Nicolas Bedaride, Periodic billiard tranjectories in polyhedra,
Forum Geometricorum, 8 (2008) 107--120.

Abstract: We 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 completely the orbit of points along this coding.

[ps file][pdf]