  The extraordinary electronic properties of Dirac materials, the
two-dimensional partners of Weyl semimetals, arise from the linear crossings in
their band structure. When the dispersion around the Dirac points is tilted,
the emergence of intricate transport phenomena has been predicted, such as
modified Klein tunnelling, intrinsic anomalous Hall effects and ferrimagnetism.
However, Dirac materials are rare, particularly with tilted Dirac cones.
Recently, artificial materials whose building blocks present orbital degrees of
freedom have appeared as promising candidates for the engineering of exotic
Dirac dispersions. Here we take advantage of the orbital structure of photonic
resonators arranged in a honeycomb lattice to implement photonic lattices with
semi-Dirac, tilted and, most interestingly, type-III Dirac cones that combine
flat and linear dispersions. The tilted cones emerge from the touching of a
flat and a parabolic band with a non-trivial topological charge. These results
open the way to the synthesis of orbital Dirac matter with unconventional
transport properties and, in combination with polariton nonlinearities, to the
study of topological and Dirac superfluids in photonic lattices.
