Triangular diprism (EntityTopic, 16)
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- | {{Shape|Triangular diprism| | + | <[#ontology [kind topic] [cats Duoprism Tapertope]]> |
+ | {{STS Shape | ||
+ | | attrib=pure | ||
+ | | name=Triangular diprism | ||
+ | | dim=4 | ||
+ | | elements=7, 19, 24, 12 | ||
+ | | genus=0 | ||
+ | | ssc=[G3G4] | ||
+ | | ssc2=++G3 | ||
+ | | extra={{STS Tapertope | ||
+ | | order=3, 1 | ||
+ | | notation=111<sup>1</sup> | ||
+ | | index=21 | ||
+ | }}{{STS Uniform polytope | ||
+ | | vlayout=([[Triangle|3]]⋅[[Square|4]]<sup>2</sup>)<sup>2</sup>⋅([[Square|4]]<sup>[[Cube|3]]</sup>)<sup>2</sup> | ||
+ | }}}} | ||
+ | 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: | *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> | ||
- | 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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[!z,!w] ⇒ triangular prism</blockquote> | [!z,!w] ⇒ triangular prism</blockquote> | ||
- | + | == 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: | ||
- | <blockquote> | + | <blockquote><[#embed [hash QYWAEH3Y6Y9FP6ZBBMK78HDNR8]]></blockquote> |
+ | |||
+ | <[#polytope [id 130]]> | ||
- | {{ | + | {{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}} |
Latest revision as of 19:29, 13 March 2016
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:
Incidence matrix
Dual: (dual of triangular diprism)
# | TXID | Va | Ea | Eb | 3a | 4a | 4b | C1a | C2a | Type | Name |
---|---|---|---|---|---|---|---|---|---|---|---|
0 | Va | = point | ; | ||||||||
1 | Ea | 2 | = digon | ; blue | |||||||
2 | Eb | 2 | = digon | ; black | |||||||
3 | 3a | 3 | 3 | 0 | = triangle | ; joins 2 triangular prisms | |||||
4 | 4a | 4 | 0 | 4 | = square | ; joins 2 cubes | |||||
5 | 4b | 4 | 2 | 2 | = square | ; joins triangular prism to cube | |||||
6 | C1a | 6 | 6 | 3 | 2 | 0 | 3 | = base of prism: triangular prism | ; | ||
7 | C2a | 8 | 4 | 8 | 0 | 2 | 4 | = cube | ; | ||
8 | H4.1a | 12 | 12 | 12 | 4 | 3 | 12 | 4 | 3 | = triangular diprism | ; |
Usage as facets
- prism: 6× 1-facets of a triangular triprism
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 |