Cyltrianglinder (EntityTopic, 11)

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{{Shape
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<[#ontology [kind topic] [cats 4D Curved Tapertope]]>
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| attrib=strange
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{{STS Shape
| name=Cyltrianglinder
| name=Cyltrianglinder
| dim=4
| dim=4
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| elements=?, ?, ?, ?
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| elements=4, 6, 3, 0
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| genus=?
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| 20=SSC
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| ssc=[(xy)G3]
| ssc=[(xy)G3]
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| rns=1<sup>1</sup>2 x<sup>y</sup>(zw)
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| ssc2=T2xG3
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| rot_i=32
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| extra={{STS Tapertope
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}}
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| order=2, 1
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| notation=21<sup>1</sup>
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| index=20
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}}}}
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The '''cyltrianglinder''' is the limiting shape of an n,3-[[duoprism]] as n approaches infinity. In other words, it is the [[Cartesian product]] of a [[circle]] and a [[triangle]]. It is bounded by three [[cylinder]]s and a curved cell formed by bending a [[triangular prism]] in 4D and joining the ends. Its faces are three circles and three curved faces formed by joining the ends of a [[rectangle]] in 3D.
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The net of a cyltrianglinder is a triangular prism surrounded by three cylinders.
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== Equations ==
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*Variables:
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<blockquote>''r'' ⇒ radius of the circular faces<br />
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''l'' ⇒ length of the edges in the triangles</blockquote>
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*The [[hypervolume]]s of a cubinder are given by:
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<blockquote>total edge length = 6π''r''<br>
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total surface area = 3π''r''(''r'' + 2''l'')<br>
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surcell volume = π''r''(3''rl'' + {{Over|√3|2}} {{DotHV}})<br>
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bulk = {{Over|√3|4}} {{DotHV|2|πr}} {{DotHV}}</blockquote>
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*The [[realmic]] [[cross-section]]s (''n'') of a cyltrianglinder are:
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<blockquote>''Unknown''</blockquote>
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== Projection ==
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The following are two possible projections of the cyltrianglinder:
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<blockquote><[#embed [hash 52ENJAZ04GKW675481DB25RSFS]]></blockquote>
{{Tetrashapes}}
{{Tetrashapes}}
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{{Rotope Nav|31|32|33|((I'I)I)<br>Triangular ditorus|I'(II)<br>Cyltrianglinder|(I'(II))<br>Cyltrianglintigroid|chora}}
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{{Tapertope Nav|19|20|21|[111]<sup>1</sup><br>Cubic pyramid|21<sup>1</sup><br>Cyltrianglinder|111<sup>1</sup><br>Triangular diprism|chora}}

Latest revision as of 23:15, 11 February 2014

The cyltrianglinder is the limiting shape of an n,3-duoprism as n approaches infinity. In other words, it is the Cartesian product of a circle and a triangle. It is bounded by three cylinders and a curved cell formed by bending a triangular prism in 4D and joining the ends. Its faces are three circles and three curved faces formed by joining the ends of a rectangle in 3D.

The net of a cyltrianglinder is a triangular prism surrounded by three cylinders.

Equations

  • Variables:
r ⇒ radius of the circular faces
l ⇒ length of the edges in the triangles
total edge length = 6πr
total surface area = 3πr(r + 2l)
surcell volume = πr(3rl + √32 · l2)
bulk = √34 · πr2 · l2
Unknown

Projection

The following are two possible projections of the cyltrianglinder:

(image)


Notable Tetrashapes
Regular: pyrochoronaerochorongeochoronxylochoronhydrochoroncosmochoron
Powertopes: triangular octagoltriatesquare octagoltriatehexagonal octagoltriateoctagonal octagoltriate
Circular: glomecubinderduocylinderspherindersphonecylindronediconeconinder
Torii: tigertorispherespheritorustorinderditorus


19. [111]1
Cubic pyramid
20. 211
Cyltrianglinder
21. 1111
Triangular diprism
List of tapertopes