Tetrahedron atop truncated tetrahedron

Tetrahedron atop truncated tetrhaedron, or tetatut, is a CRF segmentochoron (designated K-4.56 on Richard Klitzing's list). As the name suggests, it consists of a tetrahedron and a truncated tetrahedron as bases, connected by 4 further tetrahedra and 4 triangular cupolas.

It can be obtained as a segment of the rectified tesseract, which can be formed by attaching these segmentochora to both bases of the truncated tetrahedral cupoliprism.

Vertex coordinates
The vertices of a tetrahedron atop truncated tetrahedronsegmentochoron of edge length 1 are given by:
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{2}\right)$$ and all even sign changes of first three coordinates
 * $$\left(\frac{3\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,0\right)$$ and all permutatoins and even sign changes of first three coordinates