Let $Q$ be the cube with the set of vertices $\left\{ \left( x _ { 1 } , x _ { 2 } , x _ { 3 } \right) \in \mathbb { R } ^ { 3 } : x _ { 1 } , x _ { 2 } , x _ { 3 } \in \{ 0,1 \} \right\}$. Let $F$ be the set of all twelve lines containing the diagonals of the six faces of the cube $Q$. Let $S$ be the set of all four lines containing the main diagonals of the cube $Q$; for instance, the line passing through the vertices $( 0,0,0 )$ and $( 1,1,1 )$ is in $S$. For lines $\ell _ { 1 }$ and $\ell _ { 2 }$, let $d \left( \ell _ { 1 } , \ell _ { 2 } \right)$ denote the shortest distance between them. Then the maximum value of $d \left( \ell _ { 1 } , \ell _ { 2 } \right)$, as $\ell _ { 1 }$ varies over $F$ and $\ell _ { 2 }$ varies over $S$, is
(A) $\frac { 1 } { \sqrt { 6 } }$
(B) $\frac { 1 } { \sqrt { 8 } }$
(C) $\frac { 1 } { \sqrt { 3 } }$
(D) $\frac { 1 } { \sqrt { 12 } }$