Convex and discrete geometry Convex sets: basic notions Concept
Convex hull
Summary
The convex hull of a set of points is the smallest convex set that contains it. It is the set of all convex combinations of points of the set.
Where this leads
42 pages build on this one.
- Polyhedron
- Carathéodory's theorem
- Sendov's conjecture
- Jung's theorem
- Atiyah–Guillemin–Sternberg convexity theorem
- Minkowski–Weyl theorem
- Barycentric subdivision
- Simplicial polytope
- Triangulation of a point set
- Polytope combinatorics
- Radon's theorem
- Vertex of a polytope
- Wythoff construction
- Centerpoint theorem
- Shapley–Folkman lemma
- Simplex
- Bézier curve
- Straszewicz's theorem
- Helly's theorem
- Bipolar theorem
- Minkowski sum of polytopes
- Sperner's lemma
- Fractional Helly theorem
- H-representation and V-representation
- Convex join
- Minkowski–Carathéodory theorem
- Steinitz theorem on convex hull interiors
- Choquet theory
- Convex independence
- Tetrahedron
- Dugundji extension theorem
- Krein–Milman theorem
- Newton polytope
- Cyclic polytope
- Tverberg's theorem
- Delzant's theorem on toric manifolds
- Gale diagram
- Colorful Carathéodory theorem
- Face lattice
- Convex polytope
- Kirchberger's theorem
- Bochner's tube theorem
Further reading
- Web https://en.wikipedia.org/wiki/Convex_hull, lead section
About this page
| Tag | 0FQSDC2EQ2 |
|---|---|
| URI | m2://0FQSDC2EQ2 |
| Aliases | convex-envelope, convex-closure |
| Kind | concept |
| Writing | W1 stated |
| MSC | 52A20 |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
- edge specializes both: the more general notions and the special cases (0 of 1)
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What links here
Used by
- Polyhedron
- Carathéodory's theorem
- Sendov's conjecture
- Atiyah–Guillemin–Sternberg convexity theorem
- Minkowski–Weyl theorem
- Barycentric subdivision
- Simplicial polytope
- Triangulation of a point set
- Polytope combinatorics
- Radon's theorem
- Vertex of a polytope
- Wythoff construction
- Centerpoint theorem
- Shapley–Folkman lemma
- Simplex
- Bézier curve
- Straszewicz's theorem
- Bipolar theorem
- Minkowski sum of polytopes
- Sperner's lemma
- H-representation and V-representation
- Convex join
- Minkowski–Carathéodory theorem
- Steinitz theorem on convex hull interiors
- Convex independence
- Tetrahedron
- Dugundji extension theorem
- Krein–Milman theorem
- Newton polytope
- Cyclic polytope
- Tverberg's theorem
- Gale diagram
- Colorful Carathéodory theorem
- Face lattice
- Convex polytope
- Bochner's tube theorem