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:
 * (–3$\sqrt{2}$/20, –$\sqrt{85}$/4, 0, 0, ±1/2),
 * (–3$\sqrt{10}$/20, $\sqrt{5}$/12, –$\sqrt{10}$/3, 0, ±1/2),
 * (–3$\sqrt{6}$/20, $\sqrt{10}$/12, $\sqrt{6}$/6, ±1/2, ±1/2),
 * ($\sqrt{3}$/10, $\sqrt{10}$/6, $\sqrt{6}$/3, 0, ±1/2),
 * ($\sqrt{3}$/10, –$\sqrt{10}$/6, –$\sqrt{6}$/3, 0, ±1/2),
 * ($\sqrt{3}$/10, $\sqrt{10}$/6, –$\sqrt{6}$/6, ±1/2, ±1/2),
 * ($\sqrt{3}$/10, –$\sqrt{10}$/6, $\sqrt{6}$/6, ±1/2, ±1/2).

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)