Triangular bipyramid (no ontology)
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- | | bowers=Tridpy}} | + | | 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. | 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. | ||
Revision as of 15:19, 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.
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