Cross polytope (EntityClass, 11)
From Hi.gher. Space
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| + | <[#ontology [kind class] [cats Regular Polytope Bracketope]]> | ||
A '''cross polytope''' is an n-dimensional [[polytope]] which is the dual of that dimension's [[hypercube]]. They exist non-trivially in all dimensionalities of at least three, with the two-dimensional cross polytope being a rotated [[square]]. They can be represented by the [[bracketopic string]] <a<sub>1</sub>a<sub>2</sub>...a<sub>n</sub>> or by the [[combined Coxeter-Dynkin string]] o4(o3)+x. | A '''cross polytope''' is an n-dimensional [[polytope]] which is the dual of that dimension's [[hypercube]]. They exist non-trivially in all dimensionalities of at least three, with the two-dimensional cross polytope being a rotated [[square]]. They can be represented by the [[bracketopic string]] <a<sub>1</sub>a<sub>2</sub>...a<sub>n</sub>> or by the [[combined Coxeter-Dynkin string]] o4(o3)+x. | ||
In all dimensions above 4, the cross polytope is the [[regular polytope]] with the highest [[facet]] count. | In all dimensions above 4, the cross polytope is the [[regular polytope]] with the highest [[facet]] count. | ||
| - | Under the [[ | + | Under the [[elemental naming scheme]], cross polytopes are denoted by the ''aero-'' prefix, meaning the classical element of "air". |
{{Cross polytopes| }} | {{Cross polytopes| }} | ||
Latest revision as of 14:08, 15 March 2014
A cross polytope is an n-dimensional polytope which is the dual of that dimension's hypercube. They exist non-trivially in all dimensionalities of at least three, with the two-dimensional cross polytope being a rotated square. They can be represented by the bracketopic string <a1a2...an> or by the combined Coxeter-Dynkin string o4(o3)+x.
In all dimensions above 4, the cross polytope is the regular polytope with the highest facet count.
Under the elemental naming scheme, cross polytopes are denoted by the aero- prefix, meaning the classical element of "air".
| Cross polytopes |
| diamond • octahedron • aerochoron • aeroteron • aeropeton |
