  \textit{Ab initio} calculations have been performed on hexagonal layers of
M$_2$O$_3$ (M being several transition metals of the $5d$ series) sandwiched by
a band insulator such as Al$_2$O$_3$ that provides the honeycomb lattice where
the $5d$ electrons reside. This corundum-structure-based superlattice is the
most obvious way to design a honeycomb lattice with transition metal cations
avoiding the use of largely polar surfaces. We obtain that this system supports
the presence of Dirac cones at the Fermi level that open up with the
introduction of spin-orbit coupling at various fillings of the $5d$ band. The
DFT calculations performed in this work show that the $5d^5$ situation is
always a trivial insulator, whereas the $5d^8$ filling presents topological
insulating configurations which evolve into a trivial state with increasing
tensile strain or on-site Coulomb potential U. However, LDA+U calculations show
a stable antiferromagnetic solution for the $5d^8$ case at every U value, which
would break time reversal symmetry and could affect the topological properties
of the system. We also discuss the similarities with the buckled honeycomb
lattice obtained using perovskite (111) bilayers previously studied in
literature, in particular for the $5d^5$ and $5d^8$ configurations. This work
provides some clues on the stability of topological phases using metal oxides
in general.
