Geopeton (EntityTopic, 20)
From Hi.gher. Space
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The net of a hexeract is a penteract surrounded by ten more penteracts, with one more penteract 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. | ||
| + | {{Hypercubes}} | ||
{{Hexashapes}} | {{Hexashapes}} | ||
{{Rotope Nav|155|156|157|(((II)(II))I)<br>Tigric torus|IIIIII<br>Hexeract|IIIII'<br>Penteric pyramid|peta}} | {{Rotope Nav|155|156|157|(((II)(II))I)<br>Tigric torus|IIIIII<br>Hexeract|IIIII'<br>Penteric pyramid|peta}} | ||
{{Bracketope Nav|193|194|195|(<xy><(zw)φ>)<br>''Unknown shape''|[xyzwφσ]<br>Hexeract|[<xy>zwφσ]<br>Narrow hexeract|peta}} | {{Bracketope Nav|193|194|195|(<xy><(zw)φ>)<br>''Unknown shape''|[xyzwφσ]<br>Hexeract|[<xy>zwφσ]<br>Narrow hexeract|peta}} | ||
[[Category:Regular polypeta]] | [[Category:Regular polypeta]] | ||
Revision as of 16:30, 21 November 2009
A hexeract, also known as a hexacube or a regular dodecapeton is a special case of the prism where the base is a penteract. It is also the square of the cube.
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.
| Hypercubes |
| point • digon • square • cube • geochoron • geoteron • geopeton |
| 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 | ||
