Cyltrianglinder (EntityTopic, 11)
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{{STS Shape | {{STS Shape | ||
| name=Cyltrianglinder | | name=Cyltrianglinder | ||
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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. | 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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total surface area = 3π''r''(''r'' + 2''l'')<br> | total surface area = 3π''r''(''r'' + 2''l'')<br> | ||
surcell volume = π''r''(3''rl'' + {{Over|√3|2}} {{DotHV}})<br> | surcell volume = π''r''(3''rl'' + {{Over|√3|2}} {{DotHV}})<br> | ||
| - | bulk = | + | bulk = {{Over|√3|4}} {{DotHV|2|πr}} {{DotHV}}</blockquote> |
*The [[realmic]] [[cross-section]]s (''n'') of a cyltrianglinder are: | *The [[realmic]] [[cross-section]]s (''n'') of a cyltrianglinder are: | ||
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The following are two possible projections of the cyltrianglinder: | The following are two possible projections of the cyltrianglinder: | ||
| - | <blockquote><[# | + | <blockquote><[#embed [hash 52ENJAZ04GKW675481DB25RSFS]]></blockquote> |
{{Tetrashapes}} | {{Tetrashapes}} | ||
{{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}} | {{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
- The hypervolumes of a cubinder are given by:
total edge length = 6πr
total surface area = 3πr(r + 2l)
surcell volume = πr(3rl + √3∕2 · l2)
bulk = √3∕4 · πr2 · l2
- The realmic cross-sections (n) of a cyltrianglinder are:
Unknown
Projection
The following are two possible projections of the cyltrianglinder:
| 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 |
| 19. [111]1 Cubic pyramid | 20. 211 Cyltrianglinder | 21. 1111 Triangular diprism |
| List of tapertopes | ||
