| Type: | Johnson |
| Faces: | 2.10 triangles 2.5 squares 2+10 pentagons |
| Edges: | 80 |
| Vertices: | 40 |
| Dual: | - |
| Properties: | convex |
| Net: | Johnson solid 42 net.png |
In geometry, the elongated pentagonal orthobirotunda is one of the Johnson solids . Its Conway polyhedron notation is at5jP5. As the name suggests, it can be constructed by elongating a pentagonal orthobirotunda by inserting a decagonal prism between its congruent halves. Rotating one of the pentagonal rotundae through 36 degrees before inserting the prism yields the elongated pentagonal gyrobirotunda .
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(45+17\sqrt{5}+15\sqrt{5+2\sqrt{5}}\right)a3 ≈ 21.5297...a3
A=\left(10+\sqrt{30\left(10+3\sqrt{5}+\sqrt{75+30\sqrt{5}}\right)}\right)a2 ≈ 39.306...a2