Correlation between the intermediate-to-major and minor-to-major axis ratio for halos at z = 0 in the AIDA-TNG simulation. The left, central, and right panels refer to the correlation measured at the halo boundary radius R₂₀₀, R₂₀₀/2, and R₂₀₀/10, respectively. Shaded contours in the background represent the joint distribution of b/a and c/a (as measured considering all particles within R₂₀₀ and averaging over all hydrodynamic runs for the different DM models). The blue line shows the median b/a at fixed c/a, with error bars showing the range that encloses 25% of the distribution on either side of this median. The dotted black line shows the corresponding median in the DMO runs. The gray lines refer to the cases of halos with T = 1/3, 2/3, and 1 (top to bottom). The dashed gray line shows the case p = 0, the long-dashed gold curve shows the simplest prediction (for Gaussian initial conditions) described in the text, and the dotted red curve is the relation from Bonamigo et al. (2015).