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 gyroelongated 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 (J₁₇). As the name suggests, it can be constructed by gyroelongating 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 square antiprism

Square antiprism

In geometry, the square antiprism is the second in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps...

 between its congruent halves. It is a deltahedron

Deltahedron

A deltahedron is a polyhedron whose faces are all equilateral triangles. The name is taken from the Greek majuscule delta , which has the shape of an equilateral triangle. There are infinitely many deltahedra, but of these only eight are convex, having 4, 6, 8, 10, 12, 14, 16 and 20 faces...

.

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

Dual polyhedron

The dual of the gyroelongated square bipyramid is a square truncated trapezohedron

Square truncated trapezohedron

The square truncated trapezohedron is the second in an infinite series of truncated trapezohedron polyhedra. It has 8 pentagon and 2 square faces.This polyhedron can be constructed by taking a tetragonal trapezohedron and truncating the polar axis vertices....

with 10 faces: 8 pentagons and 2 square.

Dual gyroelongated square bipyramid	Net of dual