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We explore the potential of our novel triaxial modeling machinery in recovering the viewing angles, the shape and the orbit distribution of galaxies by using a high-resolution $N$-body merger simulation. Our modelling technique includes several recent advancements. (i) Our new triaxial deprojection algorithm SHAPE3D is able to significantly shrink the range of possible orientations of a triaxial galaxy and therefore to constrain its shape relying only on photometric information. It also allows to probe degeneracies, i.e. to recover different deprojections at the same assumed orientation. With this method we can constrain the intrinsic shape of the $N$-body simulation, i.e. the axis ratios $p=b/a$ and $q=c/a$, with $Δp$ and $Δq$ $\lesssim$ 0.1 using only photometric information. The typical accuracy of the viewing angles reconstruction is 15-20$^\circ$. (ii) Our new triaxial Schwarzschild code SMART exploits the full kinematic information contained in the entire non-parametric line-of-sight velocity distributions (LOSVDs) along with a 5D orbital sampling in phase space. (iii) We use a new generalised information criterion AIC$_p$ to optimise the smoothing and to select the best-fit model, avoiding potential biases in purely $χ^2$-based approaches. With our deprojected densities, we recover the correct orbital structure and anisotropy parameter $β$ with $Δβ$ $\lesssim$ 0.1. These results are valid regardless of the tested orientation of the simulation and suggest that even despite the known intrinsic photometric and kinematic degeneracies the above described advanced methods make it possible to recover the shape and the orbital structure of triaxial bodies with unprecedented accuracy.