  Vanadium Sesquioxide (V$_2$O$_3$) is an antiferromagnetic insulator below
$T_{\mathrm N}\approx$ 155 K. The magnetic order is not of C- or G-type as one
would infer from the bipartite character of the hexagonal basal plane in the
high-temperature corundum structure. In fact, the N\'eel transition is
accompanied by a monoclinic distortion that makes one bond of the honeycomb
plane inequivalent from the other two, thus justifying a magnetic structure
with one ferromagnetic bond and two antiferromagnetic ones. We show here that
the magnetic ordering, the accompanying monoclinic structural distortion, the
magnetic anisotropy and also the recently discovered high-pressure monoclinic
phase, can all be accurately described by conventional electronic structure
calculations within GGA and GGA+U. Our results are in line with DMFT
calculations for the paramagnetic phase, which predict that the insulating
character is driven by a correlation-enhanced crystal field splitting between
$e^\pi_g$ and $a_{1g}$ orbitals that pushes the latter above the chemical
potential. We find that the $a_{1g}$ orbital, although almost empty in the
insulating phase, is actually responsible for the unusual magnetic order as it
leads to magnetic frustration whose effect is similar to a
next-nearest-neighbor exchange in a Heisenberg model on a honeycomb lattice.
