Triangular diprism (EntityTopic, 16)

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{{Shape|Triangular diprism|''No image''|4|7, 19, 24, 12|0|N/A|N/A|[[Line (object)|E]][[Triangle|T]][[Triangular prism|E]]E|1<sup>1</sup>11 x<sup>y</sup>zw|N/A|N/A|N/A|23|N/A|N/A|pure}}
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<[#ontology [kind topic] [cats Duoprism Tapertope]]>
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{{STS Shape
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| attrib=pure
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| name=Triangular diprism
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| dim=4
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| elements=7, 19, 24, 12
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| genus=0
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| ssc=[G3G4]
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| ssc2=++G3
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| extra={{STS Tapertope
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| order=3, 1
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| notation=111<sup>1</sup>
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| index=21
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}}{{STS Uniform polytope
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| vlayout=([[Triangle|3]][[Square|4]]<sup>2</sup>)<sup>2</sup>⋅([[Square|4]]<sup>[[Cube|3]]</sup>)<sup>2</sup>
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}}}}
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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.
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== Geometry ==
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== Equations ==
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A '''triangular diprism''' is a special case of the [[tetraprism]] where the base is a [[triangular prism]]. It is also a [[duoprism]] with parameters of 3 and 4.
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=== Equations ===
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*Variables:
*Variables:
<blockquote>''l'' ⇒ length of each line in the triangular diprism</blockquote>
<blockquote>''l'' ⇒ length of each line in the triangular diprism</blockquote>
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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>
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total surface area = a<sup>2</sup>(15+2√3)<br>
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total surface area = (15 + 2√3) {{DotHV}}<br>
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surcell volume = 2a<sup>2</sup>√3 + 3<br>
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surcell volume = (3 + 2√3) {{DotHV|3}}<br>
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bulk = a<sup>2</sup>2<sup>-1</sup>√3</blockquote>
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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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[!z,!w] ⇒ triangular prism</blockquote>
[!z,!w] ⇒ triangular prism</blockquote>
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=== Net ===
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== Net ==
The net of a triangular diprism is three [[cube]]s with four triangular prisms attached to the middle cube:
The net of a triangular diprism is three [[cube]]s with four triangular prisms attached to the middle cube:
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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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<blockquote>http://fusion-global.org/share/triangular_diprism.png</blockquote>
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<blockquote><[#embed [hash QYWAEH3Y6Y9FP6ZBBMK78HDNR8]]></blockquote>
{{Tetrashapes}}
{{Tetrashapes}}
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{{Rotope Nav|22|23|24|((III)I)<br>Toraspherinder|I'II<br>Triangular diprism|I'I'<br>Triangular prismidal pyramid|chora}}
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{{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}}

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
total edge length = 24l
total surface area = (15 + 2√3) · l2
surcell volume = (3 + 2√3) · l3
bulk = √32 · l4
[!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:

(image)


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


20. 211
Cyltrianglinder
21. 1111
Triangular diprism
22. 22
Dicone
List of tapertopes