|Set of gyroelongated bipyramids|
The pentagonal gyroelongated bipyramid is the regular icosahedron.
|Symmetry group||Dnd, [2+,2n], (2*n), order 4n|
|Rotation group||Dn, [2,n]+, (22n), order 2n|
|Dual polyhedron||truncated trapezohedra|
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.
|Shape||Gyroelongated triangular bipyramid||Gyroelongated square bipyramid||Gyroelongated pentagonal bipyramid
|Gyroelongated hexagonal bipyramid||Gyroelongated bipyramid|
|Dual||Triangular truncated trapezohedron||Square truncated trapezohedron||Pentagonal truncated trapezohedron
|Hexagonal truncated trapezohedron||Truncated trapezohedra|