### abstract

- We perform a three-dimensional triaxial analysis of 16 X-ray regular and 4 high-magnification galaxy clusters selected from the CLASH survey by combining two-dimensional weak-lensing and central strong-lensing constraints. In a Bayesian framework, we constrain the intrinsic structure and geometry of each individual cluster assuming a triaxial Navarro–Frenk–White halo with arbitrary orientations, characterized by the mass M_(200c), halo concentration c_(200c), and triaxial axis ratios q_a ⩽ q_b, and investigate scaling relations between these halo structural parameters. From triaxial modeling of the X-ray-selected subsample, we find that the halo concentration decreases with increasing cluster mass, with a mean concentration of c_(200c) = 4.82 ± 0.30 at the pivot mass M_(200c) = 10^(15) M_⊙ h^(-1). This is consistent with the result from spherical modeling, c_(200c) = 4.51 ± 0.14. Independently of the priors, the minor-to-major axis ratio q_a of our full sample exhibits a clear deviation from the spherical configuration q_a = 0.52 ± 0.04 at 10^(15) M_⊙ h^(-1) with uniform priors), with a weak dependence on the cluster mass. Combining all 20 clusters, we obtain a joint ensemble constraint on the minor-to-major axis ratio of q_a = 0.652_(-0.078)^(+0.162) and a lower bound on the intermediate-to-major axis ratio of q_b > 0.63 at the 2σ level from an analysis with uniform priors. Assuming priors on the axis ratios derived from numerical simulations, we constrain the degree of triaxiality for the full sample to be T = 0.79 ± 0.03 at 10^(15) M_⊙ h^(-1), indicating a preference for a prolate geometry of cluster halos. We find no statistical evidence for an orientation bias (f_(geo) = 0.93 ± 0.07), which is insensitive to the priors and in agreement with the theoretical expectation for the CLASH clusters.