Gyroelongated bipyramid

The gyroelongated bipyramids are the polyhedra constructed with a bipyramid and an antiprism. Their dual polyhedra are the truncated trapezohedra. The bipyramid is sliced into two congruent pyramids and then attached to the bases of an antiprism in between; such a process of construction is known as gyroelongation. The resulting construction has triangular faces, classified as simplicial polyhedron. There are infinitely many members of gyroelongated bipyramids.^[1]

Special members in the family of gyroelongated bipyramids

Some members are special cases for having equilateral triangular faces, which are known as deltahedra: the gyroelongated square bipyramid^[2] and regular icosahedron.^[3][4] For a gyroelongated triangular bipyramid, it is a non-convex deltahedron because its faces are coplanar, thereby it is not strictly convex. Considering that each pair of its triangles merged into rhombi, the resulting polyhedron can be seen as a trigonal trapezohedron.^{[citation needed]}