  Knowledge of intrinsic shape and orientation of galaxy clusters is crucial to
understand their formation and evolution. We propose a novel model which uses
Bayesian inference to determine the intrinsic form of the hot intracluster
medium of galaxy clusters. The method exploits X-ray spectroscopic and
photometric data plus measurements of the Sunyaev-Zel'dovich effect (SZe). The
gas distribution is modelled with an ellipsoidal parametric profile who can fit
observed X-ray surface-brightness and temperature. Comparison with the SZ
amplitude fixes the elongation along the line of sight. Finally, Bayesian
inference allows us to deproject the measured elongation and the projected
ellipticity and constrain the intrinsic shape and orientation of the cluster.
We apply the method to the rich cluster Abell 1689, which was targeted by the
Chandra and XMM satellites as well as by several SZe observatories.
Observations cover in detail a region <~ 1 Mpc. Our analysis favours a mildly
triaxial cluster with a minor to major axis ratio of 0.70+-0.15, preferentially
elongated along the line of sight, as expected for massive lensing clusters.
The triaxial structure together with the orientation bias can reconcile X-ray
with lensing analyses and supports the view of A1689 as a just slightly
over-concentrated massive cluster not so far from hydrostatic equilibrium.
