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The maximum area polygon with given side lengths is convex and inscribed in a circle. Is the analogous statement for polyhedra true?

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What is the analogous statement for polyhedra? –  Rahul Nov 16 '12 at 8:27
"The maximum-area polyhedron with given number of faces is convex and inscribed in a sphere"? I guess the issue is "given number of faces" vs. "given set of face-polygons"; also it is unclear whether the 2D case refers to some given number of equal-length sides or some arbitrary collection of side-lengths (but in the latter case it would be false, as (1,2,4) is not a polygon at all, let alone a convex one inscribed in a circle). –  Dan Brumleve Nov 16 '12 at 8:39
Do you have a proof of your first statement? –  Paul Salomon Nov 5 '13 at 14:30
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