Triangular bipyramid (no ontology)
From Hi.gher. Space
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- | {{ | + | {{STS Shape |
+ | | dim=3 | ||
+ | | elements=6 [[triangle]]s, 9 [[digon]]s, 5 [[point]]s | ||
+ | | sym=[[Pyroprismatic symmetry|D<sub>3h</sub>]] | ||
+ | | genus=0 | ||
+ | | ssc=<G3x> | ||
+ | | ssc2=G3 v M1 | ||
+ | | extra={{STS Polytope | ||
+ | | dual=[[Triangular prism]] | ||
+ | | bowers=Tridpy}} | ||
+ | The triangular bipyramid is the tegum product of a triangle with a digon. If the faces are equilateral triangles, it is one of the 92 Johnson solids, J<sub>12</sub>. This form can be produced by joing two [[Tetrahedron|tetrahedra]] at the base. | ||
+ | |||
+ | == Equations == | ||
+ | *Variables: | ||
+ | <blockquote>''l'' ⇒ length of edges of triangular bipyramid</blockquote> | ||
+ | |||
+ | *The [[hypervolume]]s of a triangular prism are given by: | ||
+ | <blockquote>total edge length = 9''l''<br> | ||
+ | surface area = {{Over|3√3|2}} {{DotHV}}<br> | ||
+ | volume = {{Over|√2|6}} {{DotHV|3}}</blockquote> | ||
+ | |||
+ | *The [[planar]] [[cross-section]]s (''n'') of a triangular prism are: | ||
+ | <blockquote>[!x,!y] ⇒ Unknown | ||
+ | [!z] ⇒ [[triangle]]</blockquote> | ||
<[#polytope [id 33]]> | <[#polytope [id 33]]> |
Revision as of 02:58, 26 March 2017
{{STS Shape | dim=3 | elements=6 triangles, 9 digons, 5 points | sym=D3h | genus=0 | ssc=<G3x> | ssc2=G3 v M1 | extra= |- |colspan="2" style="text-align:center; background-color:#ccccff"| [ Polytope ] |- |style="text-align:left; background-color:#ddddff"| Symbol: |style="text-align:center; background-color:#eeeeff"| N/A |- |style="text-align:left; background-color:#ccccff"| Facet layout: |style="text-align:center; background-color:#ddddff"| Unknown |- |style="text-align:left; background-color:#ddddff"| Petrie order: |style="text-align:center; background-color:#eeeeff"| Unknown |- |style="text-align:left; background-color:#ccccff"| Alternation: |style="text-align:center; background-color:#ddddff"| N/A |- |style="text-align:left; background-color:#ddddff"| Dual: |style="text-align:center; background-color:#eeeeff"| Triangular prism |- |style="text-align:left; background-color:#ccccff"| Bowers acronym: |style="text-align:center; background-color:#ddddff"| Tridpy
The triangular bipyramid is the tegum product of a triangle with a digon. If the faces are equilateral triangles, it is one of the 92 Johnson solids, J12. This form can be produced by joing two tetrahedra at the base.
Equations
- Variables:
l ⇒ length of edges of triangular bipyramid
- The hypervolumes of a triangular prism are given by:
total edge length = 9l
surface area = 3√3∕2 · l2
volume = √2∕6 · l3
- The planar cross-sections (n) of a triangular prism are:
[!x,!y] ⇒ Unknown [!z] ⇒ triangle
Incidence matrix
Dual: triangular prism
# | TXID | Va | Vb | Ea | Eb | 3a | Type | Name |
---|---|---|---|---|---|---|---|---|
0 | Va | = point | ; | |||||
1 | Vb | = point | ; | |||||
2 | Ea | 1 | 1 | = digon | ; | |||
3 | Eb | 0 | 2 | = digon | ; | |||
4 | 3a | 1 | 2 | 2 | 1 | = triangle | ; | |
5 | C1a | 2 | 3 | 6 | 3 | 6 | = triangular bipyramid | ; |
Usage as facets
- 10× 1-facets of a (dual of pyrorectichoron)
- 4× 1-facets of a (dual of square biantiprismatic ring)
- 288× 1-facets of a (dual of rectified snub demitesseract)
- 20× 1-facets of a D4.3.1 dual
- 120× 1-facets of a D4.3.1 dual
- 2× 1-facets of a (dual of bilunabirotunda pseudopyramid)
- 3× 1-facets of a D4.16 dual
- 6× 1-facets of a D4.16 dual
- 60× 1-facets of a D4.3.2 dual
- 4× 1-facets of a (dual of bitrigonal diminished pyrocantichoron)
- 16× 1-facets of a (dual of 4D analog of J37)
- 8× 1-facets of a (dual of 4D analog of J37)
- 8× 1-facets of a (dual of 4D analog of J37)
- 16× 1-facets of a (dual of 4D analog of J37)
- 3× 1-facets of a (dual of triangular hebesphenorotunda pseudopyramid)
- 6× 1-facets of a (dual of triangular hebesphenorotundaeic rhombochoron)
- 24× 1-facets of a D4.7 dual