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.

The great disprismatotesseractihexadecachoron can be vertex-inscribed into a prismatorhombated icositetrachoron.

This polychoron can be alternated into an omnisnub tesseract, although it cannot be made uniform. The octagons can also be alternated into long rectangles to create a bialternatosnub hexadecachoron, which is also nonuniform. If the octagons are alternated alternately, then the resulting polychoron is a truncated icositetrachoron.

Vertex coordinates
Vertex coordinates for 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).