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Cross-polytope

In geometry, a cross-polytope, hyperoctahedron, orthoplex, staurotope, or cocube is a regular, convex polytope that exists in n-dimensional Euclidean space. A 2-dimensional cross-polytope is a square, a 3-dimensional cross-polytope is a regular octahedron, and a 4-dimensional cross-polytope is a 16-cell. Its facets are simplexes of the previous…

Measurement, N dimensions & Low-dimensional examples

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Overview

Low-dimensional examples

N dimensions

Generalized orthoplex

Related polytope families

Advanced semantic analysis

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Map overview Semantic statistics

Cross-polytope

Nodes56
Edges55
Triples14
Avg. degree1.96
Density0.035714
Components1

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Cross-polytope

Top relations

is a · 6
Cross-polytope → convex hull of its vertices, dual polytope of the hypercube, line segment, regular octahedron, square, Turán graph T
related to n dimensions · 3
Cross-polytope → Coxeter, The, The Schläfli
related to Low-dimensional examples · 2
Cross-polytope → If, In
related to Related polytope families · 2
Cross-polytope → Cross-polytopes, In
see also · 1
Cross-polytope → List

Important terminology Word statistics

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Important terminology

regular vertices n-dimensional polytope convex also 16-cell facets polytopes three square hypercube dimensions generalized octahedron polygon 4-dimensional dimension chosen defined

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Cross-polytopeis asquare0.90text
Cross-polytopeis aconvex hull of its vertices0.90text
Cross-polytopeis adual polytope of the hypercube0.90text
Cross-polytopeis aTurán graph T0.90text
Cross-polytopeis aline segment0.90text
Cross-polytopeis aregular octahedron0.90text
Cross-polytoperelated to Low-dimensional examplesIn0.60section
Cross-polytoperelated to Low-dimensional examplesIf0.60section
Cross-polytoperelated to n dimensionsThe0.60section
Cross-polytoperelated to n dimensionsCoxeter0.60section
Cross-polytoperelated to n dimensionsThe Schläfli0.60section
Cross-polytoperelated to Related polytope familiesCross-polytopes0.60section

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    Min side: 3
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