Hypercube (EntityClass, 17)

(Difference between revisions)

Revision as of 22:34, 15 June 2007

		Dimension of hypercube						Formula
		0	1	2	3	4	5	Formula
http://fusion-global.org/share/dimhyc_rotated.png	0	1	2	4	8	16	32	2ⁿ
	1	0	1	4	12	32	80	n2^n-1
	2	0	0	1	6	24	80	n(n-1)2^n-22^-1
	3	0	0	0	1	8	40	n(n-1)(n-2)2^n-36^-1
	4	0	0	0	0	1	10	n(n-1)(n-2)(n-3)2^n-424^-1
	5	0	0	0	0	0	1	n/a
	Sum	1	3	9	27	81	243	3ⁿ

@@ Line 3: / Line 3: @@
 == Number of hypercells in a hypercube ==
-{|cellpadding="14" cellspacing="0" width="100%"
-|valign="top" width="50%"|
 {|style="border: 1px solid; border-color:#808080; border-collapse: collapse;" cellpadding="2" width="100%"
 |valign="top" width="20%" style="background-color:#ccccff; text-align:center;" colspan="2" rowspan="2"|
@@ Line 80: / Line 78: @@
 |valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|243
 |valign="top" width="10%" style="background-color:#ddddee; text-align:center;"|3<sup>n</sup>
-|}
-Number of k-cubes in an n-cube: 2<sup>n-k</sup>n!/(k!(n-k!))
 |}
 [[Category:Shapes]]