Geoteron (EntityTopic, 20)
From Hi.gher. Space
(Redirected from Tapertope 36)
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 |