Tesserinder (EntityTopic, 13)
From Hi.gher. Space
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{{Rotope Nav|118|119|120|(I'((II)I))<br>''Unknown shape''|(II)III<br>Tesserinder|(II)II'<br>Cubindric pyramid|tera}} | {{Rotope Nav|118|119|120|(I'((II)I))<br>''Unknown shape''|(II)III<br>Tesserinder|(II)II'<br>Cubindric pyramid|tera}} | ||
{{Bracketope Nav|51|52|53|[<xy>zwφ]<br>Narrow pentacube|[(xy)zwφ]<br>Tesserinder|[<[xy]z>wφ]<br>Wide octahedral diprism|tera}} | {{Bracketope Nav|51|52|53|[<xy>zwφ]<br>Narrow pentacube|[(xy)zwφ]<br>Tesserinder|[<[xy]z>wφ]<br>Wide octahedral diprism|tera}} | ||
Revision as of 07:10, 18 August 2007
Geometry
A tesserinder is a special case of the prism where the base is a cubinder.
Equations
- Variables:
r ⇒ radius of the tesserinder
a ⇒ height of the tesserinder along z-axis
b ⇒ tridth of the tesserinder along w-axis
c ⇒ pentalength of the tesserinder along φ-axis
- All points (x, y, z, w, φ) that lie on the surteron of a tesserinder will satisfy the following equations:
x2 + y2 = r2
abs(z) ≤ a
abs(w) ≤ b
abs(φ) ≤ c
-- or --
x2 + y2 < r2
abs(z) = a
abs(w) = b
abs(φ) = c
- The hypervolumes of a tesserinder are given by:
total edge length = Unknown
total surface area = Unknown
surcell volume = Unknown
surteron bulk = Unknown
pentavolume = πr2abc
- The flunic cross-sections (n) of a tesserinder are:
Unknown
| Notable Pentashapes | |
| Flat: | pyroteron • aeroteron • geoteron |
| Curved: | tritorus • pentasphere • glone • cylspherinder • tesserinder |
| 51. [<xy>zwφ] Narrow pentacube | 52. [(xy)zwφ] Tesserinder | 53. [<[xy]z>wφ] Wide octahedral diprism |
| List of bracketopes | ||
