Gyroelongated pentagonal cupola
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| Gyroelongated pentagonal cupola | |
|---|---|
 | |
| Type | Johnson J23 – J24 – J25 |
| Faces | 3×5+10 triangles 5 squares 1 pentagon 1 decagon |
| Edges | 55 |
| Vertices | 25 |
| Vertex configuration | 5(3.4.5.4) 2.5(33.10) 10(34.4) |
| Symmetry group | C5v |
| Dual polyhedron | - |
| Properties | convex |
| Net | |
 | |
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.
A Johnson solid is one of 92 strictly convex polyhedra that are composed of regular polygon faces but are not uniform polyhedra (that is, they are not Platonic solids, Archimedean solids, prisms, or antiprisms). They were named by Norman Johnson, who first listed these polyhedra in 1966.[1]
With edge length a, the surface area is
and the volume is
