Hi,

(This is my first question on MathOverflow! :-)

Imagine you have a set of points $S = \{p_1, \ldots, p_n\}$ in $\mathbb{R}^d$, of which $t$ are "bad". I want to compute a "safe convex hull", which is defined by $$ \bigcap_{S' \subseteq S} \mathrm{Hull}(S') \mathrm{,}$$ where $S'$ is constructed from $S$ taking away $t$ points -- in other words, $|S'| = |S| - t$.

This convex hull is necessarily inside the convex hull of the good points only. That's the interpretation of the "safe convex hull".

For $n = 5$ and $t = 1$, in $\mathbb{R}^2$, this is the Pentagram Map; for any polytope and $t = 1$, this is the very central part of the interior of a star polytope.

Do you guys know any procedure that does that for arbitrary dimensions, and for $t > 1$? A reference would be fantastic.

Thanks! :-)