Elongated square bipyramid

The elongated square bipyramid 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:
 * $$\left(±\frac12,\,±\frac12,\,±\frac12\right),$$
 * $$\left(0,\,0,\,±\frac{1+\sqrt2}{2}\right).$$

Representations
An elongated square bipyramid has the following Coxeter diagrams:


 * oxxo4oooo&#xt (full symmetry)
 * oxxo oxxo&#xt (rectangular symmetry)
 * xwx xox&#xt (rectangular axial)
 * wx ox4oo&#zx (as tegum sum)
 * x(xw)x o(qo)o&#xt (edge first)
 * qoo oqo xxw&#zx (cuboid symmetry)