In
geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...
, the elongated hexagonal bipyramid is constructed by elongating a
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.
Although it is face-transiti ...
(by inserting a
hexagonal prism
In geometry, the hexagonal prism is a Prism (geometry), prism with hexagonal base. Prisms are polyhedrons; this polyhedron has 8 face (geometry), faces, 18 Edge (geometry), edges, and 12 vertex (geometry), vertices..
As a semiregular polyhedro ...
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, sometimes also known as a Johnson–Zalgaller solid, is a convex polyhedron whose faces are regular polygons. They are sometimes defined to exclude the uniform polyhedrons. There are ninety-two Solid geometry, s ...
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 is de ...
).
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 face (geometry), faces. No octadecahedron is regular polyhedron, regular; hence, the name does not commonly refer to one specific polyhedron.
In chemistry, "''the'' oc ...
. Other chemicals also have this shape.
* The ''edge-first orthogonal projection'' of a
24-cell
In four-dimensional space, four-dimensional geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol . It is also called C24, or the icositetrachoron, octaplex (short for "octa ...
is an elongated hexagonal bipyramid.
* Used as the shape of
Fruit Gushers
Fruit Gushers (also simply Gushers) are a Betty Crocker-branded fruit snack introduced in 1991. They are soft and chewy with a fruity-juice center.
History
Fruit Gushers (sometimes simply "Gushers") were introduced in 1991 as a Betty Crocker ...
candy.
* Used as a physical manifestation for assisting various branches of three-dimensional
graph theory
In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...
.
References
{{Polyhedron-stub
Bipyramids