  We introduce an alternative scheme for creating topological polaritons
(topolaritons) by exploiting the presence of photonic Dirac cones in photonic
crystals with triangular lattice symmetry. As recently proposed, topolariton
states can emerge from a coupling between photons and excitons combined with a
periodic exciton potential and a magnetic field to open up a topological gap.
We show that in photonic crystals the opening of the gap can be substantially
simplified close to photonic Dirac points. Coupling to Zeeman-split excitons
breaks time reversal symmetry and allows to gap out the Dirac cones in a
non-trival way, leading to a topological gap similar to the strength of the
periodic exciton potential. Compared to the original topolariton proposal
[Karzig {\em et al}, PRX {\bf 5}, 031001 (2015)], this scheme significantly
increases the size of the topological gap over a wide range of parameters.
Moreover, the gap opening mechanism highlights an interesting connection
between topolaritons and the Haldane and Raghu scheme [Haldane and Raghu, PRL
{\bf 100}, 013904 (2008)] to create topological photons in magneto-optically
active materials.
