Elongated hexagonal bipyramid
{{Short description|Polyhedron; hexagonal
prism capped with pyramids}}
{{Infobox polyhedron
|image=elongated_hexagonal_dipyramid.png
|type=Elongated bipyramid
|edges=30
|vertices=14
|symmetry={{math|D{{sub|6h}}, [6,2], (*226)}}
|vertex_config=2 of 3{{sup|6}}
12 of 3{{sup|2}}.4{{sup|2}}
|dual=Hexagonal bifrustum
|properties=convex
|net=Elongated_hexagonal_bipyramid_net.png
}}
In geometry, the elongated hexagonal bipyramid is constructed by elongating a hexagonal bipyramid (by inserting a hexagonal prism between its congruent halves).
Related polyhedra
This polyhedron is in the family of elongated bipyramids, of which the first three can be Johnson solids: J14, J15, and J16. The hexagonal form can be constructed by all regular faces but is not a Johnson solid because 6 equilateral triangles would form six co-planar faces (in a regular hexagon).
Uses
- A quartz crystal is an example of an elongated hexagonal bipyramid. Because it has 18 faces, it can be called an octadecahedron. Other chemicals also have this shape.{{cite journal | url=https://link.springer.com/article/10.1007/s12274-016-1142-6 | doi=10.1007/s12274-016-1142-6 | title=Controllable synthesis of elongated hexagonal bipyramid shaped La(OH)3 nanorods and the distribution of electric property by off-axis electron holography | date=2016 | last1=Wen | first1=Zhiwei | last2=Liang | first2=Chongyun | last3=Bi | first3=Han | last4=Li | first4=Yuesheng | last5=Che | first5=Renchao | journal=Nano Research | volume=9 | issue=9 | pages=2561–2571 }}
- The edge-first orthogonal projection of a 24-cell is an elongated hexagonal bipyramid.
- Used as the shape of Fruit Gushers candy.
- Used as a physical manifestation for assisting various branches of three-dimensional graph theory.