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 rotunda 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 (J₂₅). As the name suggests, it can be constructed by gyroelongating a pentagonal rotunda

Pentagonal rotunda

In geometry, the pentagonal rotunda is one of the Johnson solids . It can be seen as half an icosidodecahedron.The 92 Johnson solids were named and described by Norman Johnson in 1966.-Formulae:...

 (J₆) 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 birotunda

Gyroelongated pentagonal birotunda

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

 (J₄₈) with one pentagonal rotunda removed.

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

Dual polyhedron

The dual of the gyroelongated pentagonal rotunda has 30 faces: 12 kites, 6 rhombi, and 12 quadrilaterals.

Dual gyroelongated pentagonal rotunda	Net of dual