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 \mathrel { \lower 2.58 pt \hbox { $ \buildrel \textstyle < \over { \scriptstyle \sim } $ } } 1 ~ { } Mpc .
Our analysis favours a mildly triaxial cluster with a minor to major axis ratio of 0.70 \pm 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 .