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).
thumb|3D model of a gyroelongated triangular cupola
Formulae
The following formulae for volume and surface area can be used if all faces are regular, with edge length a:
:<math>V=\left(\frac{1}{3}\sqrt{\frac{61}{2}+18\sqrt{3}+30\sqrt{1+\sqrt{3}\right)a^3\approx3.51605...a^3</math>
:<math>A=\left(3+\frac{11\sqrt{3{2}\right)a^2\approx12.5263...a^2</math>
Dual polyhedron
The dual of the gyroelongated triangular cupola has 15 faces: 6 kites, 3 rhombi, and 6 pentagons.
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!Dual gyroelongated triangular cupola
!Net of dual
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