Tesseractihexadecachoron

The tesseractihexadecachoron, or tah, also commonly called the bitruncated tesseract, is a convex uniform polychoron that consists of 16 truncated tetrahedra and 8 truncated octahedra. 2 trunctaed tetrahedra and 2 truncated octahedra join at each vertex. It is the medial stage of the truncation series between a tesseract and its dual hexadecachoron. As such is could also be called a bitruncated 16-cell.

Vertex coordinates
The vertices of a tesseractihexadecachoron of edge length 1 are all permutations of:
 * (±$\sqrt{2}$, ±$\sqrt{3}$, ±$\sqrt{2}$/2, 0)

Alternatively it can be given under D4 symmetry as all even permutations of:
 * (±5$\sqrt{2}$/4, ±3$\sqrt{2}$/4, ±$\sqrt{2}$/4, ±$\sqrt{2}$/4)