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For the last 30 years many observational and theoretical evidences have shownthat galaxy clusters are not spherical objects, and that their shape is muchbetter described by a triaxial geometry. With the advent of multi-wavelengthdata of increasing quality, triaxial investigations of galaxy clusters isgathering a growing interest from the community, especially in the time of"precision cosmology". In this work, we aim to provide the first statisticallysignificant predictions in the unexplored mass range above 3x10^14 Mo/h, usinghaloes from two redshifts (z=0 and z=1) of the Millennium XXL simulation. Thesize of this cosmological dark matter only simulation (4.1 Gpc) allows theformation of a statistically significant number of massive cluster scale haloes(about 500 with M>2x10^15 Mo/h and 780000 with M>10^14 Mo/h). Besides, we aimto extend this investigation to lower masses in order to look for universalpredictions across nearly six orders of magnitude in mass, from 10^10 to almost10^16 Mo/h. For this purpose we use the SBARBINE simulations, allowing to modelhaloes of masses starting from 10^10 Mo/h. We use an elliptical overdensitymethod to select haloes and compute the shapes of the unimodal ones(approximately 50%), while we discard the unrelaxed. The minor to major andintermediate to major axis ratio are found to be well described by simplefunctional forms. For a given mass we can fully characterize the shape of ahalo and give predictions about the distribution of axis ratios for a givencosmology and redshift. Moreover, these results are in some disagreement withthe findings of Jing & Suto (2002) which are widely used in the community eventhough they have to be extrapolated far beyond their original mass range. This"recipe" is made available to the community in this paper and in a dedicatedweb page.

Universality of dark matter haloes shape over six decades in mass: Insights from the Millennium XXL and SBARBINE simulations