The generalized diameter is the greatest distance between any two points on the boundary of a closed figure. The diameter of a subset E of a Euclidean space R^n is therefore given by diam E = sup{|x - y|:x, y element E}, where sup denotes the supremum . For a solid object or set of points in Euclidean n-space, the generalized diameter is equal to the generalized diameter of its convex hull. This means, for example, that the generalized diameter of a polygon or polyhedron can be found simply by finding the greatest distance between any two pairs of vertices (without needing to consider other boundary points).

Blaschke's theorem | Borsuk's conjecture | convex hull | diameter | geometric span | graph diameter | Jung's theorem | minimal enclosing circle | polygon diameter