Great tesseractitesseractihexadecachoron

The great tesseractitesseractihexadecachoron, or gittith, is a nonconvex uniform polychoron that consists of 16 regular tetrahedra, 8 cubes, and 8 great cubicuboctahedra. 1 tetrahedron, 1 cube, and 3 great cubicuboctahedra join at each vertex.

The great tesseractitesseractihexadecachoron contains the vertices of a great cubicuboctahedral prism and square-octagrammic duoprism.

Vertex coordinates
Coordinates for the vertices of a great tesseractitesseractihexadecachoron with edge length 1 are given by all permutations of:
 * $$\left(±\frac{\sqrt2-1}{2},\,±\frac12,\,±\frac12,\,±\frac12\right).$$