From Hi.gher. Space
A hypercube is an n-dimensional analog to a cube. Hypercubes include the point, line, square, cube and tesseract.
Equations
Number of hypercells in a hypercube
|
| Dimension of hypercube
| Formula
|
| 0
| 1
| 2
| 3
| 4
| 5
|
| http://invhost.com/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!))
|
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