Elongated triangular pyramid

The elongated triangular pyramid is one of the 92 Johnson solids (J7). 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:
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac12\right),$$
 * $$\left(0,\,\frac{\sqrt3}{3},\,±\frac12\right),$$
 * $$\left(0,\,0,\,\frac{3+2\sqrt6}{6}\right).$$