# Geoteron (EntityTopic, 20)

(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

 # TXID Type Name Va Ea 4a C1a H4.1a 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. 2111Tesserinder 36. 11111Penteract 37. 41Glone List of tapertopes

 30. ([II][II])Duocrind 31. [IIIII]Geoteron 32. Aeroteron List of bracketopes