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 Sep 24 awarded Autobiographer Oct 12 comment Compute generalized pentagram map Does anyone know a reference (a book, or paper) where I can reference to this? Oct 5 comment Compute generalized pentagram map @Anton Petrunin: The problem is when the points are all in a single line segment, say. See the comment before yours. In that case, it is unclear how to chose a hyperplane (which should be across $d$ instead of $d+1$ processors, right?) - thanks! :) Oct 4 comment Compute generalized pentagram map @Michael Biro: Let me be more clear. Suppose all the $n$ points are in a single line in $\mathbb{R}^3$. Now, every 3 points I pick will be in a single line as well. So, the procedure would not detect that I could just remove the extremal $t$ points at both ends of the line to find the safe convex hull. It seems that I need to perform likewise in every smaller dimension before doing so in dimension $d$, but I'm not sure. Since the problem seems elementary, I suppose I could find a reference somewhere (in a paper or even in a book). Oct 4 comment Compute generalized pentagram map @Gerhard Paseman: I can show, using the Helly's Theorem, that if $n > t(d+1)$ this safe convex hull will always exist. (thanks too!) Oct 4 comment Compute generalized pentagram map @Michael Biro: Yes, $d$ is fixed. The problem is that you can pick $d$ points that are not affine; in this case, how to divide the entire space? (thanks!) Oct 4 awarded Student Oct 4 asked Compute generalized pentagram map