Geoteron (EntityTopic, 20)

From Higher Dimensions Database

(Redirected from Toratope 9a)

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
total edge length = 80l
total surface area = 80l2
total surcell volume = 40l3
surteron bulk = 10l4
pentavolume = l5
[!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

#TXIDVaEa4aC1aH4.1aTypeName
0 Va = point ;
1 Ea 2 = digon ;
2 4a 44 = square ;
3 C1a 8126 = cube ;
4 H4.1a 1632248 = base of prism: geochoron ;
5 H5.1a 3280804010 = geoteron ;

Usage as facets

This polytope does not currently appear as facets in any higher-dimensional polytopes in the database.


Hypercubes
pointdigonsquarecubegeochorongeoterongeopeton


Notable Pentashapes
Flat: pyroteronaeroterongeoteron
Curved: tritoruspentasphereglonecylspherindertesserinder


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