Geopeton (EntityTopic, 20)
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{{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|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>}} | ||
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A '''hexacube''', also known as a [[regular]] ''dodecapeton'' is a special case of the [[prism]] where the base is a [[pentacube]]. | A '''hexacube''', also known as a [[regular]] ''dodecapeton'' is a special case of the [[prism]] where the base is a [[pentacube]]. | ||
| - | + | == Equations == | |
*Variables: | *Variables: | ||
<blockquote>''l'' ⇒ length of the edges of the hexacube</blockquote> | <blockquote>''l'' ⇒ length of the edges of the hexacube</blockquote> | ||
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<blockquote>[!x, !y, !z, !w, !φ, !σ] ⇒ pentacube of side (''l'')</blockquote> | <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 hexacube is a pentacube surrounded by ten more pentacubes, with one more pentacube added to one of these. | ||
Revision as of 20:28, 22 September 2007
Template:Shape A hexacube, also known as a regular dodecapeton is a special case of the prism where the base is a pentacube.
Equations
- Variables:
l ⇒ length of the edges of the hexacube
- All points (x, y, z, w, φ, σ) that lie on the surpeton of a hexacube will satisfy the following equation:
Unknown
- The hypervolumes of a hexacube 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 hexacube are:
[!x, !y, !z, !w, !φ, !σ] ⇒ pentacube of side (l)
Net
The net of a hexacube is a pentacube surrounded by ten more pentacubes, with one more pentacube added to one of these.
| Notable Hexashapes | |
| pyropeton • aeropeton • geopeton • square cubic truncatriate | |
| 193. (<xy><(zw)φ>) Unknown shape | 194. [xyzwφσ] Hexacube | 195. [<xy>zwφσ] Narrow hexacube |
| List of bracketopes | ||
