On point sets fixing a convex body from within (Q1356596)

For a convex body \(K \subset \mathbb{R}^d\) a finite subset \(S\) is called fixing \(K\) from within if any translation \(t\neq 0\) moves at least on point of \(S\) outside \(K\). In answering a question of V. Soltan, the authors show that any finite \(S\) fixing a \(d\)-dimensional body \(K\) from within contains a subset of a most \(2d\) points with the same property.