Triangular bipyramid (no ontology)

From Hi.gher. Space

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{{Empty}}
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{{STS Shape
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| dim=3
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| elements=6 [[triangle]]s, 9 [[digon]]s, 5 [[point]]s
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| sym=[[Pyroprismatic symmetry|D<sub>3h</sub>]]
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| genus=0
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| ssc=<G3x>
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| ssc2=G3 v M1
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| extra={{STS Polytope
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| dual=[[Triangular prism]]
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| bowers=Tridpy}}}}
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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.
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==Coordinates==
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The coordinates of a triangular bipyramid with side 2 are:
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<blockquote>(±1, -√3/3, 0)<br>(0, 2√3/3, 0)<br>(0, 0, ±2√6/3)</blockquote>
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== Equations ==
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*Variables:
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<blockquote>''l'' ⇒ length of edges of triangular bipyramid</blockquote>
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*The [[hypervolume]]s of a triangular prism are given by:
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<blockquote>total edge length = 9''l''<br>
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surface area = {{Over|3√3|2}} {{DotHV}}<br>
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volume = {{Over|√2|6}} {{DotHV|3}}</blockquote>
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*The [[planar]] [[cross-section]]s (''n'') of a triangular prism are:
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<blockquote>[!x,!y] ⇒ Unknown
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[!z] ⇒ [[triangle]]</blockquote>
<[#polytope [id 33]]>
<[#polytope [id 33]]>

Latest revision as of 15:22, 26 March 2017

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.

Coordinates

The coordinates of a triangular bipyramid with side 2 are:

(±1, -√3/3, 0)
(0, 2√3/3, 0)
(0, 0, ±2√6/3)

Equations

  • Variables:
l ⇒ length of edges of triangular bipyramid
total edge length = 9l
surface area = 3√3∕2 · l2
volume = √2∕6 · l3
[!x,!y] ⇒ Unknown [!z] ⇒ triangle

Incidence matrix

Dual: triangular prism

#TXIDVaVbEaEb3aTypeName
0 Va = point ;
1 Vb = point ;
2 Ea 11 = digon ;
3 Eb 02 = digon ;
4 3a 1221 = triangle ;
5 C1a 23636 = triangular bipyramid ;

Usage as facets

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