Hypercube (EntityClass, 17)
From Hi.gher. Space
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