| Type: | Johnson |
| Faces: | 3×5 triangles 5 squares 2+5 pentagons |
| Edges: | 50 |
| Vertices: | 25 |
| Dual: | - |
| Properties: | convex |
| Net: | Johnson solid 32 net.png |
In geometry, the pentagonal orthocupolarotunda is one of the Johnson solids . As the name suggests, it can be constructed by joining a pentagonal cupola and a pentagonal rotunda along their decagonal bases, matching the pentagonal faces. A 36-degree rotation of one of the halves before the joining yields a pentagonal gyrocupolarotunda .
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}\right)a3 ≈ 9.24181...a3
| A=\left(5+ | 1 |
| 4 |
\sqrt{1900+490\sqrt{5}+210\sqrt{75+30\sqrt{5}}}\right)a2 ≈ 23.5385...a2