Great disprismatotesseractihexadecachoric prism

The great disprismatotesseractihexadecachoric prism or gidpithip is a prismatic uniform polyteron that consists of 2 great disprismatotesseractihexadecachora, 8 great rhombicuboctahedral prisms, 16 truncated octahedral prisms, 24 square-octagonal duoprisms and 32 square-hexagonal duoprisms. One of each type of facet join at each vertex. As the name suggests, it is a prism based on the great disprismatotesseractihexadecachoron, which also makes it a convex segmentoteron.

The great disprismatotesseractihexadecachoric prism can be vertex-inscribed into the celligreatorhombated triacontaditeron.

This polyteron can be alternated into a snub tesseractic antiprism, although it cannot be made uniform. The octagons can also be alternated into long rectangles to create a pyritosnub tesseractic alterprism, which is also nonuniform.

Vertex coordinates
The vertices of a great disprismatotesseractihexadecachoric prism of edge length 1 are given by all permutations and sign changes of the first four coordinates of:
 * $$\left(±\frac{1+3\sqrt2}{2},\,±\frac{1+2\sqrt2}{2},\,±\frac{1+\sqrt2}{2},\,±\frac12,\,±\frac12\right).$$