Research any topic before you write.

Find related topics. | Discover entities. | See connections. | Build a topical map.

Polytope

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…

History & Applications

Use the mouse wheel or two fingers (on touchscreens) to zoom in and out of the map.

Research this topic

Explore the main themes, entities and connections around Polytope. Start with the topic map, then use the sections below for research and deeper semantic analysis.

Explore this topic

Start with a few of the strongest sections from the source topic. These are research directions, not a list of keywords you must use.

Topics to explore

Browse the full topic structure. Each item opens a new analysis centered on that subject.

Overview

Definitions and terminology

Elements

Important classes of polytopes

Properties

Generalisations of a polytope

Duality

History

Applications

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

Map overview Semantic statistics

Polytope

Nodes136
Edges135
Triples75
Avg. degree1.99
Density0.014706
Components1

How this topic connects Entity context

See the strongest relationship patterns around the current topic before diving into the raw triples.

Polytope

Top relations

related to Convex polytopes · 9
Polytope → An, Ax, Equivalently, Every, In, It, Polytopes, The, This
related to External links · 7
Polytope → Business Week Online, Eric, Internet, Math, MathWorld, Regular, Weisstein
is a · 6
Polytope → broad term that covers a wide class of objects, convex hull of a finite number of points and is defined by its vertices.Polytopes in lower numbers of dimensions have standard names, geometric object with flat sides, partially ordered set of elements or members, set, union of finitely many simplices
related to Definitions and terminology · 6
Polytope → Ludwig Schläfli, Many, Nowadays, The, They, Thorold Gosset
related to Elements · 6
Polytope → Authors, Coxeter, For, Some, Terminology, The
related to Abstract polytopes · 4
Polytope → An, It, The, This
related to Duality · 4
Polytope → Every, For, Schläfli, This
related to Euler characteristic · 4
Polytope → Euler, Euler's, Since, This
related to Infinite polytopes · 4
Polytope → Among, Not, Plane, Where
related to Complex polytopes · 3
Polytope → Hilbert, Regular, Structures

Important terminology Word statistics

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

polytopes dimensions convex regular polyhedra polyhedron may abstract include number higher dual facets idea also example called polygons bounded star

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Polytopeis ageometric object with flat sides0.90text
Polytopeis abroad term that covers a wide class of objects0.90text
Polytopeis aunion of finitely many simplices0.90text
Polytopeis aconvex hull of a finite number of points and is defined by its vertices.Polytopes in lower numbers of dimensions have standard names0.90text
Polytopeis aset0.90text
Polytopeis apartially ordered set of elements or members0.90text
verticesinstance ofElementsA polytope comprises elements of different dimensionality0.80text
edgesinstance ofElementsA polytope comprises elements of different dimensionality0.80text
facesinstance ofElementsA polytope comprises elements of different dimensionality0.80text
cellsinstance ofElementsA polytope comprises elements of different dimensionality0.80text
so oninstance ofElementsA polytope comprises elements of different dimensionality0.80text
Arthur Cayleyinstance ofa handful of other mathematicians0.80text

Related concept clusters Concept neighborhoods

These clusters group vocabulary that occurs around closely connected concepts in the source material.

    Connections between topic areas Semantic bridges

    Bridges can reveal useful research angles that are easy to miss in a flat list of related terms.

    Min side: 3
    For writers, content strategists, SEOs, marketers and creators — from quick topic research to advanced semantic analysis.