| Type: | Johnson J24 - J25 - J26 |
| Faces: | 4x5+10 triangles 1+5 pentagons 1 decagon |
| Edges: | 65 |
| Vertices: | 30 |
| Symmetry: | C5v |
| Vertex Config: | 2.5(3.5.3.5) 2.5(33.10) 10(34.5) |
| Dual: | see above |
| Properties: | convex |
| Net: | Johnson solid 25 net.png |
In geometry, the gyroelongated pentagonal rotunda is one of the Johnson solids (J25). As the name suggests, it can be constructed by gyroelongating a pentagonal rotunda (J6) by attaching a decagonal antiprism to its base. It can also be seen as a gyroelongated pentagonal birotunda (J48) with one pentagonal rotunda removed.
With edge length a, the surface area is
| A= | 1 |
| 2 |
\left(15\sqrt{3}+\left(5+3\sqrt{5}\right)\sqrt{5+2\sqrt{5}}\right)a2 ≈ 31.007454303...a2,
and the volume is
| V=\left( | 45 | + |
| 12 |
| 17 | |
| 12 |
\sqrt{5}+
| 5 | |
| 6 |
\sqrt{2\sqrt{650+290\sqrt{5}}-2\sqrt{5}-2}\right)a3 ≈ 13.667050844...a3.
The dual of the gyroelongated pentagonal rotunda has 30 faces: 10 pentagons, 10 rhombi, and 10 quadrilaterals.