Elongated square pyramid

The elongated square pyramid is one of the 92 Johnson solids (J8). It consists of 4 triangles and 1+4 squares. It can be constructed by attaching a cube, seen as a square prism, to the base of the square pyramid.

If a second pyramid is attached to the opposite face of the cube, the result is the elongated square bipyramid.

Vertex coordinates
An elongated square pyramid of edge length 1 has the following vertices:
 * $$\left(±\frac12,\,±\frac12,\,±\frac12\right),$$
 * $$\left(0,\,0,\,\frac{1+\sqrt2}{2}\right).$$