Quasitruncated tesseract

The quasitruncated tesseract, or quitit, is a nonconvex uniform polychoron that consists of 16 regular tetrahedra and 8 quasitruncated hexahedra. 1 tetrahedron and three quasitruncated hexahedra join at each vertex. As the name suggests, it can be obtained by quasitruncating the tesseract.

Vertex coordinates
The vertices of a quasitruncated tesseract of edge length 1 are given by all permutations of:
 * $$\left(±\frac{\sqrt2-1}{2},\,±\frac{\sqrt2-1}{2},\,±\frac{\sqrt2-1}{2},\,±\frac12\right).$$