Let Q be the cube with vertex set {(x₁,x₂,x₃)∈ℝ³:x₁,x₂,x₃∈{0,1}}. Let F be the set of all twelve lines containing the diagonals of the six faces of Q. Let S be the set of all four lines containing the main diagonals of Q. For lines ℓ₁ and ℓ₂, let d(ℓ₁,ℓ₂) denote the shortest distance between them. Then the maximum value of d(ℓ₁,ℓ₂), as ℓ₁ varies over F and ℓ₂ varies over S, is