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.
Area and volume With edge length a, the surface area is
and the volume is
Dual polyhedron The dual of the gyroelongated pentagonal cupola has 25 faces: 10 kites, 5 rhombi, and 10 pentagons. Dual gyroelongated pentagonal cupolaNet of dual
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