Geoteron (EntityTopic, 20)
From Hi.gher. Space
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| - | {{Shape|Pentacube|''No image''|5|10, 40, 80, 80, 32|0|{[[Square|4,]][[Cube|3,]][[Tesseract| | + | {{Shape|Pentacube|''No image''|5|10, 40, 80, 80, 32|0|{[[Square|4,]][[Cube|3,]][[Tesseract|3,]]3}|N/A|[[Line (object)|E]][[Square|E]][[Cube|E]][[Tesseract|E]]E|11111 xyzwφ|[[Pentachoron]], edge 2|N/A|[[Icosidodecateron]]|45|[xyzwφ]|50|pure}} |
== Geometry == | == Geometry == | ||
Revision as of 09:59, 17 September 2007
Geometry
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 | ||
