| Type: | Johnson |
| Faces: | 5 triangles 15 squares 1 pentagon 1 decagon |
| Edges: | 45 |
| Vertices: | 25 |
| Dual: | - |
| Properties: | convex |
| Net: | Johnson solid 20 net.png |
In geometry, the elongated pentagonal cupola is one of the Johnson solids . As the name suggests, it can be constructed by elongating a pentagonal cupola by attaching a decagonal prism to its base. The solid can also be seen as an elongated pentagonal orthobicupola with its "lid" (another pentagonal cupola) removed.
The following formulas for the volume and surface area can be used if all faces are regular, with edge length a:[1]
| V=\left( | 1 |
| 6 |
\left(5+4\sqrt{5}+15\sqrt{5+2\sqrt{5}}\right)\right)a3 ≈ 10.0183...a3
| A=\left( | 1 |
| 4 |
\left(60+\sqrt{10\left(80+31\sqrt{5}+\sqrt{2175+930\sqrt{5}}\right)}\right)\right)a2 ≈ 26.5797...a2
The dual of the elongated pentagonal cupola has 25 faces: 10 isosceles triangles, 5 kites, and 10 quadrilaterals.