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Take O, a comer of cube OBLCMANP, as origin and OA, OB, OC. the three edges through it as the axes.

Let OA = OB = OC = α, then the co-ordinates of O, A, B, C are (0, 0, 0),
(a, 0. 0), (0, a, 0). (0, 0, a) respectively ; those of P, L, M, N are (a, a, a),(0, a. a), (a, 0, a), (a, a, 0) respectively.
The four diagonals are
OP, AL, BM, CN.
Consider the diagonals AL and BM


Let   be angle between AL and BM.


                              

Similarly the angle between the other pairs of diagonals is