The following are equivalent:

• The convex polyhedron with vertex set \(v\) is Rupert.

• The convex closure of \(v\) is a Rupert set.

Given a pose with zero offset, there exists a view pose that is equivalent to it.

If a set is point symmetric and convex, then it being Rupert implies it being purely rotationally Rupert.

Suppose \(S\) is a finite set of points in \(\operatorname{\mathbb {R}}^n\). The radius of the polyhedron \(S\) is \(r\) iff

• there is a vector \(v \in S\) with \(\| v\| = r\)

• all vectors \(v \in S\) have \(\| v\| \le r\)

Pointsymmetrization preserves radius.