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Feb 9 at 0:17 history edited Joseph O'Rourke CC BY-SA 4.0
Better image link.
Feb 7 at 7:19 comment added Nandakumar R Thanks. Even this special case looks so complex. Although I am unaware of them, there ought to be other methods to make convex polyhedrons out of convex planar regions. And it might well be the case that, in most cases, to maximize the volume of the polyhedron some part off the initial polygon's area ought to be 'wasted' - unlike in perimeter halving.
Feb 6 at 22:46 history answered Joseph O'Rourke CC BY-SA 4.0