-dimensional polytope, one can specify its collection of facet directions and measures by a finite set of
[3] To be a valid specification of a bounded polytope, these vectors must span the full
[1] It is a theorem of Hermann Minkowski that these necessary conditions are sufficient: every finite set of vectors that spans the whole space, has no two parallel with the same sign, and sums to zero describes the facet directions and measures of a polytope.
The resulting operation on polytope shapes is called the Blaschke sum.
[2] With certain additional information (including separating the facet direction and size into a unit vector and a real number, which may be negative, providing an additional bit of information per facet) it is possible to generalize these existence and uniqueness results to certain classes of non-convex polyhedra.