Elongated hexagonal bipyramid

In geometry, the elongated hexagonal bipyramid is constructed by elongating a hexagonal bipyramid (by inserting a hexagonal prism between its congruent halves).

Elongated hexagonal bipyramid
Type	Elongated bipyramid
Faces	12 triangles 6 squares
Edges	30
Vertices	14
Vertex configuration	2 of 36 12 of 32.42
Symmetry group	D6h, [6,2], (*226)
Dual polyhedron	Hexagonal bifrustum
Properties	convex
Net

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.^[1]
• 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.

References

1. Wen, Zhiwei; Liang, Chongyun; Bi, Han; Li, Yuesheng; Che, Renchao (2016). "Controllable synthesis of elongated hexagonal bipyramid shaped La(OH)3 nanorods and the distribution of electric property by off-axis electron holography". Nano Research. 9 (9): 2561–2571. doi:10.1007/s12274-016-1142-6.