KöMaL 2006 B3927

Vertex $A$ of a tetrahedron ABCD is reflected about $B$, $B$ is reflected about $C$, $C$about $D$ and $D$ about $A$. Let the respective reflections be $A$', $B$', $C$' and $D$'. By what factor is the volume of the tetrahedron $A$'$B$'$C$'$D$' larger than that of the original tetrahedron ABCD ?