Irregularly shaped space-filling truncated octahedra

For any parent tetrahedron ABCD, centroids of selected sub-tetrahedra form the vertices of an irregularly shaped space-filling truncated octahedron. To reflect these properties, such a figure will be called an ISTO. Each edge of the ISTO is parallel to and one-eighth the length of one of the edges of tetrahedron ABCD and the volume of the ISTO is 3/16-th the volume of the tetrahedron. The ISTO is symmetric about the centroid of tetrahedron ABCD and each face is symmetric about a centre and has an opposite face that is parallel and congruent. The area of the faces of the ISTO is not proportional to that of the generating tetrahedron.