  A high resolution inelastic neutron scattering (INS) study of fully
deuterated Mn$_{12}$-acetate provides the most accurate spin Hamiltonian
parameters for this prototype single molecule magnet so far. The
Mn$_{12}$-clusters deviate from axial symmetry, a non-zero rhombic term in the
model Hamiltonian leading to excellent agreement with observed positions and
intensities of the INS peaks. The following parameter set provides the best
agreement with the experimental data: $D=-0.0570(1)$ meV,
$B_{4}^0=-2.78(7)\cdot 10^{-6}$ meV, $B_{4}^4=-3.2(6)\cdot 10^{-6}$ meV and
$\mid$\textit{E}$\mid =6.8(15)\cdot 10^{-4}$ meV. Crystal dislocations are not
the likely cause of the symmetry lowering. Rather, this study lends strong
support to a recently proposed model, which is based on the presence of several
molecular isomers with distinct spin Hamiltonian parameters.
