Truncated hexadecachoron

The truncated hexadecachoron, or thex, also commonly called the truncated 16-cell, is a convex uniform polychoron that consists of 8 regular octahedra and 16 truncated tetrahedra. 1 octahedron and four truncated tetrahedra join at each vertex. As the name suggests, it can be obtained as the truncation of a hexadecachoron.

Vertex coordinates
The vertices of a truncated hexadecachoron of edge length 1 are given by all permutations of:


 * (±$\sqrt{3}$, ±$\sqrt{10}$/2, 0, 0).

Alternatively under D4 symmetry it can be given by all permutations and even sign changes of:


 * (3$\sqrt{2}$/4, 3$\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4).

Representations
A truncated hexadecachoron has the following Coxeter diagrams:


 * o4o3x3x (full symmetry)
 * x3x3o *b3o (D4 symmetry, as truncated demitesseract)
 * s4o3x3o (as cantic tesseract)
 * xuxo3xoox3oxux&#xt (A3 axial, truncated tetrahedron-first)
 * ooooo4ooxoo3xuxux&#xt (BC3 axial, octahedron-first)
 * ooxoo3xuxux3ooxoo&#xt (A3 axial, octahedron-first)
 * ooxxuuxd ooxxuudx QqQoqooo qQoQoqoo &#zx (A1×A1×A1×A1 symmetry)
 * oxux4oqoo xoxu4qooo&#zx (BC2×BC2 symmetry)
 * Qqo ooo4oxo3xux&#zx (BC3×A1 symmetry)

Related polychora
The truncated hexadecachoron is the colonel of a regiment that also includes the truncated tesseractihemioctachoron.