  GaAs/Fe$_{3}$Si core/shell nanowire structures were fabricated by
molecular-beam epitaxy on oxidized Si(111) substrates and investigated by
synchrotron x-ray diffraction. The surfaces of the Fe$_3$Si shells exhibit
nanofacets. These facets consist of well pronounced Fe$_3$Si{111} planes.
Density functional theory reveals that the Si-terminated Fe$_3$Si{111} surface
has the lowest energy in agreement with the experimental findings. We can
analyze the x-ray diffuse scattering and diffraction of the ensemble of
nanowires avoiding the signal of the substrate and poly-crystalline films
located between the wires. Fe$_3$Si nanofacets cause streaks in the x-ray
reciprocal space map rotated by an azimuthal angle of 30{\deg} compared with
those of bare GaAs nanowires. In the corresponding TEM micrograph the facets
are revealed only if the incident electron beam is oriented along
[1$\overline{1}$0] in accordance with the x-ray results. Additional maxima in
the x-ray scans indicate the onset of chemical reactions between Fe$_{3}$Si
shells and GaAs cores occurring at increased growth temperatures.
