In elementary geometry, a **polytope** is a geometric object with flat sides, which exists in any general number of dimensions. A polygon is a polytope in two dimensions, a polyhedron in three dimensions, and so on in higher dimensions (such as a polychoron in four dimensions). Some theories further generalize the idea to include such things as unbounded polytopes (apeirotopes and tessellations), and abstract polytopes.

When referring to an *n*-dimensional generalization, the term ** n-polytope** is used. For example, a polygon is a 2-polytope, a polyhedron is a 3-polytope, and a polychoron is a 4-polytope.

The term was coined by the mathematician Hoppe, writing in German, and was later introduced to the English Mathematicians by Alicia Boole Stott, the daughter of logician George Boole.

Read more about Polytope: Different Approaches To Definition, Elements, History, Uses

### Other articles related to "polytope, polytopes":

... score) The Thessaloniki World Fair, 1-track (1961) Bohor, 8-track (1962) Hibiki-Hana-Ma, 12-track (

**Polytope**of Osaka, 1969–70) Persépolis, 8-track (

**Polytope**of Persepolis, 1971)

**Polytope**de Cluny, 8-tra ...

**Polytope**

... In geometry, a simplicial

**polytope**is a d-

**polytope**whose facets are all simplices ... They are topologically dual to simple

**polytopes**...

**Polytopes**which are both simple and simplicial are either simplices or two-dimensional polygons ...

**Polytope**- Uses

... functions constricted to the boundary of an n-dimensional

**polytope**... In linear programming,

**polytopes**occur in the use of Generalized barycentric coordinates and Slack variables ...

**Polytope**- 1_32

**Polytope**

132 Type Uniform 7-

**polytope**Family 1k2

**polytope**Schläfli symbol {3,33,2} Coxeter symbol 132 Coxeter-Dynkin diagram 6-faces 131. 5-faces 2016 ... {3 ...

**Polytope**

... two competing definitions for a chiral

**polytope**... One is that it is a

**polytope**that is chiral (or "enantiomorphic"), meaning that it does not have mirror symmetry ... By this definition, a

**polytope**that lacks any symmetry at all would be an example of a chiral

**polytope**...