  Artificial honeycomb lattices with Dirac cone dispersion provide a
macroscopic platform to study the massless Dirac quasiparticles and their novel
geometric phases. In this paper, a quadruple-degenerate state is achieved at
the center of Brillouin zone (BZ) in a two-dimensional honeycomb lattice
phononic crystal, which is a result of accidental degeneracy of two
double-degenerate states. In the vicinity of the quadruple-degenerate state,
the dispersion relation is linear. Such quadruple degeneracy is analyzed by
rigorous representation theory of groups. Using method, a reduced Hamiltonian
is obtained to describe the linear Dirac dispersion relations of such
quadruple-degenerate state, which is well consistent with the simulation
results. Near such accidental degeneracy, we observe some unique wave
propagating properties, such as defect insensitive propagating character and
Talbot effect.
