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 square bipyramid is one of the 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 (J₁₅). As the name suggests, it can be constructed by elongating an octahedron

Octahedron

In geometry, an octahedron is a polyhedron with eight faces. A regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex....

 by inserting a cube between its congruent halves.

The 92 Johnson solids were named and described by Norman Johnson in 1966.

A zircon

Zircon

Zircon is a mineral belonging to the group of nesosilicates. Its chemical name is zirconium silicate and its corresponding chemical formula is ZrSiO4. A common empirical formula showing some of the range of substitution in zircon is 1–x4x–y...

 crystal is an example of an elongated square bipyramid.

Dual polyhedron

The dual of the elongated square bipyramid has 10 faces: 8 trapezoidal and 2 square.

Dual elongated square bipyramid	Net of dual

Honeycomb

The elongated square bipyramid allows a self-tessellation of Euclidean space. The cells are colored white, red, and blue based on their orientation in space. The square pyramid

Square pyramid

In geometry, a square pyramid is a pyramid having a square base. If the apex is perpendicularly above the center of the square, it will have C4v symmetry.- Johnson solid :...

caps have shortened isosceles triangle faces, with six of these pyramids meeting together to form a cube.