  In this paper we study the triaxial properties of dark matter haloes of a
wide range of masses extracted from a set of cosmological N-body simulations.
We measure the shape at different distances from the halo centre (characterised
by different overdensity thresholds), both in three and in two dimensions. We
discuss how halo triaxiality increases with mass, redshift and distance from
the halo centre. We also examine how the orientation of the different
ellipsoids are aligned with each other and what is the gradient in internal
shapes for halos with different virial configurations. Our findings highlight
that the internal part of the halo retains memory of the violent formation
process keeping the major axis oriented toward the preferential direction of
the in-falling material while the outer part becomes rounder due to continuous
isotropic merging events. This effect is clearly evident in high mass haloes -
which formed more recently - while it is more blurred in low mass haloes. We
present simple distributions that may be used as priors for various mass
reconstruction algorithms, operating in different wavelengths, in order to
recover a more complex and realistic dark matter distribution of isolated and
relaxed systems.
