Geoteron (EntityTopic, 20)
From Hi.gher. Space
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*The [[hypervolume]]s of a pentacube are given by: | *The [[hypervolume]]s of a pentacube are given by: | ||
| - | <blockquote>total edge length = | + | <blockquote>total edge length = 80''l''<br> |
| - | total surface area = | + | total surface area = 80''l''<sup>2</sup><br> |
| - | total surcell volume = | + | total surcell volume = 40''l''<sup>3</sup><br> |
| - | surteron bulk = | + | surteron bulk = 10''l''<sup>4</sup><br> |
| - | pentavolume = l<sup>5</sup></blockquote> | + | pentavolume = ''l''<sup>5</sup></blockquote> |
*The [[flunic]] [[cross-section]]s (''n'') of a pentacube are: | *The [[flunic]] [[cross-section]]s (''n'') of a pentacube are: | ||
Revision as of 18:19, 16 September 2007
Geometry
A pentacube, also known as 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 pentacube
- All points (x, y, z, w, φ) that lie on the surteron of a pentacube will satisfy the following equation:
Unknown
- The hypervolumes of a pentacube 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 pentacube are:
[!x, !y, !z, !w, !φ] ⇒ tesseract of side (l)
Net
The net of a pentacube 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 | ||
