  We discuss the statistical distribution of galaxy shapes and viewing angles
under the assumption of triaxiality by deprojecting observed Surface Brightness
(SB) profiles of 56 Brightest Cluster Galaxies coming from a recently published
large deep-photometry sample. For the first time, we address this issue by
directly measuring axis ratio profiles without limiting ourselves to a
statistical analysis of average ellipticities. We show that these objects are
strongly triaxial, with triaxiality parameters 0.39 $ \leq T \leq $ 0.72, have
on average axis ratios $< p(r) > = $ 0.84 and $< q(r) > =$ 0.68, and are more
spherical in the central regions but flatten out at large radii. Measured
shapes in the outskirts agree well with the shapes found for simulated massive
galaxies and their dark matter halos from both the IllustrisTNG and the
Magneticum simulations, possibly probing the nature of dark matter. In
contrast, both simulations fail to reproduce the observed inner regions of
BCGs, producing too flattened objects.
