Hypercube (EntityClass, 17)
From Hi.gher. Space
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+ | <[#ontology [kind class] [cats Regular Polytope Rotatope Prism]]> | ||
+ | A '''hypercube''' is an n-dimensional [[polytope]] which is the dual of that dimension's [[cross polytope]]. They exist in all dimensions. 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]] x4o(3o)*. | ||
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+ | Under the [[elemental naming scheme]], hypercubes are denoted by the ''geo-'' prefix, meaning the classical element of "earth". | ||
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== Number of hypercells in a hypercube == | == Number of hypercells in a hypercube == | ||
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Latest revision as of 14:08, 15 March 2014
A hypercube is an n-dimensional polytope which is the dual of that dimension's cross polytope. They exist in all dimensions. They can be represented by the bracketopic string [a1a2...an] or by the combined Coxeter-Dynkin string x4o(3o)*.
Under the elemental naming scheme, hypercubes are denoted by the geo- prefix, meaning the classical element of "earth".
Number of hypercells in a hypercube
Number of k-cubes in an n-cube: 2n-kn!/(k!(n-k)!)
Hypercubes |
point • digon • square • cube • geochoron • geoteron • geopeton |