Prismatorhombated hexadecachoric prism

The prismatorhombated hexadecachoric prism or prohp is a prismatic uniform polyteron that consists of 2 prismatorhombated hexadecachora, 8 truncated cubic prisms, 16 cuboctahedral prisms, 24 square-octagonal duoprisms, and 32 triangular-square duoprisms. 1 prismatorhombated hexadecachoron, 1 truncated cubic prism, 2 square-octagonal duoprisms, and 1 triangular-square duoprism join at each vertex. As the name suggests, it is a prism based on the prismatorhombated hexadecachoron, which also makes it a convex segmentoteron.

The prismatorhombated hexadecachoric prism can be vertex-inscribed into the cellirhombated penteractitriacontaditeron.

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