Great disprismatotesseractihexadecachoron

The great disprismatotesseractihexadecachoron, or gidpith, also commonly called the omnitruncated tesseract, is a convex uniform polychoron that consists of 32 hexagonal prisms, 24 octagonal prisms, 16 truncated octahedra, and 8 great rhombicuboctahedra. 1 of each type of cell join at each vertex. It is the omnitruncate of the BC4 family of uniform polychora, and could also be considered to be the omintruncated hexadecachoron.

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