Hollow cuboid cupoliprism

The hollow cubic cupoliprism or hocucup is a prismatic scaliform polychoron that consists of 6 stella octangulae (or 12 tetrahedra) and 12 blends of 2 triangular prisms. Each vertex is met by two tetrahedra and four blends of 2 triangular prisms.

This polychoron can be created as a blend of 6 tetrahedral prisms (in the form of 6 digonal antiduoprisms). In the process all the tetrahedra compound in pairs, while the triangular prisms blend in pairs at a square face. The object has cube prismatic symmetry and has the vertices of a scaled cuboctahedral prism.

It was first discovered and described by Polytope Discord user _Geometer on November 20, 2020.

Vertex coordinates
The vertices of a hollow cubic cupoliprism of edge length 1 are given by all permutations of the first three coordinates of:
 * $$\left(±\frac12,\,±\frac12,\,0,\,±\frac{\sqrt2}{4}\right).$$