Rectified pentachoric prism

The rectified pentachoric prism or rappip is a prismatic uniform polyteron that consists of 2 rectified pentachora, 5 octahedral prisms and 5 tetrahedral prisms. 1 rectified pentachoron, 2 tetrahedral prisms, and 3 octahedral prisms join at each vertex. As the name suggests, it is a prism based on the rectified pentachoron. As such it is also a convex segmentoteron.

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

Representations
A rectified pentachoric prism has the following Coxeter diagrams:


 * x o3x3o3o (full symmetry)
 * oo3xx3oo3oo&#x (A4 symmetry, as segmentoteron)
 * xx xo3ox3oo&#x (A3×A1 axial, tetrahedral prism atop octahedral prism)
 * xxx oxo oxo3oox&#xt (A2×A1×A1 symmetry, edge-first)