Editing Convex hull (section)

===Finite point sets===
[[File:Convex hull.png|thumb|upright|Convex hull of points in the plane]]
{{main|Convex polytope}}
The convex hull of a finite point set <math>S \subset \R^d</math> forms a [[convex polygon]] when <math>d=2</math>, or more generally a [[convex polytope]] in <math>\R^d</math>. Each extreme point of the hull is called a [[Vertex (geometry)|vertex]], and (by the Krein–Milman theorem) every convex polytope is the convex hull of its vertices. It is the unique convex polytope whose vertices belong to <math>S</math> and that encloses all of <math>S</math>.{{sfnp|de Berg|van Kreveld|Overmars|Schwarzkopf|2008|page=3}}
For sets of points in [[general position]], the convex hull is a [[simplicial polytope]].{{sfnp|Grünbaum|2003|page=57}}

According to the [[upper bound theorem]], the number of faces of the convex hull of <math>n</math> points in <math>d</math>-dimensional Euclidean space is <math>O(n^{\lfloor d/2\rfloor})</math>.{{sfnp|de Berg|van Kreveld|Overmars|Schwarzkopf|2008|page=256}} In particular, in two and three dimensions the number of faces is at most linear in <math>n</math>.{{sfnp|de Berg|van Kreveld|Overmars|Schwarzkopf|2008|page=245}}