Hexadecachoric prism

{{Infobox polytope }} 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.
 * type=Uniform
 * img=auto
 * off=auto
 * dim = 5
 * obsa = Hexip
 * tera = 16 tettrahedral prisms, 2 hexadecachora
 * cells = 32 tetrahedra, 32 triangular prisms
 * faces = 64 triangles, 24 squares
 * edges = 8+48
 * vertices = 16
 * verf = Octahedral pyramid, edge lengths 1 (base), $\sqrt{2}$ (legs)
 * coxeter = x o4o3o3x
 * symmetry = BC4×A1, order 768
 * army=Hexip
 * reg=Hexip
 * circum=$$\frac{\sqrt3]{2} ≈ 0.86603$$
 * height = Hex atop hex: 1
 * height2 = Tepe atop dual tepe: $$\frac{\sqrt2}{2} ≈ 0.70711$$
 * hypervolume = $$\frac16 ≈ 0.16667$$
 * dit = Tepe–tet–tepe: 120°
 * dit2 = Hex–tet–tepe: 90°
 * pieces = 18
 * loc = 5
 * dual = Tesseractic tegum
 * conjugate=Hexadecachoric prism
 * conv = Yes
 * orientable=Yes
 * nat=Tame
 * bracket = [i]

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)