Geoteron (EntityTopic, 20)
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{{Shape|Pentacube|''No image''|5|10, 40, 80, 80, 32|0|{[[Square|4,]][[Cube|3,]][[Tesseract|3,]]3}|N/A|[[Line (object)|E]][[Square|E]][[Cube|E]][[Tesseract|E]]E|11111 xyzwφ|[[Pentachoron]], edge 2|N/A|[[Icosidodecateron]]|45|[xyzwφ]|50|pure|''Unknown''|1|(([[Square|4]][[Cube|<sup>3</sup>]])[[Tesseract|<sup>4</sup>]])<sup>5</sup>}} | {{Shape|Pentacube|''No image''|5|10, 40, 80, 80, 32|0|{[[Square|4,]][[Cube|3,]][[Tesseract|3,]]3}|N/A|[[Line (object)|E]][[Square|E]][[Cube|E]][[Tesseract|E]]E|11111 xyzwφ|[[Pentachoron]], edge 2|N/A|[[Icosidodecateron]]|45|[xyzwφ]|50|pure|''Unknown''|1|(([[Square|4]][[Cube|<sup>3</sup>]])[[Tesseract|<sup>4</sup>]])<sup>5</sup>}} | ||
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A '''pentacube''', also known as a [[regular]] ''decateron'' is a special case of the [[prism]] where the base is a [[tesseract]]. | A '''pentacube''', also known as a [[regular]] ''decateron'' is a special case of the [[prism]] where the base is a [[tesseract]]. | ||
| - | + | == Equations == | |
*Variables: | *Variables: | ||
<blockquote>''l'' ⇒ length of the edges of the pentacube</blockquote> | <blockquote>''l'' ⇒ length of the edges of the pentacube</blockquote> | ||
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<blockquote>[!x, !y, !z, !w, !φ] ⇒ tesseract of side (''l'')</blockquote> | <blockquote>[!x, !y, !z, !w, !φ] ⇒ tesseract of side (''l'')</blockquote> | ||
| - | + | == Net == | |
The net of a pentacube is a tesseract surrounded by eight more tesseracts, with one more tesseract added to one of these. | The net of a pentacube is a tesseract surrounded by eight more tesseracts, with one more tesseract added to one of these. | ||
Revision as of 20:25, 22 September 2007
Template:Shape 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 | ||
