In geometry, the gyroelongated pentagonal cupola is one of the Johnson solids (J24). As the name suggests, it can be constructed by gyroelongating a pentagonal cupola (J5) by attaching a decagonal antiprism to its base. It can also be seen as a gyroelongated pentagonal bicupola (J46) with one pentagonal cupola removed.
The 92 Johnson solids were named and described by Norman Lloyd Johnson in 1966.
Read more about Gyroelongated Pentagonal Cupola: Dual Polyhedron