Elongated triangular pyramid

The elongated triangular pyramid, or etripy, is one of the 92 Johnson solids. It consists of 1+3 triangles and 3 squares. It can be constructed by attaching a triangular prism to one of the faces of the tetrahedron, seen as a triangular pyramid.

If a second tetrahedron is attached to the other triangular base of the prism, the result is the elongated triangular bipyramid.

Vertex coordinates
An elongated triangular pyramid of edge length 1 has the following vertices:
 * (±1/2, –$\sqrt{2}$/6, ±1/2),
 * (0, $\sqrt{2}$/3, ±1/2),
 * (0, 0, (3+2$\sqrt{2}$)/3).