Triangular bipyramid (no ontology)

(Difference between revisions)
 Revision as of 00:37, 26 February 2014 (view source)Hayate (Talk | contribs)m (creating otherwise empty page for incidence matrix)← Older edit Revision as of 02:58, 26 March 2017 (view source)Newer edit → Line 1: Line 1: - {{Empty}} + {{STS Shape + | dim=3 + | elements=6 [[triangle]]s, 9 [[digon]]s, 5 [[point]]s + | sym=[[Pyroprismatic symmetry|D3h]] + | genus=0 + | ssc= + | 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, J12. This form can be produced by joing two [[Tetrahedron|tetrahedra]] at the base. + + == Equations == + *Variables: +
''l'' ⇒ length of edges of triangular bipyramid
+ + *The [[hypervolume]]s of a triangular prism are given by: +
total edge length = 9''l''
+ surface area = {{Over|3√3|2}} {{DotHV}}
+ volume = {{Over|√2|6}} {{DotHV|3}}
+ + *The [[planar]] [[cross-section]]s (''n'') of a triangular prism are: +
[!x,!y] ⇒ Unknown + [!z] ⇒ [[triangle]]
<[#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
total edge length = 9l
surface area = 3√32 · l2
volume = √26 · l3
[!x,!y] ⇒ Unknown [!z] ⇒ triangle

Incidence matrix

Dual: triangular prism

 # TXID Type Name Va Vb Ea Eb 3a 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 ;