  We study the transverse self-structuring of a cloud of cold atoms with
effective atomic interactions mediated by a coherent driving beam
retro-reflected by means of a single mirror. The resulting self-structuring due
to optomechanical forces is much richer than that of an effective-Kerr medium,
displaying hexagonal, stripe and honeycomb phases depending on the interaction
strength parametrized by the linear susceptibility. Phase domains are described
by real Ginzburg-Landau amplitude equations. In the stripe phase the system
recovers inversion symmetry. Moreover, the subcritical character of the
honeycomb phase allows for light-density feedback solitons functioning as
self-sustained dark atomic traps with motion controlled by phase gradients in
the driving beam.
