Hexadecachoric prism

The hexadecachoric prism or hexip is a prismatic uniform polyteron that consists of 2 hexadecachora and 16 tetrahedral prisms. 1 hexadecachoron and 8 tetrahedral prisms join at each vertex. As the name suggests, it is a prism based on a hexadecachoron, which makes it a convex segmentoteron.

Vertex coordinates
The vertices of a hexadecachoric prism of edge length 1 are given by all permutations and sign changes of the first four coordinates of:
 * $$\left(±\frac{\sqrt2}{2},\,0,\,0,\,0,\,±\frac12\right).$$

Representations
A hexadecachoric prism has the following Coxeter diagrams:


 * x o4o3o3ox (full symmetry)
 * x x3o3o *d3o (D4×A1 symmetry, demitesseract prism)
 * oo4oo3oo3xx&#x (BC4 symmetry)
 * xx3oo3oo *b3oo&#x (D4 symmetry)
 * xoox3oooo3oxxo&#xr (A3 symmetry only)
 * xxx ooo4ooo3oxo&#xt (BC3×A1 axial, edge-first, as octahedral bipyramid prism)
 * xx xo3oo3ox&#x (A3×A1 axial, tetrahedral antiprism prism)