The tetrhedron which is formed by the centers of the balls has sides of 2d. We can constuct a right triangle from the center of the top ball to the plane defined by the centers of the balls at the lowest level. This triangle has a hypotenuse of 2d and the length the horizontal side is d; thus the remaining side is d*sqrt(3). we must then add d to this value to account for the height of plane above the base level and to the top of the ball. Thus the total height is d*(1+sqrt(3)) or aprox 2.73d.
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