VN-TST 1991 Problem 4

Let $T$ be an arbitrary tetrahedron satisfying the following conditions:

I. Each its side has length not greater than 1, II. Each of its faces is a right triangle.

Let $s(T) = S^2_{ABC} + S^2_{BCD} + S^2_{CDA} + S^2_{DAB}$ . Find the maximal possible value of $s(T)$ .