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.
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