Covering the -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.