A new molecular dynamics-like modelling approach aimed at simulating the mechanical behaviour of true polyhedra dense assemblies is presented. Thanks to an improved version of the Gilbert-Johnson-Keerthi contact detection algorithm called GJK - TD, this approach involves no edge or corner rounding and accounts for multipoint face - face or edge - face contacts between any set of two particles. Furthermore, torques equations are simply and efficiently solved using an improved leap-frog Verlet non-iterative method suggested by Omelyan [I.P. Omelyan, Molecular Simulation, 22 : 3, 213-236 (1999)], in which no periodic renormalization of the quaternions is necessary. The potential of this new discrete element approach is then highlighted by simulating the gravity packing of frictionless polyhedra and the gavity flow of frictional polyhedra down an incline, and comparing the results with those reported in the literature. Of particular interest in the stationary flow regime, a linear decrease of the bulk solid fraction and a power law decrease of the bulk coordination number with increasing inertial number are observed, thus generalizing to polyhedra these observations initially made with disks in plane shear flow by da Cruz and co-workers [F.da Cruz, S. Emam, M. Prochnow, J.N. Roux and F. Chevoir, Phys. Rev. E 72, 021309, (2005)]. Beyond this regime, in the collisional regime, the granular temperature was found to achieve its maximum a few particle diameter above the rough bottom, suggesting the localization of significant particle agitation close to the flowing bed.