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- Cross-polytope abstract "In geometry, a cross-polytope, orthoplex, hyperoctahedron, or cocube is a regular, convex polytope that exists in any number of dimensions. The vertices of a cross-polytope are all the permutations of (±1, 0, 0, …, 0). The cross-polytope is the convex hull of its vertices. Its facets are simplexes of the previous dimension, while the cross-polytope's vertex figure is another cross-polytope from the previous dimension.The n-dimensional cross-polytope can also be defined as the closed unit ball (or, according to some authors, its boundary) in the ℓ1-norm on Rn:In 1 dimension the cross-polytope is simply the line segment [−1, +1], in 2 dimensions it is a square (or diamond) with vertices {(±1, 0), (0, ±1)}. In 3 dimensions it is an octahedron—one of the five convex regular polyhedra known as the Platonic solids. Higher-dimensional cross-polytopes are generalizations of these.The cross-polytope is the dual polytope of the hypercube. The 1-skeleton of a n-dimensional cross-polytope is a Turán graph T(2n,n).".
- Cross-polytope thumbnail 2-orthoplex.svg?width=300.
- Cross-polytope wikiPageExternalLink TesseractApplet.html.
- Cross-polytope wikiPageID "716401".
- Cross-polytope wikiPageRevisionID "572602945".
- Cross-polytope anchor "Cross".
- Cross-polytope bot "AnomieBOT".
- Cross-polytope date "November 2010".
- Cross-polytope hasPhotoCollection Cross-polytope.
- Cross-polytope title "Cross polytope".
- Cross-polytope urlname "CrossPolytope".
- Cross-polytope subject Category:Four-dimensional_geometry.
- Cross-polytope subject Category:Multi-dimensional_geometry.
- Cross-polytope subject Category:Polytopes.
- Cross-polytope comment "In geometry, a cross-polytope, orthoplex, hyperoctahedron, or cocube is a regular, convex polytope that exists in any number of dimensions. The vertices of a cross-polytope are all the permutations of (±1, 0, 0, …, 0). The cross-polytope is the convex hull of its vertices.".
- Cross-polytope label "Cross-polytope".
- Cross-polytope label "Hyperoctaèdre".
- Cross-polytope label "Kreuzpolytop".
- Cross-polytope label "Politopo de cruce".
- Cross-polytope label "正軸体".
- Cross-polytope label "正轴形".
- Cross-polytope sameAs Kreuzpolytop.
- Cross-polytope sameAs Υπεροκτάεδρο.
- Cross-polytope sameAs Politopo_de_cruce.
- Cross-polytope sameAs Hyperoctaèdre.
- Cross-polytope sameAs 正軸体.
- Cross-polytope sameAs 십자_폴리토프.
- Cross-polytope sameAs m.0359j6.
- Cross-polytope sameAs Q1187914.
- Cross-polytope sameAs Q1187914.
- Cross-polytope wasDerivedFrom Cross-polytope?oldid=572602945.
- Cross-polytope depiction 2-orthoplex.svg.
- Cross-polytope isPrimaryTopicOf Cross-polytope.