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 pentagonal 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 (J₂₄). As the name suggests, it can be constructed by gyroelongating a pentagonal cupola

Pentagonal cupola

In geometry, the pentagonal cupola is one of the Johnson solids . It can be obtained as a slice of the rhombicosidodecahedron.The 92 Johnson solids were named and described by Norman Johnson in 1966....

 (J₅) by attaching a decagonal antiprism

Decagonal antiprism

In geometry, the decagonal antiprism is the eighth 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.- External links :*...

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

Gyroelongated pentagonal bicupola

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

 (J₄₆) with one pentagonal cupola removed.

The 92 Johnson solids were named and described by Norman Lloyd Johnson

Norman Lloyd Johnson

Norman Lloyd Johnson was a professor of statistics and author or editor of several standard reference works in statistics and probability theory.-Education:...

in 1966.

Dual polyhedron

The dual of the gyroelongated pentagonal cupola has 25 faces: 10 kites, 5 rhombi, and 10 quadrilaterals.

Dual gyroelongated pentagonal cupola	Net of dual