| Set of gyroelongated bipyramids | |
|---|---|
The pentagonal gyroelongated bipyramid is the regular icosahedron. |
|
| Faces | 4n triangles |
| Edges | 6n |
| Vertices | 2n+2 |
| Symmetry group | Dnd, [2+,2n], (2*n) |
| Dual polyhedron | truncated trapezohedra |
| Properties | convex |
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.
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. The other members can be constructed with isosceles triangles.
| n | 3 | 4 | 5 | 6 | n |
|---|---|---|---|---|---|
| Shape | Gyroelongated triangular bipyramid | Gyroelongated square bipyramid | Gyroelongated pentagonal bipyramid (icosahedron) |
Gyroelongated hexagonal bipyramid | Gyroelongated bipyramid |
| Image | |||||
| Dual | Triangular truncated trapezohedron | Square truncated trapezohedron | Pentagonal truncated trapezohedron (Dodecahedron) |
Hexagonal truncated trapezohedron | Truncated trapezohedra |
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