  I study the buckling transition under compression of a two-dimensional,
hexagonal, regular elastic honeycomb. Under isotropic compression, the system
buckles to a configuration consisting of a unit cell containing four of the
original hexagons. This buckling pattern preserves the sixfold rotational
symmetry of the original lattice but is chiral, and can be described as a
combination of three different elemental distortions in directions rotated
2pi/3 from each other. Non-isotropic compression may induce patterns consisting
in a single elemental distortion or a superposition of two of them. The
numerical results compare very well with the outcome of a Landau theory of
second order phase transitions.
