| bgcolor=#e7dcc3 colspan=2 | Set of gyroelongated cupolae | |
|---|---|---|
| align=center colspan=2 | 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 2n-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.
| name | faces | ||
|---|---|---|---|
| 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 | ||
| 18 triangles, 6 squares, 1 hexagon, 1 dodecagon |