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 cupola 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 (J₂₃). As the name suggests, it can be constructed by gyroelongating a square cupola

Square cupola

In geometry, the square cupola, sometimes called lesser dome, is one of the Johnson solids . It can be obtained as a slice of the rhombicuboctahedron...

 (J₄) by attaching an octagonal antiprism

Octagonal antiprism

In geometry, the octagonal antiprism is the 6th in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps.If faces are all regular, it is a semiregular polyhedron.- See also :* Set of antiprisms...

 to its base. It can also be seen as a gyroelongated square bicupola

Gyroelongated square bicupola

In geometry, the gyroelongated square bicupola is one of the Johnson solids . As the name suggests, it can be constructed by gyroelongating a square bicupola by inserting an octagonal antiprism between its congruent halves....

 (J₄₅) with one square bicupola removed.

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

Dual polyhedron

The dual of the gyroelongated square cupola has 25 faces: 8 kites, 4 rhombi, and 8 quadrilaterals.

Dual gyroelongated square cupola	Net of dual