# Elongated cupola

Set of elongated cupolae

Example pentagonal form
Faces n triangles
3n squares
1 n-gon
1 2n-gon
Edges 9n
Vertices 5n
Symmetry group Cnv, [n], (*nn)
Rotational group Cn, [n]+, (nn)
Dual polyhedron
Properties convex

In geometry, the elongated cupolae are an infinite set of polyhedra, constructed by adjoining an n-gonal cupola to an n-gonal prism.

There are three elongated cupolae that are Johnson solids made from regular triangles and square, and pentagons. Higher forms can be constructed with isosceles triangles. Adjoining a triangular prism to a cube also generates a polyhedron, but has adjacent parallel faces, so is not a Johnson solid. Higher forms can be constructed without regular faces.

## Forms

name faces
elongated triangular prism 2 triangles, 6+1 squares
elongated triangular cupola (J18) 3+1 triangles, 9 squares, 1 hexagon
elongated square cupola (J19) 4 triangles, 12+1 squares, 1 octagon
elongated pentagonal cupola (J20) 5 triangles, 15 squares, 1 pentagon, 1 decagon
elongated hexagonal cupola 6 triangles, 18 squares, 1 hexagon, 1 dodecagon