Prismatorhombated hexadecachoron

The prismatorhombated hexadecachoron, or proh, also commonly called the runcitruncated tesseract, is a convex uniform polychoron that consists of 32 triangular prisms, 24 octagonal prisms, 16 cuboctahedra, and 8 truncated cubes. 1 triangular prism, 2 octagonal prisms, 1 cuboctahedron, and 1 truncated cubejoin at each vertex. As one of its names suggests, it can be obtained by runcintruncating the tesseract.

The prismatorhombated hexadecachoron can be vertex-inscribed into a small rhombated icositetrachoron.

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


 * (±(1+2$\sqrt{2}$)/2, ±(1+$\sqrt{2}$)/2, ±(1+$\sqrt{2}$)/2, ±1/2).

Representations
A prismatorhombated hexadecachoron has the following Coxeter diagrams:


 * x4x3o3x (full symmetry)
 * xxwwxx4xxooxx3oxxxxo&#xt (BC3 axial, truncated cube-first)
 * wx3oo3xw *b3xx&#zx (D4 symmetry)
 * Xwx xxw4xxo3oxx&#zx (BC3×A1 symmetry)

Related polychora
The segmentochoron truncated cube atop great rhombicuboctahedron can be obtained as a cap of the prismatorhombated hexadecachoron.

The truncated cubes of the prismatorhombated hexadecachoron can be augmented by cuboctahedron atop truncated cube segmentochora. If all 8 truncated cubes are augmented, the result is the small rhombated icositetrachoron, as square cupolas from the segmentochora merge with octagonal prisms to form small rhombicuboctahedra.