In Euclidean space, a convex set is the region such that, for every pair of points within the region, every point on the straight line segment that joins the pair of points is also within the region. For example, a solid cube is a convex set, but anything that is hollow or has a dent in it, for example, a crescent shape, is not convex. The boundary of a convex set is always a convex curve. The intersection of all convex sets containing a given subset A of Euclidean space is called the convex hull of A. It is the smallest convex set containing A.