Magic Angle Spinning. The angle at which if one rotated a cube that every 120o rotation the ordinated bases, maps to maps to maps to etc... Consider a cube, draw a line from [0,0,0] to [1,1,1] the diametrically opposite vertex to the origin, the angle that line makes with each axis is 54o 44' . Alternatively, consider the solution to 3 cos2 theta - 1 = 0.