  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 $\Delta p$ and $\Delta q$ $\lesssim$
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 $\chi^2$-based approaches. With our
deprojected densities, we recover the correct orbital structure and anisotropy
parameter $\beta$ with $\Delta \beta$ $\lesssim$ 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.
