Hypercube (EntityClass, 17)

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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

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