Duocylinder (EntityTopic, 14)
From Hi.gher. Space
(Difference between revisions)
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| ssc=[(xy)(zw)] | | ssc=[(xy)(zw)] | ||
| ssc2=T2<sup>2</sup> | | ssc2=T2<sup>2</sup> | ||
- | | extra={{STS | + | | extra={{STS Tapertope |
- | | | + | | order=2, 0 |
- | | notation=22 | + | | notation=22 |
- | | | + | | index=14 |
- | | index= | + | }}{{STS Toratope |
+ | | holeseq=[2] | ||
+ | | notation=(II)(II) | ||
+ | | index=6a | ||
}}{{STS Bracketope | }}{{STS Bracketope | ||
| index=43 | | index=43 | ||
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{{Tetrashapes}} | {{Tetrashapes}} | ||
- | {{ | + | {{Tapertope Nav|13|14|15|31<br>Spherinder|22<br>Duocylinder|211<br>Cubinder|chora}} |
+ | {{Toratope Nav A|5|6|7|(II)II<br>Cubinder|((II)II)<br>Toracubinder|(II)(II)<br>Duocylinder|((II)(II))<br>Tiger|(III)I<br>Spherinder|((III)I)<br>Toraspherinder|chora}} | ||
{{Bracketope Nav|42|43|44|[(xy)<zw>]<br>Narrow cubinder|[(xy)(zw)]<br>Duocylinder|<[xy][zw]><br>Large hexadecachoron|chora}} | {{Bracketope Nav|42|43|44|[(xy)<zw>]<br>Narrow cubinder|[(xy)(zw)]<br>Duocylinder|<[xy][zw]><br>Large hexadecachoron|chora}} | ||
[[Category:Duoprisms]] | [[Category:Duoprisms]] |
Revision as of 20:19, 24 November 2009
A duocylinder is the Cartesian product of two circles, and is therefore the square of the circle. It is also the limit of the set of duoprisms as m and n tend to infinity.
Equations
- Variables:
a ⇒ radius of the circle in the xy plane
b ⇒ radius of the circle in the zw plane
- All points (x, y, z, w) that lie on the sole 2D face of a duocylinder will satisfy the following equations:
x2 + y2 = a2
z2 + w2 = b2
- A duocylinder has two cells which meet at the 2D face. These are given respectively by the systems of equations:
- x2 + y2 = a2; z2 + w2 ≤ b2
- x2 + y2 ≤ a2; z2 + w2 = b2
- Each of these bounding volumes are topologically equivalent to the inside of a 3D torus. The set of points (w,x,y,z) that satisfy either the first or the second set of equations constitute the surface of the duocylinder.
- The hypervolumes of a duocylinder are given by:(?)
total surface area = 4π2ab
surcell volume = 2π2ab(a + b)
bulk = π2a2b2
- The realmic cross-sections (n) of a duocylinder are cylinders of varying heights.
Projection
The perspective projection of a duocylinder is the following shape. The purple part is one cell, and the black part is the other cell.
http://teamikaria.com/share/?caption=duocylinder-04.png
In a parallel projection, both cells collapse to cylinders, one capped and one uncapped, resulting in a single cylinder being observed as the projection.
Notable Tetrashapes | |
Regular: | pyrochoron • aerochoron • geochoron • xylochoron • hydrochoron • cosmochoron |
Powertopes: | triangular octagoltriate • square octagoltriate • hexagonal octagoltriate • octagonal octagoltriate |
Circular: | glome • cubinder • duocylinder • spherinder • sphone • cylindrone • dicone • coninder |
Torii: | tiger • torisphere • spheritorus • torinder • ditorus |
13. 31 Spherinder | 14. 22 Duocylinder | 15. 211 Cubinder |
List of tapertopes |
5a. (II)II Cubinder | 5b. ((II)II) Toracubinder | 6a. (II)(II) Duocylinder | 6b. ((II)(II)) Tiger | 7a. (III)I Spherinder | 7b. ((III)I) Toraspherinder |
List of toratopes |
42. [(xy)<zw>] Narrow cubinder | 43. [(xy)(zw)] Duocylinder | 44. ExPar: unexpected closing bracket Large hexadecachoron |
List of bracketopes |