| Gyroelongated pentagonal pyramid | |
|---|---|
| Type | Johnson J10 - J11 - J12 |
| Faces | 3x5 triangles 1 pentagon |
| Edges | 25 |
| Vertices | 11 |
| Vertex configuration | 5(33.5) 1+5(35) |
| Symmetry group | C5v |
| Dual polyhedron | - |
| Properties | convex |
| Net | |
In geometry, the gyroelongated pentagonal pyramid is one of the Johnson solids (J11). As its name suggests, it is formed by taking a pentagonal pyramid and "gyroelongating" it, which in this case involves joining a pentagonal antiprism to its base.
It can also be seen as a diminished icosahedron, an icosahedron with the top (a pentagonal pyramid, J2) chopped off by a plane. Other Johnson solids can be formed by cutting off multiple pentagonal pyramids from an icosahedron: the pentagonal antiprism and metabidiminished icosahedron (two pyramids removed), and the tridiminished icosahedron (three pyramids removed).
The 92 Johnson solids were named and described by Norman Johnson in 1966.
The dual of the gyroelongated pentagonal pyramid has 11 faces: 5 kites, 1 regular pentagonal and 5 irregular pentagons.
| Dual gyroelongated pentagonal pyramid | Net of dual |
|---|---|