  We study a generalized three-dimensional stadium billiard and present strong
numerical evidence that this system is completely chaotic. In this convex
billiard chaos is generated by the defocusing mechanism. The construction of
this billiard uses cylindrical components as the focusing elements and thereby
differs from the recent approach pioneered by Bunimovich and Rehacek [Commun.
Math. Phys. 189, 729 (1997)]. We investigate the stability of lower-dimensional
invariant manifolds and discuss bouncing ball modes.
