Geoteron (EntityTopic, 20)
From Hi.gher. Space
(Difference between revisions)
m |
m |
||
| Line 47: | Line 47: | ||
{{Hypercubes}} | {{Hypercubes}} | ||
{{Pentashapes}} | {{Pentashapes}} | ||
| - | {{Tapertope Nav|35|36|37|2111<br>Tesserinder|11111<br>Penteract|4<sup>1</sup><br>Glone| | + | {{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| | + | {{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|49|50|51|(<xy><zw>)<br>Doubly-narrow duocrind|[xyzwφ]<br>Penteract|[<xy>zwφ]<br>Narrow penteract|tera}} | {{Bracketope Nav|49|50|51|(<xy><zw>)<br>Doubly-narrow duocrind|[xyzwφ]<br>Penteract|[<xy>zwφ]<br>Narrow penteract|tera}} | ||
[[Category:Regular polytera]] | [[Category:Regular polytera]] | ||
Revision as of 14:17, 26 November 2009
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.
| 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 | |||||
| 49. (<xy><zw>) Doubly-narrow duocrind | 50. [xyzwφ] Penteract | 51. [<xy>zwφ] Narrow penteract |
| List of bracketopes | ||
