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arXiv:1503.01482v2.-- et al., We perform a three-dimensional multi-probe analysis of the rich galaxy cluster A1689, one of the most powerful known lenses on the sky, by combining improved weak-lensing data from new wide-field ${{BVR}}_{{\rm C}}i\prime z\prime $ Subaru/Suprime-Cam observations with strong-lensing, X-ray, and Sunyaev–Zel'dovich effect (SZE) data sets. We reconstruct the projected matter distribution from a joint weak-lensing analysis of two-dimensional shear and azimuthally integrated magnification constraints, the combination of which allows us to break the mass-sheet degeneracy. The resulting mass distribution reveals elongation with an axis ratio of ~0.7 in projection, aligned well with the distributions of cluster galaxies and intracluster gas. When assuming a spherical halo, our full weak-lensing analysis yields a projected halo concentration of ${c}_{200{\rm c}}^{2{\rm D}}=8.9\pm 1.1$ (${c}_{\mathrm{vir}}^{2{\rm D}}\sim 11$), consistent with and improved from earlier weak-lensing work. We find excellent consistency between independent weak and strong lensing in the region of overlap. In a parametric triaxial framework, we constrain the intrinsic structure and geometry of the matter and gas distributions, by combining weak/strong lensing and X-ray/SZE data with minimal geometric assumptions. We show that the data favor a triaxial geometry with minor–major axis ratio 0.39±0.15 and major axis closely aligned with the line of sight (22°±10°). We obtain a halo mass ${M}_{200{\rm c}}=(1.2\pm 0.2)\times {10}^{15}\;{M}_{\odot }\;{h}^{-1}$ and a halo concentration ${c}_{200{\rm c}}=8.4\pm 1.3$, which overlaps with the $\gtrsim 1\sigma $ tail of the predicted distribution. The shape of the gas is rounder than the underlying matter but quite elongated with minor–major axis ratio 0.60 ± 0.14. The gas mass fraction within 0.9 Mpc is ${10}_{-2}^{+3}\%$, a typical value for high-mass clusters. The thermal gas pressure contributes to ~60% of the equilibrium pressure, indicating a significant level of non-thermal pressure support. When compared to Planck's hydrostatic mass estimate, our lensing measurements yield a spherical mass ratio of MPlanck/MGL = 0.70 ± 0.15 and 0.58 ± 0.10 with and without corrections for lensing projection effects, respectively., The work is partially supported by the Ministry of Science and Technology of Taiwan under the grant MOST 103-2112-M-001-030-MY3. M. S. acknowledges financial contributions from contracts ASI/INAF I/023/12/0, by the PRIN MIUR 2010–2011 “The dark universe and the cosmic evolution of baryons: from current surveys to Euclid” and by the PRIN INAF 2012 “The universe in the box: multiscale simulations of cosmic structure.” M. N. acknowledges financial support from PRIN INAF 2014. J. M. D. acknowledges support of the consolider project CSD2010-00064 and AYA2012-39475-C02-01 funded by the Ministerio de Economia y Competitividad. N. O. is supported by a Grant-in-Aid from the Ministry of Education, Culture, Sports, Science, and Technology of Japan (26800097). This work was partially supported by “World Premier International Research Center Initiative (WPI Initiative)” and the Funds for the Development of Human Resources in Science and Technology under MEXT, Japan.