In geometry, the gyroelongated triangular cupola is one of the Johnson solids (J<sub>22</sub>). It can be constructed by attaching a hexagonal antiprism to the base of a triangular cupola (J<sub>3</sub>). 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 (J<sub>44</sub>) 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:
The dual of the gyroelongated triangular cupola has 15 faces: 6 kites, 3 rhombi, and 6 pentagons.