Gyroelongated square pyramid

The gyroelongated square pyramid, or gyesp, is one of the 92 Johnson solids (J10). It consists of 4+4+4 triangles and 1 square. It can be constructed by attaching a square antiprism to the base of the square pyramid.

If a second pyramid is attached to the other base of the square antiprism, the result is the gyroelongated square bipyramid.

Vertex coordinates
A gyroelongated square pyramid of edge length 1 has the following vertices:
 * (0, 0, (2$\sqrt{2}$+$\sqrt{2}$)/4),
 * (±1/2, ±1/2, $\sqrt{4+3√2}$/4),
 * (0, ±$\sqrt{2}$/2, –$\sqrt$/4),
 * (±$\sqrt{2}$/2, 0, –$\sqrt{6}$/4).