Geoteron (EntityTopic, 20)
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== Equations == | == Equations == | ||
*Variables: | *Variables: | ||
| - | <blockquote>''l'' ⇒ length of the edges of the | + | <blockquote>''l'' ⇒ length of the edges of the penteract</blockquote> |
| - | *All points (''x'', ''y'', ''z'', ''w'', ''φ'') that lie on the [[surteron]] of a | + | *All points (''x'', ''y'', ''z'', ''w'', ''φ'') that lie on the [[surteron]] of a penteract will satisfy the following equation: |
<blockquote>''Unknown''</blockquote> | <blockquote>''Unknown''</blockquote> | ||
| - | *The [[hypervolume]]s of a | + | *The [[hypervolume]]s of a penteract are given by: |
<blockquote>total edge length = 80''l''<br> | <blockquote>total edge length = 80''l''<br> | ||
total surface area = 80''l''<sup>2</sup><br> | total surface area = 80''l''<sup>2</sup><br> | ||
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pentavolume = ''l''<sup>5</sup></blockquote> | pentavolume = ''l''<sup>5</sup></blockquote> | ||
| - | *The [[flunic]] [[cross-section]]s (''n'') of a | + | *The [[flunic]] [[cross-section]]s (''n'') of a penteract are: |
<blockquote>[!x, !y, !z, !w, !φ] ⇒ tesseract of side (''l'')</blockquote> | <blockquote>[!x, !y, !z, !w, !φ] ⇒ tesseract of side (''l'')</blockquote> | ||
== Net == | == Net == | ||
| - | The net of a | + | The net of a penteract is a tesseract surrounded by eight more tesseracts, with one more tesseract added to one of these. |
{{Pentashapes}} | {{Pentashapes}} | ||
Revision as of 21:53, 18 November 2007
A penteract, also known as a pentacube or a regular decateron is a special case of the prism where the base is a tesseract.
Equations
- Variables:
l ⇒ length of the edges of the penteract
- All points (x, y, z, w, φ) that lie on the surteron of a penteract will satisfy the following equation:
Unknown
- The hypervolumes of a penteract are given by:
total edge length = 80l
total surface area = 80l2
total surcell volume = 40l3
surteron bulk = 10l4
pentavolume = l5
- The flunic cross-sections (n) of a penteract are:
[!x, !y, !z, !w, !φ] ⇒ tesseract of side (l)
Net
The net of a penteract is a tesseract surrounded by eight more tesseracts, with one more tesseract added to one of these.
| Notable Pentashapes | |
| Flat: | pyroteron • aeroteron • geoteron |
| Curved: | tritorus • pentasphere • glone • cylspherinder • tesserinder |
| 49. (<xy><zw>) Doubly-narrow duocrind | 50. [xyzwφ] Pentacube | 51. [<xy>zwφ] Narrow pentacube |
| List of bracketopes | ||
