Triangular bipyramid (no ontology)

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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.
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>
== Equations ==
== Equations ==
*Variables:
*Variables:

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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