Triangular triprism (EntityTopic, 13)
From Hi.gher. Space
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+ | <[#ontology [kind topic] [cats 5D Tapertope Uniform Polytope]]> | ||
{{STS Shape | {{STS Shape | ||
| attrib=pure | | attrib=pure | ||
| name=Triangular triprism | | name=Triangular triprism | ||
| dim=5 | | dim=5 | ||
- | | elements=9, 33, | + | | elements=9, 33, 62, 60, 24 |
| genus=0 | | genus=0 | ||
| ssc=[G3G4x] | | ssc=[G3G4x] | ||
| ssc2=+++G3 | | ssc2=+++G3 | ||
- | | extra={{STS | + | | extra={{STS Tapertope |
- | | | + | | order=4, 1 |
- | | notation= | + | | notation=1111<sup>1</sup> |
- | | index= | + | | index=44 |
+ | }}{{STS Uniform polytope | ||
+ | }}{{STS Polytope | ||
}}}} | }}}} | ||
- | |||
A '''triangular triprism''' is a special case of the [[prism]] where the base is a [[triangular diprism]]. It is also the [[Cartesian product]] of a [[triangle]] and a [[cube]]. | A '''triangular triprism''' is a special case of the [[prism]] where the base is a [[triangular diprism]]. It is also the [[Cartesian product]] of a [[triangle]] and a [[cube]]. | ||
== Net == | == Net == | ||
The net of a triangular diprism is three [[tesseract]]s with six triangular diprisms attached to the middle tesseract. | The net of a triangular diprism is three [[tesseract]]s with six triangular diprisms attached to the middle tesseract. | ||
+ | |||
+ | <[#polytope [id 138]]> | ||
{{Pentashapes}} | {{Pentashapes}} | ||
- | {{ | + | {{Tapertope Nav|43|44|45|211<sup>1</sup><br>Cyltriandyinder|1111<sup>1</sup><br>Triangular triprism|3<sup>2</sup><br>Disphone|tera}} |
Latest revision as of 00:22, 14 March 2016
A triangular triprism is a special case of the prism where the base is a triangular diprism. It is also the Cartesian product of a triangle and a cube.
Net
The net of a triangular diprism is three tesseracts with six triangular diprisms attached to the middle tesseract.
Incidence matrix
Dual: (dual of triangular triprism)
# | TXID | Va | Ea | Eb | 3a | 4a | 4b | C1a | C2a | C2b | H4.1a | H4.2a | Type | Name |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | Va | = point | ; | |||||||||||
1 | Ea | 2 | = digon | ; blue | ||||||||||
2 | Eb | 2 | = digon | ; black | ||||||||||
3 | 3a | 3 | 3 | 0 | = triangle | ; joins 3 triangular prisms | ||||||||
4 | 4a | 4 | 0 | 4 | = square | ; joins base-cubes with 2 sweep-cubes | ||||||||
5 | 4b | 4 | 2 | 2 | = square | ; joins 1 triangular prism with 2 sweep-cubes | ||||||||
6 | C1a | 6 | 6 | 3 | 2 | 0 | 3 | = triangular prism | ; | |||||
7 | C2a | 8 | 0 | 12 | 0 | 6 | 0 | = cube | ; base | |||||
8 | C2b | 8 | 4 | 8 | 0 | 2 | 4 | = cube | ; sweep | |||||
9 | H4.1a | 16 | 8 | 24 | 0 | 12 | 12 | 0 | 2 | 6 | = geochoron | ; | ||
10 | H4.2a | 12 | 12 | 12 | 4 | 3 | 12 | 4 | 0 | 3 | = base of prism: triangular diprism | ; | ||
11 | H5.1a | 24 | 24 | 36 | 8 | 18 | 36 | 12 | 3 | 18 | 3 | 6 | = triangular triprism | ; |
Usage as facets
This polytope does not currently appear as facets in any higher-dimensional polytopes in the database.
Notable Pentashapes | |
Flat: | pyroteron • aeroteron • geoteron |
Curved: | tritorus • pentasphere • glone • cylspherinder • tesserinder |
43. 2111 Cyltriandyinder | 44. 11111 Triangular triprism | 45. 32 Disphone |
List of tapertopes |