| Type: | Johnson |
| Faces: | 3x5 triangles 3x5 squares 2+5 pentagons |
| Edges: | 70 |
| Vertices: | 35 |
| Dual: | - |
| Properties: | convex |
| Net: | Johnson solid 41 net.png |
In geometry, the elongated pentagonal gyrocupolarotunda is one of the Johnson solids . As the name suggests, it can be constructed by elongating a pentagonal gyrocupolarotunda by inserting a decagonal prism between its halves. Rotating either the pentagonal cupola or the pentagonal rotunda through 36 degrees before inserting the prism yields an elongated pentagonal orthocupolarotunda .
The following formulae for volume and surface area can be used if all faces are regular, with edge length a:[1]
| V= | 5 |
| 12 |
\left(11+5\sqrt{5}+6\sqrt{5+2\sqrt{5}}\right)a3 ≈ 16.936...a3
| A= | 1 |
| 4 |
\left(60+\sqrt{10\left(190+49\sqrt{5}+21\sqrt{75+30\sqrt{5}}\right)}\right)a2 ≈ 33.5385...a2