  Two-dimensional lattices of coupled micropillars etched in a planar
semiconductor microcavity offer a workbench to engineer the band structure of
polaritons. We report experimental studies of honeycomb lattices where the
polariton low-energy dispersion is analogous to that of electrons in graphene.
Using energy-resolved photoluminescence we directly observe Dirac cones, around
which the dynamics of polaritons is described by the Dirac equation for
massless particles. At higher energies, we observe p orbital bands, one of them
with the nondispersive character of a flatband. The realization of this
structure which holds massless, massive and infinitely massive particles opens
the route towards studies of the interplay of dispersion, interactions, and
frustration in a novel and controlled environment.
