Periodic billiard trajectories in polyhedra

15 pages, 3 figures Journal: Forum geometricorum Volume 8 (2008), pages 107-120We consider the billiard map inside a polyhedron. We give a condition for the stability of the periodic trajectories. We apply this result to the case of the tetrahedron. We deduce the existence of an open set of tetrahedra which have a periodic orbit of length four (generalization of Fagnano's orbit for triangles), moreover we can study completly the orbit of points along this coding