Triangular prism (EntityTopic, 20)
From Hi.gher. Space
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== Equations == | == Equations == | ||
*Variables: | *Variables: | ||
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*The [[planar]] [[cross-section]]s (''n'') of a triangular prism are: | *The [[planar]] [[cross-section]]s (''n'') of a triangular prism are: | ||
<blockquote>''Unknown''</blockquote> | <blockquote>''Unknown''</blockquote> | ||
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| + | <[#polytope [id 32]]> | ||
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{{Polyhedra}} | {{Polyhedra}} | ||
{{Tapertope Nav|9|10|11|[11]<sup>1</sup><br>Square pyramid|11<sup>1</sup><br>Triangular prism|1<sup>2</sup><br>Tetrahedron|hedra}} | {{Tapertope Nav|9|10|11|[11]<sup>1</sup><br>Square pyramid|11<sup>1</sup><br>Triangular prism|1<sup>2</sup><br>Tetrahedron|hedra}} | ||
Revision as of 22:22, 16 February 2014
Equations
- Variables:
l ⇒ length of edges of triangular prism
- The hypervolumes of a triangular prism are given by:
total edge length = 9l
surface area = (3 + √3∕2) · l2
volume = √3∕4 · l3
- The planar cross-sections (n) of a triangular prism are:
Unknown
Incidence matrix
Dual: triangular bipyramid
| # | TXID | Va | Ea | Eb | 4a | 3a | Type | Name |
|---|---|---|---|---|---|---|---|---|
| 0 | Va | = point | ; | |||||
| 1 | Ea | 2 | = digon | ; | ||||
| 2 | Eb | 2 | = digon | ; | ||||
| 3 | 4a | 4 | 2 | 2 | = square | ; | ||
| 4 | 3a | 3 | 0 | 3 | = base of prism: triangle | ; | ||
| 5 | C1a | 6 | 3 | 6 | 3 | 2 | = triangular prism | ; |
Usage as facets
- 6× 1-facets of a duotrianglinder
- 8× 1-facets of a octahedral prism
- 4× 1-facets of a tetrahedral prism
- prism: 4× 1-facets of a triangular diprism
- 18× 1-facets of a (dual of triangular octagoltriate) (named squashed prisms)
- 6× 1-facets of a triangular octagoltriate (named prisms)
- 4× 1-facets of a square pyramid prism
- 4× 1-facets of a gyrated octahedral prism (named in-out)
- 4× 1-facets of a gyrated octahedral prism (named walls)
- 8× 1-facets of a K4.13 dual
- 2× 1-facets of a K4.8
- 2× 1-facets of a bilunabirotunda pseudopyramid
- 1× 1-facets of a D4.16
- 4× 1-facets of a bitrigonal diminished pyrocantichoron
- 16× 1-facets of a (4D analog of J37)
- 8× 1-facets of a (4D analog of J37)
- 8× 1-facets of a (4D analog of J37)
- 3× 1-facets of a triangular hebesphenorotunda pseudopyramid (named square to roof)
- 6× 1-facets of a triangular hebesphenorotundaeic rhombochoron
- 6× 1-facets of a tetraaugmented triangular hebesphenorotundaeic rhombochoron (named oooogg)
- 12× 1-facets of a tetraaugmented triangular hebesphenorotundaeic rhombochoron (named square to roof)
- 6× 1-facets of a D4.7
- 12× 2-facets of a triangular triprism
| Notable Trishapes | |
| Regular: | tetrahedron • cube • octahedron • dodecahedron • icosahedron |
| Direct truncates: | tetrahedral truncate • cubic truncate • octahedral truncate • dodecahedral truncate • icosahedral truncate |
| Mesotruncates: | stauromesohedron • stauroperihedron • stauropantohedron • rhodomesohedron • rhodoperihedron • rhodopantohedron |
| Snubs: | snub staurohedron • snub rhodohedron |
| Curved: | sphere • torus • cylinder • cone • frustum • crind |
| 9. [11]1 Square pyramid | 10. 111 Triangular prism | 11. 12 Tetrahedron |
| List of tapertopes | ||
