Geoteron (EntityTopic, 20)
From Hi.gher. Space
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| - | {{Shape| | + | {{Shape |
| + | | dim=5 | ||
| + | | elements=10, 40, 80, 80, 32 | ||
| + | | genus=0 | ||
| + | | schlaefli={[[Square|4,]][[Cube|3,]][[Tesseract|3,]]3} | ||
| + | | ssc=[xyzwφ] | ||
| + | | rns=11111 xyzwφ | ||
| + | | rot_i=45 | ||
| + | | bracket=[xyzwφ] | ||
| + | | bra_i=50 | ||
| + | | attrib=pure | ||
| + | | pv_square=1 | ||
| + | | vfigure=[[Pentachoron]], edge 2 | ||
| + | | vlayout=(([[Square|4]][[Cube|<sup>3</sup>]])[[Tesseract|<sup>4</sup>]])<sup>5</sup> | ||
| + | | dual=[[Icosidodecateron]] | ||
| + | }} | ||
| + | |||
A '''pentacube''', also known as a [[regular]] ''decateron'' is a special case of the [[prism]] where the base is a [[tesseract]]. | A '''pentacube''', also known as a [[regular]] ''decateron'' is a special case of the [[prism]] where the base is a [[tesseract]]. | ||
Revision as of 21:50, 18 November 2007
A pentacube, also known as a regular decateron is a special case of the prism where the base is a tesseract.
Equations
- Variables:
l ⇒ length of the edges of the pentacube
- All points (x, y, z, w, φ) that lie on the surteron of a pentacube will satisfy the following equation:
Unknown
- The hypervolumes of a pentacube 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 pentacube are:
[!x, !y, !z, !w, !φ] ⇒ tesseract of side (l)
Net
The net of a pentacube 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] Pentacube | 51. [<xy>zwφ] Narrow pentacube |
| List of bracketopes | ||
