## parallelepiped

Let $ABCD.A'B'C'D'$ be a parallelepiped and let $S_1,S_2,S_3$ denote the areas of the sides $ABCD,ABB'A',ADD'A'$,respectively.Given that the sum of squares of areas of all sides of tetrahedron $AB'CD'$ equals $3$,find the smallest possible value of
$T = 2(\frac {1}{S_1} + \frac {1}{S_2} + \frac {1}{S_3}) + 3(S_1 + S_2 + S_3)$