Hypercube (EntityClass, 17)
From Hi.gher. Space
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== Number of hypercells in a hypercube == | == Number of hypercells in a hypercube == | ||
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Number of k-cubes in an n-cube: 2<sup>n-k</sup>n!/(k!(n-k!)) | Number of k-cubes in an n-cube: 2<sup>n-k</sup>n!/(k!(n-k!)) | ||
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| + | {{generalization-dimensions|[[Point (object)]] • [[Line (object)]] • [[Square]] • [[Cube]] • [[Tesseract]] • [[Pentacube]]}} | ||
[[Category:Polytopes]] | [[Category:Polytopes]] | ||
Revision as of 18:25, 17 June 2007
Number of hypercells in a hypercube
| Dimension of hypercube | Formula | |||||||
| 0 | 1 | 2 | 3 | 4 | 5 | |||
| http://fusion-global.org/share/dimhyc_rotated.png | 0 | 1 | 2 | 4 | 8 | 16 | 32 | 2n |
| 1 | 0 | 1 | 4 | 12 | 32 | 80 | n2n-1 | |
| 2 | 0 | 0 | 1 | 6 | 24 | 80 | n(n-1)2n-22-1 | |
| 3 | 0 | 0 | 0 | 1 | 8 | 40 | n(n-1)(n-2)2n-36-1 | |
| 4 | 0 | 0 | 0 | 0 | 1 | 10 | n(n-1)(n-2)(n-3)2n-424-1 | |
| 5 | 0 | 0 | 0 | 0 | 0 | 1 | n/a | |
| Sum | 1 | 3 | 9 | 27 | 81 | 243 | 3n | |
Number of k-cubes in an n-cube: 2n-kn!/(k!(n-k!))
Template:Generalization-dimensions
