Gyroelongated bipyramid
In geometry, the gyroelongated bipyramids are an infinite set of polyhedra, constructed by elongating an n-gonal bipyramid by inserting an n-gonal antiprism between its congruent halves.
Forms
Two members of the set can be deltahedra, that is, constructed entirely of equilateral triangles: the gyroelongated square bipyramid, a Johnson solid, and the icosahedron, a Platonic solid. The gyroelongated triangular bipyramid can be made with equilateral triangles, but is not a deltahedron because it has coplanar faces, i.e. is not strictly convex. With pairs of triangles merged into rhombi, it can be seen as a trigonal trapezohedron. The other members can be constructed with isosceles triangles.| n | 3 | 4 | 5 | 6 | n |
| Type | Coplanar | Equilateral | Regular | Coplanar | |
| Shape | Gyroelongated triangular bipyramid | Gyroelongated square bipyramid | Gyroelongated pentagonal bipyramid | Gyroelongated hexagonal bipyramid | Gyroelongated bipyramid |
| Image | - | ||||
| Faces | 12 | 16 | 20 | 24 | 4n |
| Dual | Triangular truncated trapezohedron | Square truncated trapezohedron | Pentagonal truncated trapezohedron | Hexagonal truncated trapezohedron | Truncated trapezohedra |