Geoteron (EntityTopic, 20)
From Hi.gher. Space
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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. | ||
| - | {{ | + | {{Pentashapes}} |
{{Rotope Nav|44|45|46|((II)(II))<br>Tiger|IIIII<br>Pentacube|IIII'<br>Tesseric pyramid|tera}} | {{Rotope Nav|44|45|46|((II)(II))<br>Tiger|IIIII<br>Pentacube|IIII'<br>Tesseric pyramid|tera}} | ||
{{Bracketope Nav|49|50|51|(<xy><zw>)<br>Doubly-narrow duocrind|[xyzwφ]<br>Pentacube|[<xy>zwφ]<br>Narrow pentacube|tera}} | {{Bracketope Nav|49|50|51|(<xy><zw>)<br>Doubly-narrow duocrind|[xyzwφ]<br>Pentacube|[<xy>zwφ]<br>Narrow pentacube|tera}} | ||
| + | [[Category:Regular polytera]] | ||
Revision as of 07:10, 18 August 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 | ||
