Covering the k-skeleton of the 3-dimensional unit cube by six balls

We give the best covering of the unit cube by six balls. Let b(d,n,k) denote the least number r with the property that the k-skeleton of the d-dimensional unit cube can be covered by n balls of radius r. We show that b(3,6,3)=b(3,6,2)=b(3,6,1) and we give this value.