# Gyroelongated cupola

Set of gyroelongated cupolae

Example pentagonal form
Faces 3n triangles
n 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 gyroelongated cupolae are an infinite set of polyhedra, constructed by adjoining an n-gonal cupola to an n-gonal antiprism.

There are three gyroelongated 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 square antiprism also generates a polyhedron, but has adjacent parallel faces, so is not a Johnson solid. The hexagonal form can be constructed from regular polygons, but the cupola faces are all in the same plane. Topologically other forms can be constructed without regular faces.

## Forms

name faces
gyroelongated triangular prism 2+8 triangles, 2+1 square
gyroelongated triangular cupola (J22) 9+1 triangles, 3 squares, 1 hexagon
gyroelongated square cupola (J23) 12 triangles, 4+1 squares, 1 octagon
gyroelongated pentagonal cupola (J24) 15 triangles, 5 squares, 1 pentagon, 1 decagon
gyroelongated hexagonal cupola 18 triangles, 6 squares, 1 hexagon, 1 dodecagon