Geopeton (EntityTopic, 20)
From Hi.gher. Space
(Difference between revisions)
m |
m |
||
| Line 12: | Line 12: | ||
| bracket=[xyzwφσ] | | bracket=[xyzwφσ] | ||
| index=156 | | index=156 | ||
| + | }}{{STS Bracketope | ||
| + | | index=194 | ||
}}{{STS Uniform polytope | }}{{STS Uniform polytope | ||
| schlaefli={[[Square|4,]][[Cube|3,]][[Tesseract|3,]][[Pentacube|3,]]3} | | schlaefli={[[Square|4,]][[Cube|3,]][[Tesseract|3,]][[Pentacube|3,]]3} | ||
| Line 19: | Line 21: | ||
}}}} | }}}} | ||
| - | 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]]. It is also the [[square]] of the [[cube]]. |
== Equations == | == Equations == | ||
Revision as of 22:52, 6 November 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. 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.
| 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 | ||
