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 pyramid 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 (J₁₀). As its name suggests, it can be constructed by taking a 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 :...

 and "gyroelongating" it, which in this case involves joining 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...

 to its base.

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

Dual polyhedron

The dual of the gyroelongated square pyramid has 9 faces: 4 trapezoidal, 1 square and 4 pentagonal.

Dual gyroelongated square pyramid	Net of dual