Geopeton (EntityTopic, 20)

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Revision as of 22:43, 18 November 2007

A hexeract, also known as a hexacube or a regular dodecapeton is a special case of the prism where the base is a penteract.

Equations

Variables:

l ⇒ length of the edges of the hexeract

All points (x, y, z, w, φ, σ) that lie on the surpeton of a hexeract will satisfy the following equation:

Unknown

The hypervolumes of a hexeract are given by:

total edge length = 192l
total surface area = 240l²
total surcell volume = 160l³
surteron bulk = 60l⁴
surpeton pentavolume = 12l⁵
hexavolume = l⁶

The pentaplanar cross-sections (n) of a hexeract are:

[!x, !y, !z, !w, !φ, !σ] ⇒ pentacube of side (l)

Net

The net of a hexeract is a penteract surrounded by ten more penteracts, with one more penteract added to one of these.

Notable Hexashapes
	pyropeton • aeropeton • geopeton • square cubic truncatriate

Template:Rotope Nav

193. (<xy><(zw)φ>) Unknown shape	194. [xyzwφσ] Hexeract	195. [<xy>zwφσ] Narrow hexeract
List of bracketopes

@@ Line 1: / Line 1: @@
-{{Shape|Hexacube|''No image''|6|12, 60, 160, 240, 192, 64|0|{[[Square|4,]][[Cube|3,]][[Tesseract|3,]][[Pentacube|3,]]3}|N/A|[[Line (object)|E]][[Square|E]][[Cube|E]][[Tesseract|E]][[Pentacube|E]]E|111111 xyzwφσ|[[Hexateron]], edge √5|N/A|[[Tricositetrapeton]]|156|[xyzwφσ]|194|pure|''Unknown''|1|((([[Square|4]][[Cube|<sup>3</sup>]])[[Tesseract|<sup>3</sup>]])[[Pentacube|<sup>3</sup>]])<sup>3</sup>}}
+{{Shape
-A '''hexacube''', also known as a [[regular]] ''dodecapeton'' is a special case of the [[prism]] where the base is a [[pentacube]].
+| dim=6
+| elements=12, 60, 160, 240, 192, 64
+| genus=0
+| schlaefli={[[Square|4,]][[Cube|3,]][[Tesseract|3,]][[Pentacube|3,]]3}
+| 20=SSC
+| ssc=[xyzwφσ]
+| rns=111111 xyzwφσ
+| rot_i=156
+| bracket=[xyzwφσ]
+| bra_i=194
+| attrib=pure
+| pv_square=1
+| vfigure=[[Hexateron]], edge √5
+| vlayout=((([[Square|4]][[Cube|<sup>3</sup>]])[[Tesseract|<sup>3</sup>]])[[Pentacube|<sup>3</sup>]])<sup>3</sup>
+| dual=[[Tricositetrapeton]]
+}}
+A '''hexeract''', also known as a ''hexacube'' or a [[regular]] ''dodecapeton'' is a special case of the [[prism]] where the base is a [[penteract]].
 == Equations ==
 *Variables:
-<blockquote>''l'' ⇒ length of the edges of the hexacube</blockquote>
+<blockquote>''l'' ⇒ length of the edges of the hexeract</blockquote>
-*All points (''x'', ''y'', ''z'', ''w'', ''φ'', ''σ'') that lie on the [[surpeton]] of a hexacube will satisfy the following equation:
+*All points (''x'', ''y'', ''z'', ''w'', ''φ'', ''σ'') that lie on the [[surpeton]] of a hexeract will satisfy the following equation:
 <blockquote>''Unknown''</blockquote>
-*The [[hypervolume]]s of a hexacube are given by:
+*The [[hypervolume]]s of a hexeract are given by:
 <blockquote>total edge length = 192''l''<br>
 total surface area = 240''l''<sup>2</sup><br>
@@ Line 17: / Line 34: @@
 hexavolume = ''l''<sup>6</sup></blockquote>
-*The [[pentaplanar]] [[cross-section]]s (''n'') of a hexacube are:
+*The [[pentaplanar]] [[cross-section]]s (''n'') of a hexeract are:
 <blockquote>[!x, !y, !z, !w, !φ, !σ] ⇒ pentacube of side (''l'')</blockquote>
 == Net ==
-The net of a hexacube is a pentacube surrounded by ten more pentacubes, with one more pentacube added to one of these.
+The net of a hexeract is a penteract surrounded by ten more penteracts, with one more penteract added to one of these.
 {{Hexashapes}}
-{{Rotope Nav|155|156|157|(((II)(II))I)<br>Tigric torus|IIIIII<br>Hexacube|IIIII'<br>Pentacubic pyramid|peta}}
+{{Rotope Nav|155|156|157|(((II)(II))I)<br>Tigric torus|IIIIII<br>Hexeract|IIIII'<br>Penteractic pyramid|peta}}
-{{Bracketope Nav|193|194|195|(<xy><(zw)φ>)<br>''Unknown shape''|[xyzwφσ]<br>Hexacube|[<xy>zwφσ]<br>Narrow hexacube|peta}}
+{{Bracketope Nav|193|194|195|(<xy><(zw)φ>)<br>''Unknown shape''|[xyzwφσ]<br>Hexeract|[<xy>zwφσ]<br>Narrow hexeract|peta}}
 [[Category:Regular polypeta]]