polytope
Sign in to save{| class="wikitable" style="margin-left:1em" align="right" |- |50px |50px |50px |50px |50px |50px |- | colspan="6" | A polyhedron is a 3-dimensional polytope |} thumb|400px|right|A polygon is a 2-dimensional polytope. Polygons can be characterised according to various criteria. Some examples are: open (excluding its boundary), bounding circuit only (ignoring its interior), closed (including both its boundary and its interior), and self-intersecting with varying densities of different regions.
Article
22 sectionsContents
- Definitions and terminology
- Elements
- Important classes of polytopes
- Convex polytopes
- Regular polytopes
- Star polytopes
- Properties
- Euler characteristic
- Internal angles
- Generalisations of a polytope
- Infinite polytopes
- Abstract polytopes
- Complex polytopes
- Duality
- Self-dual polytopes
- History
- Applications
- See also
- References
- Citations
- Bibliography
- External links
{| class="wikitable" style="margin-left:1em" align="right" |- |50px |50px |50px |50px |50px |50px |- | colspan="6" | A polyhedron is a 3-dimensional polytope |} thumb|400px|right|A polygon is a 2-dimensional polytope. Polygons can be characterised according to various criteria. Some examples are: open (excluding its boundary), bounding circuit only (ignoring its interior), closed (including both its boundary and its interior), and self-intersecting with varying densities of different regions.
In elementary geometry, a polytope is a geometric object with flat sides (faces). Polytopes are the generalization of three-dimensional polyhedra to any number of dimensions. Polytopes may exist in any general number of dimensions as an -dimensional polytope or -polytope. For example, a two-dimensional polygon is a 2-polytope and a three-dimensional polyhedron is a 3-polytope. In this context, "flat sides" means that the sides of a -polytope consist of -polytopes that may have -polytopes in common.