| Type: | Johnson |
| Faces: | 10 triangles 20 squares 2 pentagons |
| Edges: | 60 |
| Vertices: | 30 |
| Dual: | - |
| Properties: | convex |
| Net: | Johnson solid 39 net.png |
In geometry, the elongated pentagonal gyrobicupola is one of the Johnson solids . As the name suggests, it can be constructed by elongating a pentagonal gyrobicupola by inserting a decagonal prism between its congruent halves. Rotating one of the pentagonal cupolae through 36 degrees before inserting the prism yields an elongated pentagonal orthobicupola .
The following formulae for volume and surface area can be used if all faces are regular, with edge length a:[1]
| V= | 1 |
| 6 |
\left(10+8\sqrt{5}+15\sqrt{5+2\sqrt{5}}\right)a3 ≈ 12.3423...a3
| A=\left(20+\sqrt{ | 5 |
| 2 |
\left(10+\sqrt{5}+\sqrt{75+30\sqrt{5}}\right)}\right)a2 ≈ 27.7711...a2