Hexateric prism

The hexateric prism or hixip is a prismatic uniform polypeton that consists of 2 hexatera and 6 pentachoric prisms as facets. Each vertex joins 1 hexateron and 5 pentachoric prisms. As the name suggests, it is a prism based on the hexateron, which also makes it a convex segmentoteron.

A hexateric prism can be vertex-inscribed into the icosiheptaheptacontadipeton.

Vertex coordinates
The vertices of a hexateric prism of edge length 1 are given by:
 * $$\left(±\frac{1}{2},\,-\frac{\sqrt{3}}{6},\,-\frac{\sqrt{6}}{12},\,-\frac{\sqrt{10}}{20},\,-\frac{\sqrt{15}}{30},\,±\frac12\right),$$
 * $$\left(0,\,\frac{\sqrt{3}}{3},\,-\frac{\sqrt{6}}{12},\,-\frac{\sqrt{10}}{20},\,-\frac{\sqrt{15}}{30},\,±\frac12\right),$$
 * $$\left(0,\,0,\,\frac{\sqrt{6}}{4},\,-\frac{\sqrt{10}}{20},\,-\frac{\sqrt{15}}{30},\,±\frac12\right),$$
 * $$\left(0,\,0,\,0,\,\frac{\sqrt{10}}{5},\,-\frac{\sqrt{15}}{30},\,±\frac12\right),$$
 * $$\left(0,\,0,\,0,\,0,\,\frac{\sqrt{15}}{6},\,±\frac12\right).$$

Representations
A hexateric prism has the following Coxeter diagrams:


 * x x3o3o3o3o (full symmetry)
 * xx3oo3oo3oo3oo&#x (hexateron atop hexateron)
 * xx ox3oo3oo3oo&#x (dyad atop pentachoric prism)
 * xx xo oo3oo3ox&#x (square atop orthogonal tetrahedral prism)
 * xx xo3oo ox3oo&#x (triangular prism atop orthogonal triangular prism)
 * xxoo3oooo3oooo3oooo&#xr (A4 axial symmetry)
 * xxoo3oooo3oooo ooxx&#xr (A3×A1 axial)
 * xxoo3oooo ooxx3oooo&#xr (A2×A2 axial)