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Hyperrectangle

In geometry, a hyperrectangle (also called a box, hyperbox, k {\displaystyle k} -cell or orthotope), is the generalization of a rectangle (a plane figure) and the rectangular cuboid (a solid figure) to higher dimensions. A necessary and sufficient condition is that it is congruent to the Cartesian product of finite intervals. This means that a k…

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Coxeter diagram
···
Dual polyhedron
Rectangular n-fusil
Edges
n × 2n−1
Faces
2n
Properties
convex, zonohedron, isogonal
Schläfli symbol
{}×{}×···×{} = {}n

Topics to explore

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Overview

Formal definition

Intuition

Types

Dual polytope

Advanced semantic analysis

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Map overview Semantic statistics

Hyperrectangle

Nodes33
Edges32
Triples10
Avg. degree1.94
Density0.060606
Components1

How this topic connects Entity context

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Hyperrectangle

Top relations

Coxeter diagram · 1
Hyperrectangle → ···
Dual polyhedron · 1
Hyperrectangle → Rectangular n-fusil
Edges · 1
Hyperrectangle → n × 2n−1
Faces · 1
Hyperrectangle → 2n
Properties · 1
Hyperrectangle → convex, zonohedron, isogonal
Schläfli symbol · 1
Hyperrectangle → {}×{}×···×{} = {}n
Symmetry group · 1
Hyperrectangle → [2n−1], order 2n
Type · 1
Hyperrectangle → Prism
Vertices · 1
Hyperrectangle → 2n
is a · 1
Hyperrectangle → special case of a parallelotope

Important terminology Word statistics

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Important terminology

displaystyle rectangular edges -cell intervals orthotope equal cuboid solid rectangle dual cartesian length also definition hypercube real called plane product

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
HyperrectangleCoxeter diagram···1.00infobox
HyperrectangleDual polyhedronRectangular n-fusil1.00infobox
HyperrectangleEdgesn × 2n−11.00infobox
HyperrectangleFaces2n1.00infobox
HyperrectanglePropertiesconvex, zonohedron, isogonal1.00infobox
HyperrectangleSchläfli symbol{}×{}×···×{} = {}n1.00infobox
HyperrectangleSymmetry group[2n−1], order 2n1.00infobox
HyperrectangleTypePrism1.00infobox
HyperrectangleVertices2n1.00infobox
Hyperrectangleis aspecial case of a parallelotope0.90text

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