(In reply to
solution by Lorne Hrynkiw)
You write "This triangle has a hypotenuse of 2d and the length the horizontal side is d; thus the remaining side is d*sqrt(3)." But this triangle is a (slanting) face of the tetrahedron with side length 2d, and its height is slanting, too. We need instead the vertical height of that tetrahedron, which is the slightly smaller value 2d*sqrt(2/3)=(2d/3)*sqrt(6)=1.632993162d. See, e. g.,
http://mathforum.org/library/drmath/view/55009.html

Posted by Richard
on 20040805 00:35:59 