  We consider theoretically a system of exciton-polariton micropillars arranged
in a honeycomb lattice. The naturally present TE-TM splitting and an
alternating Zeeman splitting, where the different sublattices experience
opposite Zeeman splitting, shifts the Dirac points in energy, giving rise to
antichiral behavior. In a strip geometry having zigzag edges, two pairs of edge
states exist and propagate in the same direction (including the states at the
opposite edges). The edge modes localized at the opposite edges have opposite
spins (circular polarizations), which leads to co-propagating "+-" spin
channels. The antichiral edge states are protected by non-zero winding numbers
and can propagate around a 60 degree bend without being reflected. We further
compare the transport properties of these edge states with chiral edge modes
and propose a scheme to realize them experimentally.
