Geoteron (EntityTopic, 20)
From Hi.gher. Space
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| + | <[#ontology [kind topic] [cats 5D Hypercube]]> | ||
{{STS Shape | {{STS Shape | ||
| - | | image= | + | | image=<[#embed [hash T0AB6F1XQAXC4F5VQ1QQG132B3] [width 180]]><br>[[Petrie polygon]] |
| dim=5 | | dim=5 | ||
| elements=10, 40, 80, 80, 32 | | elements=10, 40, 80, 80, 32 | ||
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| index=9a | | index=9a | ||
}}{{STS Bracketope | }}{{STS Bracketope | ||
| - | | index= | + | | index=31 |
| + | }}{{STS Polytope | ||
| + | | altern=[[Demipenteract]] | ||
| + | | dual=[[Aeroteron]] | ||
}}{{STS Uniform polytope | }}{{STS Uniform polytope | ||
| - | | vfigure=[[ | + | | vfigure=[[Pyrochoron]], edge 2 |
| vlayout=(([[Square|4]][[Cube|<sup>3</sup>]])[[Tesseract|<sup>4</sup>]])<sup>5</sup> | | vlayout=(([[Square|4]][[Cube|<sup>3</sup>]])[[Tesseract|<sup>4</sup>]])<sup>5</sup> | ||
| dual=[[Icosidodecateron]] | | dual=[[Icosidodecateron]] | ||
}}}} | }}}} | ||
| - | |||
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]]. | 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]]. | ||
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== Net == | == Net == | ||
The net of a penteract is a tesseract surrounded by eight more tesseracts, with one more tesseract added to one of these. | The net of a penteract is a tesseract surrounded by eight more tesseracts, with one more tesseract added to one of these. | ||
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| + | <[#polytope [id 90]]> | ||
{{Hypercubes|5}} | {{Hypercubes|5}} | ||
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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}} |
| - | + | ||
Latest revision as of 21:12, 14 March 2014
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.
Incidence matrix
Dual: aeroteron
| # | TXID | Va | Ea | 4a | C1a | H4.1a | Type | Name |
|---|---|---|---|---|---|---|---|---|
| 0 | Va | = point | ; | |||||
| 1 | Ea | 2 | = digon | ; | ||||
| 2 | 4a | 4 | 4 | = square | ; | |||
| 3 | C1a | 8 | 12 | 6 | = cube | ; | ||
| 4 | H4.1a | 16 | 32 | 24 | 8 | = base of prism: geochoron | ; | |
| 5 | H5.1a | 32 | 80 | 80 | 40 | 10 | = geoteron | ; |
Usage as facets
This polytope does not currently appear as facets in any higher-dimensional polytopes in the database.
| 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 | ||
