from analysis of Skyrmions with baryon number 16.
