  We have explored the outskirts of dark matter haloes out to 2.5 times the
virial radius using a large sample of halos drawn from Illustris, along with a
set of zoom simulations (MUGS). Using these, we make a systematic exploration
of the shape profile beyond R$_{vir}$. In the mean sphericity profile of
Illustris halos we identify a dip close to the virial radius, which is robust
across a broad range of masses and infall rates. The inner edge of this feature
may be related to the virial radius and the outer edge with the splashback
radius. Due to the high halo-to-halo variation this result is visible only on
average. However, in four individual halos in the MUGS sample, a decrease in
the sphericity and a subsequent recovery is evident close to the splashback
radius. We find that this feature persists for several Gyr, growing with the
halo. This feature appears at the interface between the spherical halo density
distribution and the filamentary structure in the environment. The shape
feature is strongest when there is a high rate of infall, implying that the
effect is due to the mixing of accreting and virializing material. The
filamentary velocity field becomes rapidly mixed in the halo region inside the
virial radius, with the area between this and the splashback radius serving as
the transition region. We also identify a long-lasting and smoothly evolving
splashback region in the radial density gradient in many of the MUGS halos.
