Measuring the intrinsic shape and orientation of dark matter ( DM ) and intracluster ( IC ) gas in galaxy clusters is crucial to constraining their formation and evolution , and for enhancing the use of clusters as more precise cosmological probes . Extending our previous works , we present for the first time results from a triaxial joint analysis of the galaxy cluster Abell 1835 , by means of X-ray , strong lensing ( SL ) and Sunyaev Zel ’ dovich ( SZ ) data . We parametrically reconstruct the full three-dimensional structure ( triaxial shape and principal axis orientation ) of both the DM and the IC gas , and the level of non-thermal pressure of the IC gas . We find that the intermediate-major and minor-major axis ratios of the DM are 0.71 \pm 0.08 and 0.59 \pm 0.05 , respectively , and the major axis of the DM halo is inclined with respect to the line of sight at 18.3 \pm 5.2 deg . We present the first observational measurement of the non-thermal pressure out to R _ { 200 } , which has been evaluated to be a few percent of the total energy budget in the internal regions , while reaching approximately 20 % in the outer volumes . We discuss the implications of our method for the viability of the CDM scenario , focusing on the concentration parameter C and the inner slope of the DM \gamma in order to test the cold dark matter ( CDM ) paradigm for structure formation : we measure \gamma = 1.01 \pm 0.06 and C = 4.32 \pm 0.44 , values which are close to the predictions of the CDM model . The combination of X-ray/SL data at high spatial resolution , capable of resolving the cluster core , with the SZ data , which are more sensitive to the cluster outer volume , allows us to characterize the level and the gradient of the gas entropy distribution and non-thermal pressure out to R _ { 200 } , breaking the degeneracy among the physical models describing the thermal history of the ICM .