In geometry, the gyroelongated bipyramids are an infinite set of polyhedra, constructed by elongating an bipyramid by inserting an 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. See also Elongated bipyramid Gyroelongated pyramid Elongated pyramid Diminished trapezohedron External links Conway Notation for Polyhedra Try: "knAn", where n=4,5,6... example "k5A5" is an icosahedron. Pyramids and bipyramids