It appears that the optimum shape for a _hollow_ stalactite of uniform thickness d (d small wrt all other dimensions) is also exponentially tapering, except that instead of a function proportional to exp(-h/B), we have a function proportional to exp(-h/(B/2))=exp(-2h/B). Suppose the thickness of the stalactite surface is the radius of 1 iron atom = 126 picometers = 126*10-12 m. We keep a base of radius 1/sqrt(pi) = 1.834'. With this radius and this thickness, the load-bearing area of our base is 2*pi*R*d = 4.4666x10-10 m^2. If we solve for h where R(h)=the radius of an iron atom, we get 44.7 miles -- exactly 1/2 of the height for the solid stalactite case. If we still want to reach a height of 89 miles, we double the size of the base, for a radius of 2/sqrt(pi) = 3.667'. But the entire weight of the structure is still only 0.1259878322205 kgf ~= 126 gf ~= 4.5 oz. The solid structure weighs about 600,000 times as much as the hollow structure. We have only checked the vertical forces on this thin membrane, but given the extremely small amount of taper, the horizontal forces aren't going to be very large relative to the vertical forces. Notice that if we flip this structure upside down, so that tension becomes compression and vice versa, then the compressive strength of steel is a good deal less than the tensile strength of steel. Furthermore, with compressive loads, we now have to deal with Euler buckling in addition to simple compressive crush strength, so that the structure would have a somewhat different shape and could not reach as high. Finally, the structure would have to be further strengthened in order to withstand wind loads. The result would be something not much different from the Eiffel Tower in Paris.