HMMT 2006 E9

Take a unit sphere $S$, i.e., a sphere with radius 1 . Circumscribe a cube $C$ about $S$, and inscribe a cube $D$ in $S$, so that every edge of cube $C$ is parallel to some edge of cube $D$. What is the shortest possible distance from a point on a face of $C$ to a point on a face of $D$ ?