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 even permutations of:


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