Geopeton (EntityTopic, 20)
From Hi.gher. Space
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*The [[hypervolume]]s of a hexacube are given by: | *The [[hypervolume]]s of a hexacube are given by: | ||
| - | <blockquote>total edge length = | + | <blockquote>total edge length = 192''l''<br> |
| - | total surface area = | + | total surface area = 240''l''<sup>2</sup><br> |
| - | total surcell volume = | + | total surcell volume = 160''l''<sup>3</sup><br> |
| - | surteron bulk = | + | surteron bulk = 60''l''<sup>4</sup><br> |
| - | surpeton pentavolume = | + | surpeton pentavolume = 12''l''<sup>5</sup><br> |
| - | hexavolume = l<sup>6</sup></blockquote> | + | hexavolume = ''l''<sup>6</sup></blockquote> |
*The [[pentaplanar]] [[cross-section]]s (''n'') of a hexacube are: | *The [[pentaplanar]] [[cross-section]]s (''n'') of a hexacube are: | ||
Revision as of 18:18, 16 September 2007
Geometry
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 | |
| ?. Unknown | ?. [xyzwφσ] Hexacube | ?. [<xy>zwφσ] Narrow hexacube |
| List of bracketopes | ||
