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Let $S$ be a set of points in $\mathbf{R}^n$:

$$S=\{ (x_1,\dots,x_n) \ | \ x_i \in \mathbf{R} \ ; i=1,\dots, n \}$$

Is there a way to find the interior boundary of such set of points?

Since there is an efficient way to find the exterior boundary or the convex hull of a set of points. I would expect to have a similar way to find the "interior hull" / "interior boundary".

It seems like some kernel transformation to higher dimension, Mobious transformation or Inclusion Exclusion Principle might help here, though I am not sure how to use any of them.

Clarification: Convex Hull gives the minimal convex polytope $P$ s.t. $S \subseteq P$. I am looking for a polytope $P'$ with the maximum volume such that $O$ is in its volume and $S \cap P' = \emptyset $.

We say that a point is contained in a polytope's volume if there exists an infinitesimal ball around the point s.t. $B_\epsilon \subset P$.

If finding the polytope is hard what about finding the largest ellipsoid rather than polytope?