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He conjectured that the minimal volume product $V(C)V(C^*)$ for these curves is attained if the curve consists of the longest diagonals of a regular $(2k+1)$-gon, with centre $0$, these diagonals taken always in the positive orientation. This conjectured minimum is of the form $k^2 + O(k)$. We investigate special cases of this conjecture. 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