In geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

, the elongated hexagonal bipyramid is constructed by elongating a hexagonal bipyramid

Hexagonal bipyramid

A hexagonal bipyramid is a polyhedron formed from two hexagonal pyramids joined at their bases. The resulting solid has 12 triangular faces, 8 vertices and 18 edges. The 12 faces are identical isosceles triangles.It is one of an infinite set of bipyramids...

 (by inserting a hexagonal prism

Hexagonal prism

In geometry, the hexagonal prism is a prism with hexagonal base. The shape has 8 faces, 18 edges, and 12 vertices.Since it has eight faces, it is an octahedron. However, the term octahedron is primarily used to refer to the regular octahedron, which has eight triangular faces...

 between its congruent halves).

Related polyhedra

This polyhedron is in the family of elongated bipyramids, of which the first three can be Johnson solid

Johnson solid

In geometry, a Johnson solid is a strictly convex polyhedron, each face of which is a regular polygon, but which is not uniform, i.e., not a Platonic solid, Archimedean solid, prism or antiprism. There is no requirement that each face must be the same polygon, or that the same polygons join around...

s: J₁₄, J₁₅ and J₁₆. The hexagonal form can be constructed by all regular faces, but isn't 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.
• The edge-first orthogonal projection of a 24-cell is an elongated hexagonal bipyramid.