Truncated tetrahedral alterprism

The truncated tetrahedral cupoliprism, or tutcup, is a convex scaliform polychoron. It consists of two truncated tetrahedra as bases, joined by 8 triangular cupolas and 6 tetrahedra.

The two truncated tetrahedra are in opposite orientation, so that the hexagonal faces of one base are parallel to the triangular faces of the other.

It can also be seen as a diminishing of the rectified tesseract, specifically one where two caps shaped like the tetrahedral-truncated tetrahedral segmentochoron are removed.

Vertex coordinates
The vertices of a truncated tetrahedral cupoliprism of edge length 1, centered at the origin, are given by all even changes of sign, and all permutations in the first three coordinates of:
 * (3$\sqrt{2}$/4, $\sqrt{3}$/4, $\sqrt{6}$/4, $\sqrt{2}$/4).