| Type: | Johnson J21 - J22 - J23 |
| Faces: | 1+3x3+6 triangles 3 squares 1 hexagon |
| Edges: | 33 |
| Vertices: | 15 |
| Symmetry: | C3v |
| Vertex Config: | 3(3.4.3.4) 2.3(33.6) 6(34.4) |
| Dual: | - |
| Properties: | convex |
| Net: | Johnson solid 22 net.png |
In geometry, the gyroelongated triangular cupola is one of the Johnson solids (J22). It can be constructed by attaching a hexagonal antiprism to the base of a triangular cupola (J3). This is called "gyroelongation", which means that an antiprism is joined to the base of a solid, or between the bases of more than one solid.
The gyroelongated triangular cupola can also be seen as a gyroelongated triangular bicupola (J44) with one triangular cupola removed. Like all cupolae, the base polygon has twice as many sides as the top (in this case, the bottom polygon is a hexagon because the top is a triangle).
The following formulae for volume and surface area can be used if all faces are regular, with edge length a:[1]
| V=\left( | 1 | \sqrt{ |
| 3 |
| 61 | |
| 2 |
+18\sqrt{3}+30\sqrt{1+\sqrt{3}}}\right)a3 ≈ 3.51605...a3
| A=\left(3+ | 11\sqrt{3 |
The dual of the gyroelongated triangular cupola has 15 faces: 6 kites, 3 rhombi, and 6 pentagons.