Elongated square bipyramid

The elongated square bipyramid, or esquidpy, is one of the 92 Johnson solids (J15). It consists of 8 triangles and 4 squares. It can be constructed by inserting a cube, seen as a square prism, between the two pyramidal halves of the regular octahedron, seen as a square bipyramid.

Vertex coordinates
An elongated square pyramid of edge length 1 has the following vertices:
 * (±1/2, ±1/2, ±1/2),
 * (0, 0, ±(1+$\sqrt{2}$)/2).