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/dl/53XdjTekuHgkmy3it1dwNHjoxEx6aAvGVcFtlKBiqRtTM2DK.png | 0 | 1 | 2 | 4 | 8 | 16 | 32 | 2<sup>n</sup> |
| 1 | 0 | 1 | 4 | 12 | 32 | 80 | n2<sup>n-1</sup> | |
| 2 | 0 | 0 | 1 | 6 | 24 | 80 | n(n-1)2<sup>n-2</sup>2<sup>-1</sup> | |
| 3 | 0 | 0 | 0 | 1 | 8 | 40 | n(n-1)(n-2)2<sup>n-3</sup>6<sup>-1</sup> | |
| 4 | 0 | 0 | 0 | 0 | 1 | 10 | n(n-1)(n-2)(n-3)2<sup>n-4</sup>24<sup>-1</sup> | |
| 5 | 0 | 0 | 0 | 0 | 0 | 1 | n/a | |
| Sum | 1 | 3 | 9 | 27 | 81 | 243 | 3<sup>n</sup> |
Number of k-cubes in an n-cube: 2<sup>n-k</sup>n!/(k!(n-k)!)
| Hypercubes |
| point • digon • square • cube • geochoron • geoteron • geopeton |
