Dependence of DM halo dynamical properties on halo isolation. The frequency distributions of each property, for the two extreme isolation bins 1 < R_isol/r_vir < 4 (red) and 30 < R_isol/r_vir < 70 (blue), are presented in the inset plots. (a) Mean flatness, ⟨c/a⟩, with isolation: We find a systematic decrease with increasing isolation radius, implying that more isolated objects are statistically less spherical than those residing in dense regions. (b) Mean Triaxiality, ⟨T⟩, with isolation: A systematic increase of ⟨T⟩ with increasing isolation radius is observed, implying that isolated objects are statistically more prolate than those residing in dense regions. (c) Mean spin, ⟨λ⟩, with isolation: A systematic decrease of ⟨λ⟩ with increasing halo isolation is observed. (d) Virialization status, ⟨|U/K|⟩, with isolation: A systematic increase of ⟨|U/K|⟩ with halo isolation is observed. The increase is significantly faster for the lower isolation bins (R_isol/r_vir ≲ 15).