Truncated tetrahedral alterprism

The truncated tetrahedral cupoliprism, or tutcup, also known as the truncated tetrahedral alterprism, is a convex scaliform polychoron. It consists of two truncated tetrahedra as bases, joined by 8 triangular cupolas and 6 tetrahedra. 1 truncated tetrahedron, 1 tetrahedron, and 3 triangular cupolas join at each vertex. It can be formed by tetrahedrally alternating the small rhombicuboctahedral prism's triangles in such a way that the bases turn into truncated tetrahedra in opposite orientations.

It is also a convex segmentochoron (designated K-4.55 in Richard Klitzing's list), as truncated tetrahedron atop truncated tetrahedron.

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 tetrahedron atop truncated tetrahedron caps are removed.

This polychoron was discovered in 2000 by Richard Klitzing while he was searching for convex segmentochora. After its discovery he came up with the concept of scaliform polytopes, so this polychoron can in fact be said to be the first non-uniform scaliform polytope discovered.

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:
 * $$\left(\frac{3\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4}\right).$$

Representations
The truncated tetrahedral cupoliprism has the following Coxeter diagrams:


 * s2s4o3x (as snub derivation)
 * xo3xx3ox&#x (as segmentochoron)