Truncated tesseract

The truncated tesseract, or tat, is a convex uniform polychoron that consists of 16 regular tetrahedra and 8 truncated cubes. 1 tetrahedron and three truncated cubes join at each vertex. As the name suggests, it can be obtained by truncating the tesseract.

Vertex coordinates
The vertices of a truncated tesseract of edge length 1 are given by all permutations of:
 * (±(1+$\sqrt{2+√2}$)/2, ±(1+$\sqrt{(5+3√2)/2}$)/2, ±(1+$\sqrt{2}$)/2, ±1/2).

Representations
A truncated tesseract has the following Coxeter diagramms:


 * x4x3o3o (full symmetry)
 * xwwx4xoox3oooo&#xt (BC3 symmetry, truncated cube-first)
 * xwwxoooo3ooxwwxoo3ooooxwwx&#xt (A3 axial, tetrahedron-first)
 * wx3oo3xw *b3oo&#zx (D4 symmetry)
 * wx xw4xo3oo&#zx (BC3×A1 symmetry)
 * ox4wx xo4xw&#zx (BC2×BC2 symmetry, truncated square duoprism)
 * xwww wxww wwxw wwwx&#zx (A1×A1×A1×A1 symmetry)