  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 $M_{200\mathrm{c}}$, halo concentration
$C_{200\mathrm{c}}$, and triaxial axis ratios ($q_{\mathrm{a}} \le
q_{\mathrm{b}}$), 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 $C_{200\mathrm{c}} = 4.82\pm0.30$ at the pivot
mass $M_{200\mathrm{c}}=10^{15}M_{\odot}h^{-1}$. This is consistent with the
result from spherical modeling, $C_{200\mathrm{c}}=4.51\pm 0.14$. Independently
of the priors, the minor-to-major axis ratio $q_{\mathrm{a}}$ of our full
sample exhibits a clear deviation from the spherical configuration
($q_{\mathrm{a}}=0.52 \pm 0.04$ at $10^{15}M_{\odot}h^{-1}$ 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
$q_{\mathrm{a}}=0.652^{+0.162}_{-0.078}$ and a lower bound on the
intermediate-to-major axis ratio of $q_{\mathrm{b}}>0.63$ at the $2\sigma$
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 $\mathcal{T}=0.79 \pm 0.03$ at $10^{15}M_{\odot}h^{-1}$,
indicating a preference for a prolate geometry of cluster halos. We find no
statistical evidence for an orientation bias ($f_{\mathrm{geo}}=0.93 \pm 0.07$)
(abridged)
