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Apr 13, 2017 at 12:57 history edited CommunityBot
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Mar 31, 2011 at 18:18 comment added Aubrey da Cunha You probably have already seen this, but for anyone else happening across this question, you probably want to look for papers about John's ellipsoids. In particular, look for papers by Keith Ball. I took a course from him a few years ago about this stuff which I don't remember as much of as I would like. However, one thing we did do was show that the simplex was, in some rigorous sense, the "least centrally symmetric" convex body, which agrees with your naive assessment.
Mar 31, 2011 at 15:16 history edited Roland Bacher CC BY-SA 2.5
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Mar 31, 2011 at 14:16 history edited Roland Bacher CC BY-SA 2.5
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Mar 31, 2011 at 14:08 history asked Roland Bacher CC BY-SA 2.5