Covering the 3-dimensional unit cube by six rectangular boxes

Let l be the smallest positive real number for which the 3-dimensional unit cube can be covered by six rectangular boxes of diameter at most l . Joós (Studies of the University of Z̆ ilina, vol. 25, pp. 15–22, 2011 ) showed that l≤√(153128) . We prove that l=√(153128) .