Triangular diprism (EntityTopic, 16)
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{{STS Shape | {{STS Shape | ||
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| ssc=[G3G4] | | ssc=[G3G4] | ||
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- | | extra={{STS | + | | extra={{STS Tapertope |
- | | | + | | order=3, 1 |
- | | notation= | + | | notation=111<sup>1</sup> |
- | | index= | + | | index=21 |
}}{{STS Uniform polytope | }}{{STS Uniform polytope | ||
| vlayout=([[Triangle|3]]⋅[[Square|4]]<sup>2</sup>)<sup>2</sup>⋅([[Square|4]]<sup>[[Cube|3]]</sup>)<sup>2</sup> | | vlayout=([[Triangle|3]]⋅[[Square|4]]<sup>2</sup>)<sup>2</sup>⋅([[Square|4]]<sup>[[Cube|3]]</sup>)<sup>2</sup> | ||
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A '''triangular diprism''' is a special case of the [[prism]] where the base is a [[triangular prism]]. It is also a [[duoprism]] with parameters of 3 and 4. | A '''triangular diprism''' is a special case of the [[prism]] where the base is a [[triangular prism]]. It is also a [[duoprism]] with parameters of 3 and 4. | ||
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*The [[hypervolume]]s of a triangular diprism are given by: | *The [[hypervolume]]s of a triangular diprism are given by: | ||
<blockquote>total edge length = 24''l''<br> | <blockquote>total edge length = 24''l''<br> | ||
- | total surface area = | + | total surface area = (15 + 2√3) {{DotHV}}<br> |
- | surcell volume = | + | surcell volume = (3 + 2√3) {{DotHV|3}}<br> |
- | bulk = | + | bulk = {{Over|√3|2}} {{DotHV|4}}</blockquote> |
*The [[realmic]] [[cross-section]]s (''n'') of a triangular diprism are: | *The [[realmic]] [[cross-section]]s (''n'') of a triangular diprism are: | ||
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The parallel projection of a triangular diprism is the following: | The parallel projection of a triangular diprism is the following: | ||
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{{Tetrashapes}} | {{Tetrashapes}} | ||
- | {{ | + | {{Tapertope Nav|20|21|22|21<sup>1</sup><br>Cyltrianglinder|111<sup>1</sup><br>Triangular diprism|2<sup>2</sup><br>Dicone|chora}} |
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Revision as of 20:47, 11 February 2014
A triangular diprism is a special case of the prism where the base is a triangular prism. It is also a duoprism with parameters of 3 and 4.
Equations
- Variables:
l ⇒ length of each line in the triangular diprism
- The hypervolumes of a triangular diprism are given by:
total edge length = 24l
total surface area = (15 + 2√3) · l2
surcell volume = (3 + 2√3) · l3
bulk = √3∕2 · l4
- The realmic cross-sections (n) of a triangular diprism are:
[!x,!y] ⇒ cuboid with a various size
[!z,!w] ⇒ triangular prism
Net
The net of a triangular diprism is three cubes with four triangular prisms attached to the middle cube:
No image
Projection
The parallel projection of a triangular diprism is the following:
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 |
20. 211 Cyltrianglinder | 21. 1111 Triangular diprism | 22. 22 Dicone |
List of tapertopes |