  Single crystal neutron diffraction is combined with synchrotron x-ray
scattering to identify the different superlattice phases present in
$Cs_{0.8}Fe_{1.6}Se_2$. A combination of single crystal refinements and first
principles modelling are used to provide structural solutions for the
$\sqrt{5}\times\sqrt{5}$ and $\sqrt{2}\times\sqrt{2}$ superlattice phases. The
$\sqrt{5}\times\sqrt{5}$ superlattice structure is predominantly composed of
ordered Fe vacancies and Fe distortions, whereas the $\sqrt{2}\times\sqrt{2}$
superlattice is composed of ordered Cs vacancies. The Cs vacancies only order
within the plane, causing Bragg rods in reciprocal space. By mapping x-ray
diffraction measurements with narrow spatial resolution over the surface of the
sample, the structural domain pattern was determined, consistent with the
notion of a majority antiferromagnetic $\sqrt{5}\times\sqrt{5}$ phase and a
superconducting $\sqrt{2}\times\sqrt{2}$ phase.
