Let Q be the cube with the set of vertic...

Let Q be the cube with the set of vertices `{(x_1,x_2,x_3) in RR^3:x_1x_2,x^3 in {0,1}}` .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 `l_1` and `l_2` , let `d(l_1,l_2)` denote the shortest distance between them. Then the maximum value of `d(l_1,l_2)` , as `l_1` varies over F and `l_2` varies over S , is

`1/sqrt6`

`1/sqrt8`

`1/sqrt3`

`1/sqrt12`

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