Editing Triangular cupola (section)

== Related polyhedra ==
The triangular cupola can be found in the construction of many polyhedrons. An example is the [[cuboctahedron]] in which the triangular cupola may be considered as its hemisphere.{{r|cromwell}} A construction that involves the attachment of its base to another polyhedron is known as [[Augmentation (geometry)|augmentation]]; attaching it to [[Prism (geometry)|prisms]] or [[Antiprism|antiprisms]] is known as [[Elongation (geometry)|elongation]] or [[gyroelongation]].{{r|demey|slobodan}} Some of the other Johnson solids constructed in such a way are [[elongated triangular cupola]] <math> J_{18} </math>, [[gyroelongated triangular cupola]] <math> J_{22} </math>, [[triangular orthobicupola]] <math> J_{27} </math>, [[elongated triangular orthobicupola]] <math> J_{35} </math>, [[elongated triangular gyrobicupola]] <math> J_{36} </math>, [[gyroelongated triangular bicupola]] <math> J_{44} </math>, [[augmented truncated tetrahedron]] <math> J_{65} </math>.{{r|rajwade}}

The triangular cupola may also be applied in constructing [[truncated tetrahedron]], although it leaves some hollows and a regular tetrahedron as its interior. {{harvtxt|Cundy|1956}} constructed such polyhedron in a similar way as the [[rhombic dodecahedron]] constructed by attaching six [[square pyramid]]s outwards, each of which apices are in the [[Cube (geometry)|cube]]'s center. That being said, such truncated tetrahedron is constructed by attaching four triangular cupolas rectangle-by-rectangle; those cupolas in which the alternating sides of both right isosceles triangle and rectangle have the edges in terms of ratio <math display="inline> 1 : \frac{1}{2}\sqrt{2} </math>. The [[truncated octahedron]] can be constructed by attaching eight of those same triangular cupolas triangle-by-triangle.{{r|cundy}}