Geoteron (EntityTopic, 20)

(Difference between revisions)

Revision as of 14:33, 14 March 2008

A penteract, also known as a pentacube or a regular decateron is a special case of the prism where the base is a tesseract.

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)

The net of a penteract is a tesseract surrounded by eight more tesseracts, with one more tesseract added to one of these.

Notable Pentashapes
Flat:	pyroteron • aeroteron • geoteron
Curved:	tritorus • pentasphere • glone • cylspherinder • tesserinder

49. (<xy><zw>) Doubly-narrow duocrind	50. [xyzwφ] Penteract	51. [<xy>zwφ] Narrow penteract
List of bracketopes

@@ Line 1: / Line 1: @@
-{{Shape
+{{STS Shape
 | dim=5
 | elements=10, 40, 80, 80, 32
 | genus=0
-| schlaefli={[[Square|4,]][[Cube|3,]][[Tesseract|3,]]3}
-| 20=SSC
 | ssc=[xyzwφ]
-| rns=11111 xyzwφ
-| rot_i=45
-| bracket=[xyzwφ]
-| bra_i=50
-| attrib=pure
 | pv_square=1
+| extra={{STS Rotope
+| attrib=pure
+| notation=11111 xyzwφ
+| bracket=[xyzwφ]
+| index=50
+}}{{STS Bracketope
+| index=50
+}}{{STS Uniform polytope
 | vfigure=[[Pentachoron]], edge 2
 | vlayout=(([[Square|4]][[Cube|<sup>3</sup>]])[[Tesseract|<sup>4</sup>]])<sup>5</sup>
 | dual=[[Icosidodecateron]]
-}}
+}}}}
 A '''penteract''', also known as a ''pentacube'' or a [[regular]] ''decateron'' is a special case of the [[prism]] where the base is a [[tesseract]].