Geopeton (EntityTopic, 20)
From Hi.gher. Space
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{{Toratope Nav A|20|21|22|(((II)I)I)I<br>Ditorinder|((((II)I)I)I)<br>Tritorus|IIIIII<br>Hexeract|(IIIIII)<br>Hexasphere|(II)IIII<br>Penterinder|((II)III)<br>Torapenterinder|peta}} | {{Toratope Nav A|20|21|22|(((II)I)I)I<br>Ditorinder|((((II)I)I)I)<br>Tritorus|IIIIII<br>Hexeract|(IIIIII)<br>Hexasphere|(II)IIII<br>Penterinder|((II)III)<br>Torapenterinder|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}} | ||
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Revision as of 19:13, 9 March 2011
The geopeton, also known as the hexeract, the hexacube and the regular dodecapeton is the six-dimensional hypercube. It is a special case of the prism where the base is a geoteron. 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 | |
| 83. 21111 Penterinder | 84. 111111 Hexeract | 85. 51 Pentaspheric cone |
| List of tapertopes | ||
| 20a. (((II)I)I)I Ditorinder | 20b. ((((II)I)I)I) Tritorus | 21a. IIIIII Hexeract | 21b. (IIIIII) Hexasphere | 22a. (II)IIII Penterinder | 22b. ((II)III) Torapenterinder |
| List of toratopes | |||||
| 193. (<xy><(zw)φ>) Unknown shape | 194. [xyzwφσ] Hexeract | 195. [<xy>zwφσ] Narrow hexeract |
| List of bracketopes | ||
