Vertex of a polytope

Summary

A vertex of a convex polytope is a face of dimension zero, that is, a corner point of the polytope. Vertices are exactly the extreme points of the polytope: the points that are not inside a segment between two other points of it. A convex polytope is the convex hull of its vertices, and no smaller set of points has this hull. So the vertices form the most economical description of a polytope, the V-description.