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 sign changes of:
 * (5$\sqrt{2}$/4, 3$\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4)

Representations
The tesseractihexadecachoron has the following Coxeter diagrams:


 * o4x3x3o (full symmetry)
 * x3x3x *b3o (D4 symmetry, great rhombated demitesseract)
 * s4o3x3x (as runcicantic tesseract)
 * s4x3x3o (also as snub)
 * ooqoo4xuxux3xooox&#xt (BC3 axial, truncated octahedron-first)
 * xxuxoo3xuxxux3ooxuxx&#xt (A3 axial, truncated tetrahedron-first)
 * Qqo ooq4xux3xoo&#zx (BC3×A1 symmetry)