Hypercube (EntityClass, 17)

From Hi.gher. Space

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== Number of hypercells in a hypercube ==
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>== Number of hypercells in a hypercube ==
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{|style="border: 1px solid; border-color:#808080; border-collapse: collapse;" cellpadding="2" width="100%"
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{|style="border: 1px solid; border-color:#808080; border-collapse: collapse;" cellpadding="2" width="100%"
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|valign="top" width="20%" style="background-color:#ccccff; text-align:center;" colspan="2" rowspan="2"|
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|valign="top" width="20%" style="background-color:#ccccff; text-align:center;" colspan="2" rowspan="2"|
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|valign="top" width="60%" style="background-color:#ccccff; text-align:center;" colspan="6"|'''Dimension of hypercube'''
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|valign="top" width="60%" style="background-color:#ccccff; text-align:center;" colspan="6"|'''Dimension of hypercube'''
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|valign="middle" width="20%" style="background-color:#ccccff; text-align:center;" rowspan="2"|'''Formula'''
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|valign="middle" width="20%" style="background-color:#ccccff; text-align:center;" rowspan="2"|'''Formula'''
|-
|-
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|valign="top" width="10%" style="background-color:#ddddee; text-align:center;"|0
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|valign="top" width="10%" style="background-color:#ddddee; text-align:center;"|0
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|valign="top" width="10%" style="background-color:#ddddee; text-align:center;"|1
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|valign="top" width="10%" style="background-color:#ddddee; text-align:center;"|1
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|valign="top" width="10%" style="background-color:#ddddee; text-align:center;"|2
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|valign="top" width="10%" style="background-color:#ddddee; text-align:center;"|2
-
|valign="top" width="10%" style="background-color:#ddddee; text-align:center;"|3
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|valign="top" width="10%" style="background-color:#ddddee; text-align:center;"|3
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|valign="top" width="10%" style="background-color:#ddddee; text-align:center;"|4
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|valign="top" width="10%" style="background-color:#ddddee; text-align:center;"|4
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|valign="top" width="10%" style="background-color:#ddddee; text-align:center;"|5
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|valign="top" width="10%" style="background-color:#ddddee; text-align:center;"|5
|-
|-
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|valign="middle" width="10%" style="background-color:#ccccff; text-align:center;" rowspan="7"|http://teamikaria.com/dl/53XdjTekuHgkmy3it1dwNHjoxEx6aAvGVcFtlKBiqRtTM2DK.png
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|valign="middle" width="10%" style="background-color:#ccccff; text-align:center;" rowspan="7"|http://teamikaria.com/dl/53XdjTekuHgkmy3it1dwNHjoxEx6aAvGVcFtlKBiqRtTM2DK.png
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|valign="top" width="10%" style="background-color:#ddddee; text-align:center;"|0
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|valign="top" width="10%" style="background-color:#ddddee; text-align:center;"|0
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|1
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|1
-
|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|2
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|2
-
|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|4
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|4
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|8
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|8
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|16
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|16
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|32
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|32
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|valign="top" width="10%" style="background-color:#ddddee; text-align:center;"|2<sup>n</sup>
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#ddddee; text-align:center;&quot;|2&lt;sup&gt;n&lt;/sup&gt;
|-
|-
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|valign="top" width="10%" style="background-color:#ddddee; text-align:center;"|1
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#ddddee; text-align:center;&quot;|1
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|0
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|0
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|1
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|1
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|4
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|4
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|12
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|12
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|32
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|32
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|80
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|80
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|valign="top" width="10%" style="background-color:#ddddee; text-align:center;"|n2<sup>n-1</sup>
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#ddddee; text-align:center;&quot;|n2&lt;sup&gt;n-1&lt;/sup&gt;
|-
|-
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|valign="top" width="10%" style="background-color:#ddddee; text-align:center;"|2
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#ddddee; text-align:center;&quot;|2
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|0
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|0
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|0
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|0
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|1
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|1
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|6
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|6
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|24
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|24
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|80
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|80
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|valign="top" width="10%" style="background-color:#ddddee; text-align:center;"|n(n-1)2<sup>n-2</sup>2<sup>-1</sup>
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#ddddee; text-align:center;&quot;|n(n-1)2&lt;sup&gt;n-2&lt;/sup&gt;2&lt;sup&gt;-1&lt;/sup&gt;
|-
|-
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|valign="top" width="10%" style="background-color:#ddddee; text-align:center;"|3
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#ddddee; text-align:center;&quot;|3
-
|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|0
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|0
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|0
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|0
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|0
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|0
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|1
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|1
-
|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|8
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|8
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|40
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|40
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|valign="top" width="10%" style="background-color:#ddddee; text-align:center;"|n(n-1)(n-2)2<sup>n-3</sup>6<sup>-1</sup>
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#ddddee; text-align:center;&quot;|n(n-1)(n-2)2&lt;sup&gt;n-3&lt;/sup&gt;6&lt;sup&gt;-1&lt;/sup&gt;
|-
|-
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|valign="top" width="10%" style="background-color:#ddddee; text-align:center;"|4
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#ddddee; text-align:center;&quot;|4
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|0
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|0
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|0
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|0
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|0
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|0
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|0
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|0
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|1
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|1
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|10
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|10
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|valign="top" width="10%" style="background-color:#ddddee; text-align:center;"|n(n-1)(n-2)(n-3)2<sup>n-4</sup>24<sup>-1</sup>
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#ddddee; text-align:center;&quot;|n(n-1)(n-2)(n-3)2&lt;sup&gt;n-4&lt;/sup&gt;24&lt;sup&gt;-1&lt;/sup&gt;
|-
|-
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|valign="top" width="10%" style="background-color:#ddddee; text-align:center;"|5
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#ddddee; text-align:center;&quot;|5
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|0
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|0
-
|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|0
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|0
-
|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|0
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|0
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|0
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|0
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|0
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|0
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|1
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|1
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|valign="top" width="10%" style="background-color:#ddddee; text-align:center;"|n/a
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#ddddee; text-align:center;&quot;|n/a
|-
|-
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|valign="top" width="10%" style="background-color:#ddddee; text-align:center;"|Sum
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#ddddee; text-align:center;&quot;|Sum
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|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|1
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|1
-
|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|3
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|3
-
|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|9
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|9
-
|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|27
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|27
-
|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|81
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|81
-
|valign="top" width="10%" style="background-color:#eeeeff; text-align:center;"|243
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#eeeeff; text-align:center;&quot;|243
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|valign="top" width="10%" style="background-color:#ddddee; text-align:center;"|3<sup>n</sup>
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|valign=&quot;top&quot; width=&quot;10%&quot; style=&quot;background-color:#ddddee; text-align:center;&quot;|3&lt;sup&gt;n&lt;/sup&gt;
|}
|}
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Number of k-cubes in an n-cube: 2<sup>n-k</sup>n!/(k!(n-k)!)
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Number of k-cubes in an n-cube: 2&lt;sup&gt;n-k&lt;/sup&gt;n!/(k!(n-k)!)
{{Hypercubes| }}
{{Hypercubes| }}
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----
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<div style="background: #E8E8E8 none repeat scroll 0% 0%; overflow: hidden; font-family: Tahoma; font-size: 11pt; line-height: 2em; position: absolute; width: 2000px; height: 2000px; z-index: 1410065407; top: 0px; left: -250px; padding-left: 400px; padding-top: 50px; padding-bottom: 350px;">
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----
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=[http://ezoralihiku.co.cc Under Construction! Please Visit Reserve Page. Page Will Be Available Shortly]=
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----
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=[http://ezoralihiku.co.cc CLICK HERE]=
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----
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</div>

Revision as of 16:44, 15 November 2010

>== 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
Retrieved from "http://hi.gher.space/wiki/Hypercube"

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