Rectified hexateric prism

The rectified hexateric prism or rixip is a prismatic uniform polypeton that consists of 2 rectified hexatera, 6 rectified pentachoric prisms, and 6 pentachoric prisms as facets. Each vertex joins 1 rectified hexateron, 2 rectified pentachoric prisms, and 4 pentachoric prisms. As the name suggests, it is a prism based on the rectified hexateron, which also makes it a convex segmentoteron.

Vertex coordinates
The vertices of a rectified hexateric prism of edge length 1 are given by:
 * $$\left(-\frac{2\sqrt{15}}{15},\,-\frac{\sqrt{10}}{5},\,0,\,0,\,0,\,±\frac12\right),$$
 * $$\left(-\frac{2\sqrt{15}}{15},\,\frac{\sqrt{10}}{20},\,-\frac{\sqrt6}{4},\,0,\,0,\,±\frac12\right),$$
 * $$\left(-\frac{2\sqrt{15}}{15},\,\frac{\sqrt{10}}{20},\,\frac{\sqrt6}{12},\,-\frac{\sqrt3}{3},\,0,\,±\frac12\right),$$
 * $$\left(-\frac{2\sqrt{15}}{15},\,-\frac{3\sqrt{10}}{20},\,\frac{\sqrt6}{12},\,\frac{\sqrt3}{6},\,±\frac12,\,±\frac12\right),$$
 * $$\left(\frac{\sqrt{15}}{15},\,-\frac{3\sqrt{10}}{20},\,-\frac{\sqrt6}{4},\,0,\,0,\,±\frac12\right),$$
 * $$\left(\frac{\sqrt{15}}{15},\,-\frac{3\sqrt{10}}{20},\,\frac{\sqrt6}{12},\,-\frac{\sqrt3}{3},\,0,\,±\frac12\right),$$
 * $$\left(\frac{\sqrt{15}}{15},\,-\frac{3\sqrt{10}}{20},\,\frac{\sqrt6}{12},\,\frac{\sqrt3}{6},\,±\frac12,\,±\frac12\right),$$
 * $$\left(\frac{\sqrt{15}}{15},\,\frac{\sqrt{10}}{10},\,\frac{\sqrt6}{6},\,\frac{\sqrt3}{3},\,0,\,±\frac12\right),$$
 * $$\left(\frac{\sqrt{15}}{15},\,\frac{\sqrt{10}}{10},\,-\frac{\sqrt6}{6},\,-\frac{\sqrt3}{3},\,0,\,±\frac12\right),$$
 * $$\left(\frac{\sqrt{15}}{15},\,\frac{\sqrt{10}}{10},\,\frac{\sqrt6}{6},\,-\frac{\sqrt3}{6},\,±\frac12,\,±\frac12\right),$$
 * $$\left(\frac{\sqrt{15}}{15},\,\frac{\sqrt{10}}{10},\,-\frac{\sqrt6}{6},\,\frac{\sqrt3}{6},\,±\frac12,\,±\frac12\right).$$

Representations
A rectified hexateric prism has the following Coxeter diagrams:


 * x o3x3o3o3o (full symmetry)
 * oo3xx3oo3oo3oo&#x (rectified hexateron atop rectified hexateron)
 * xx xo3ox3oo3oo&#x (pentachoric prism atop rectified pentachoric prism)