In
geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
, 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 solid
In geometry, a Johnson solid is a strictly convex polyhedron each face of which is a regular polygon. There is no requirement that each face must be the same polygon, or that the same polygons join around each vertex. An example of a Johns ...
s:
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
In geometry, a hexagon (from Greek , , meaning "six", and , , meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°.
Regular hexagon
A ''regular hexagon'' h ...
).
Uses
* A quartz crystal is an example of an elongated hexagonal bipyramid. Because it has 18 faces, it can be called an
octadecahedron
In geometry, an octadecahedron (or octakaidecahedron) is a polyhedron with 18 faces. No octadecahedron is regular; hence, the name does not commonly refer to one specific polyhedron.
In chemistry, "''the'' octadecahedron" commonly refers to a s ...
. Other chemicals also have this shape.
Controllable synthesis of elongated hexagonal bipyramid shaped La(OH)3 nanorods and the distribution of electric property by off-axis electron holography
September 2016, Volume 9, Issue 9, pp 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
In mathematics, graph theory is the study of '' graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conn ...
.
References
{{Polyhedron-stub
Pyramids and bipyramids