Image: Wikimedia Commons

polytope

Geometric object with flat sides

EntityQ747980

Also known as polytopes

Subclass of: geometric shape

Overview

From Wikipedia, the free encyclopedia · Read full article · Text CC BY-SA 4.0

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 n as an n-dimensional polytope or n-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 (k + 1)-polytope consist of k-polytopes that may have (k − 1)-polytopes in common.

Overview

All data

46 statements · 20% with external sources · numbers in brackets are citations

Has facet polytope: polytope
Properties for this type: has facet polytope use with qualifier: quantity
has vertex figure
dual to
Bowers acronym
Schläfli symbol
base
has part(s) use with qualifier: quantity
has boundary use with qualifier: object of statement has role
Members / parts: polygon applies to part: two-dimensional space
polyhedron applies to part: three-dimensional space
4-polytope applies to part: four-dimensional space
5-polytope applies to part: five-dimensional space
Different from: union of polytopes
convex polytope
Studied by: Euclidean solid geometry
Model item: hexagon applies to use with property: instance of
icosahedron applies to use with property: instance of
tesseract applies to use with property: instance of
Disjoint with: polytope compound
Manifestation of: abstract polytope

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Source last edited November 2, 2026. AIDb refreshes this page daily.

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AIDb. (2026). polytope (Q747980). Retrieved from https://aidb.si/e/polytope-Q747980