  We present the analysis of a local (z = 0.04 - 0.2) sample of 31 galaxy
clusters with the aim of measuring the density of the X-ray emitting gas in
cluster outskirts. We compare our results with numerical simulations to set
constraints on the azimuthal symmetry and gas clumping in the outer regions of
galaxy clusters. We exploit the large field-of-view and low instrumental
background of ROSAT/PSPC to trace the density of the intracluster gas out to
the virial radius. We perform a stacking of the density profiles to detect a
signal beyond r200 and measure the typical density and scatter in cluster
outskirts. We also compute the azimuthal scatter of the profiles with respect
to the mean value to look for deviations from spherical symmetry. Finally, we
compare our average density and scatter profiles with the results of numerical
simulations. As opposed to some recent Suzaku results, and confirming previous
evidence from ROSAT and Chandra, we observe a steepening of the density
profiles beyond \sim r500. Comparing our density profiles with simulations, we
find that non-radiative runs predict too steep density profiles, whereas runs
including additional physics and/or treating gas clumping are in better
agreement with the observed gas distribution. We report for the first time the
high-confidence detection of a systematic difference between cool-core and
non-cool core clusters beyond \sim 0.3r200, which we explain by a different
distribution of the gas in the two classes. Beyond \sim r500, galaxy clusters
deviate significantly from spherical symmetry, with only little differences
between relaxed and disturbed systems. We find good agreement between the
observed and predicted scatter profiles, but only when the 1% densest clumps
are filtered out in the simulations. [Abridged]
