| bgcolor=#e7dcc3 colspan=2 | Set of elongated cupolae | |
|---|---|---|
| align=center colspan=2 | 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 2n-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 two pairs of coplanar faces, so is not a Johnson solid. Higher forms can be constructed without regular faces.
| name | faces | ||
|---|---|---|---|
| 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 | ||
| 6 triangles, 18 squares, 1 hexagon, 1 dodecagon |