Gyroelongated square bipyramid

The gyroelongated square bipyramid, or gyesqidpy, is one of the 92 Johnson solids. It consists of 8+8 triangles as faces. It can be constructed by inserting a square antiprism between the two pyramidal halves of the regular octahedron, seen as a square bipyramid.

Vertex coordinates
A gyroelongated square bipyramid of edge length 1 has the following vertices:
 * (0, 0, ±(2$\sqrt{2}$+$\sqrt{4+3√2}$)/4),
 * (±1/2, ±1/2, $\sqrt{2}$/4),
 * (0, ±$\sqrt$/2, –$\sqrt{2}$/4),
 * (±$\sqrt{2}$/2, 0, –$\sqrt{2√2}$/4).