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:
 * $$\left(±\frac{\sqrt2-1}{2},\,±\frac12,\,±\frac12,\,±\frac12\right).$$

Related polychora
The great tesseractitesseractihexadecachoron is the colonel of a regiment with a total of 8 uniform, 1 uniform compound, and 6 scaliform members. Of these members, 6 have full tesseractic symmetry, namely the quasidisprismatotesseractihexadecachoron, the prismatocubintercepted tesseract, the great tesseractifaceted cubitesseractihexadecachoron, the great hexadecafaceted prismatotesseractioctachoron]], the great spinoprismatotesseractihexadecachoron, and the great spinoprismatotesseractioctachoron. The eighth member, the great quasiprismatodishexadecachoron, has square duoprism symmetry, as does the compound octagonal diorthoprism and the 6 scaliform members.