The $2nd-$convex hull of every optimal rectilinear drawing of $K_{n}$ is   a triangle
  A rectilinear drawing of a graph $G$ is optimal if it has the smallest number of crossings among all rectilinear drawings of $G$. In this paper it is shown that for $n\geq 8$, the second convex hull of every optimal rectilinear drawing of the complete graph $K_n$ is a triangle. 
J. Lea\~nos, M. Lomeli, M. Ram\'irez-Ib\'a\~nez, L. M.   Rivera-Mart\'inez
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