Geopeton (EntityTopic, 20)
From Hi.gher. Space
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| - | {{Shape | + | {{STS Shape |
| image=http://fusion-global.org/share/hexeract.png<br>Graph | | image=http://fusion-global.org/share/hexeract.png<br>Graph | ||
| dim=6 | | dim=6 | ||
| elements=12, 60, 160, 240, 192, 64 | | elements=12, 60, 160, 240, 192, 64 | ||
| genus=0 | | genus=0 | ||
| - | |||
| - | |||
| ssc=[xyzwφσ] | | ssc=[xyzwφσ] | ||
| - | |||
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| - | |||
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| pv_square=1 | | pv_square=1 | ||
| + | | extra={{STS Rotope | ||
| + | | attrib=pure | ||
| + | | notation=111111 xyzwφσ | ||
| + | | bracket=[xyzwφσ] | ||
| + | | index=156 | ||
| + | }}{{STS Uniform polytope | ||
| + | | schlaefli={[[Square|4,]][[Cube|3,]][[Tesseract|3,]][[Pentacube|3,]]3} | ||
| vfigure=[[Hexateron]], edge √5 | | vfigure=[[Hexateron]], edge √5 | ||
| vlayout=((([[Square|4]][[Cube|<sup>3</sup>]])[[Tesseract|<sup>3</sup>]])[[Pentacube|<sup>3</sup>]])<sup>3</sup> | | vlayout=((([[Square|4]][[Cube|<sup>3</sup>]])[[Tesseract|<sup>3</sup>]])[[Pentacube|<sup>3</sup>]])<sup>3</sup> | ||
| dual=[[Tricositetrapeton]] | | 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]]. | A '''hexeract''', also known as a ''hexacube'' or a [[regular]] ''dodecapeton'' is a special case of the [[prism]] where the base is a [[penteract]]. | ||
Revision as of 15:06, 14 March 2008
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 | |
| 193. (<xy><(zw)φ>) Unknown shape | 194. [xyzwφσ] Hexeract | 195. [<xy>zwφσ] Narrow hexeract |
| List of bracketopes | ||
