Hypercube (EntityClass, 17)
From Hi.gher. Space
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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)!) | ||
- | {{generalization-dimensions|[[Point (object)]] • [[Line (object)]] • [[Square]] • [[Cube]] • [[Tesseract]] • [[ | + | {{generalization-dimensions|[[Point (object)]] • [[Line (object)]] • [[Square]] • [[Cube]] • [[Tesseract]] • [[Penteract]] • [[Hexeract]]}} |
Revision as of 22:39, 5 November 2008
Number of hypercells in a hypercube
Dimension of hypercube | Formula | |||||||
0 | 1 | 2 | 3 | 4 | 5 | |||
http://teamikaria.com/share/?caption=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