  We experimentally reveal the emergence of edge states in a photonic lattice
with orbital bands. We use a two-dimensional honeycomb lattice of coupled
micropillars whose bulk spectrum shows four gapless bands arising from the
coupling of $p$-like photonic orbitals. We observe zero-energy edge states
whose topological origin is similar to that of conventional edge states in
graphene. Additionally, we report novel dispersive edge states that emerge not
only in zigzag and bearded terminations, but also in armchair edges. The
observations are reproduced by tight-binding and analytical calculations. Our
work shows the potentiality of coupled micropillars in elucidating some of the
electronic properties of emergent 2D materials with orbital bands.
