  We study billiards on polytopes in $\Rr^d$ with contracting reflection laws,
i.e. non-standard reflection laws that contract the reflection angle towards
the normal. We prove that billiards on generic polytopes are uniformly
hyperbolic provided there exists a positive integer $k$ such that for any $k$
consecutive collisions, the corresponding normals of the faces of the polytope
where the collisions took place generate $\Rr^d$. As an application of our main
result we prove that billiards on generic polytopes are uniformly hyperbolic if
either the contracting reflection law is sufficiently close to the specular or
the polytope is obtuse. Finally, we study in detail the billiard on a family of
$3$-dimensional simplexes.
