Geoteron (EntityTopic, 20)
From Hi.gher. Space
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{{Tapertope Nav|35|36|37|2111<br>Tesserinder|11111<br>Penteract|4<sup>1</sup><br>Glone|tera}} | {{Tapertope Nav|35|36|37|2111<br>Tesserinder|11111<br>Penteract|4<sup>1</sup><br>Glone|tera}} | ||
{{Toratope Nav A|8|9|10|((II)I)I<br>Torinder|(((II)I)I)<br>Ditorus|IIIII<br>Penteract|(IIIII)<br>Pentasphere|(II)III<br>Tesserinder|((II)III)<br>Toratesserinder|tera}} | {{Toratope Nav A|8|9|10|((II)I)I<br>Torinder|(((II)I)I)<br>Ditorus|IIIII<br>Penteract|(IIIII)<br>Pentasphere|(II)III<br>Tesserinder|((II)III)<br>Toratesserinder|tera}} | ||
| - | {{Bracketope Nav| | + | {{Bracketope Nav|30|31|32|([II][II])<br>Duocrind|[IIIII]<br>Geoteron|<nowiki><IIIII></nowiki><br>Aeroteron|tera}} |
Revision as of 17:35, 18 November 2011
The geoteron, also known as the penteract, the pentacube and the regular decateron is the five-dimensional hypercube. It is a special case of the prism where the base is a geochoron.
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.
| Hypercubes |
| point • digon • square • cube • geochoron • geoteron • geopeton |
| Notable Pentashapes | |
| Flat: | pyroteron • aeroteron • geoteron |
| Curved: | tritorus • pentasphere • glone • cylspherinder • tesserinder |
| 35. 2111 Tesserinder | 36. 11111 Penteract | 37. 41 Glone |
| List of tapertopes | ||
| 8a. ((II)I)I Torinder | 8b. (((II)I)I) Ditorus | 9a. IIIII Penteract | 9b. (IIIII) Pentasphere | 10a. (II)III Tesserinder | 10b. ((II)III) Toratesserinder |
| List of toratopes | |||||
| 30. ([II][II]) Duocrind | 31. [IIIII] Geoteron | 32. <IIIII> Aeroteron |
| List of bracketopes | ||
