Prismatorhombated pentachoric prism

The prismatorhombated pentachoric prism or prippip is a prismatic uniform polyteron. It consists of 2 prismatorhombated pentachora, 5 cuboctahedral prisms, 5 truncated tetrahedral prisms, 10 square-hexagonal duoprisms, and 10 triangular-square duoprisms. 1 prismatorhombated pentachoron, 1 cuboctahedral prism, 1 truncated tetrahedral prism, 2 square-hexagonal duoprisms, and 1 triangular-square duoprism join at each vertex. As the name suggests, it is a prism based on the prismatorhombated pentachoron, which also makes it a convex segmentoteron.

Vertex coordinates
The vertices of a prismatorhombated pentachoric prism of edge length 1 are given by:
 * $$\left(\frac{\sqrt{10}}{10},\,-\frac{\sqrt6}{6},\,\frac{\sqrt3}{6},\,±\frac32,\,±\frac12\right),$$
 * $$\left(\frac{\sqrt{10}}{10},\,\frac{\sqrt6}{6},\,-\frac{\sqrt3}{6},\,±\frac32,\,±\frac12\right),$$
 * $$\left(\frac{\sqrt{10}}{10},\,-\frac{\sqrt6}{6},\,\frac{2\sqrt3}{3},\,±1,\,±\frac12\right),$$
 * $$\left(\frac{\sqrt{10}}{10},\,\frac{\sqrt6}{6},\,-\frac{2\sqrt3}{3},\,±1,\,±\frac12\right),$$
 * $$\left(\frac{\sqrt{10}}{10},\,-\frac{\sqrt6}{6},\,-\frac{5\sqrt3}{6},\,±\frac12,\,±\frac12\right),$$
 * $$\left(\frac{\sqrt{10}}{10},\,\frac{\sqrt6}{6},\,\frac{5\sqrt3}{6},\,±\frac12,\,±\frac12\right),$$
 * $$\left(\frac{\sqrt{10}}{10},\,±\frac{\sqrt6}{2},\,0,\,±1,\,±\frac12\right),$$
 * $$\left(\frac{\sqrt{10}}{10},\,±\frac{\sqrt6}{2},\,±\frac{\sqrt3}{2},\,±\frac12,\,±\frac12\right),$$
 * $$\left(\frac{7\sqrt{10}}{20},\,-\frac{\sqrt6}{12},\,\frac{\sqrt3}{3},\,±1,\,±\frac12\right),$$
 * $$\left(\frac{7\sqrt{10}}{20},\,-\frac{\sqrt6}{12},\,-\frac{2\sqrt3}{3},\,0,\,±\frac12\right),$$
 * $$\left(\frac{7\sqrt{10}}{20},\,\frac{\sqrt6}{4},\,0,\,±1,\,±\frac12\right),$$
 * $$\left(\frac{7\sqrt{10}}{20},\,\frac{\sqrt6}{4},\,±\frac{\sqrt3}{2},\,±\frac12,\,±\frac12\right),$$
 * $$\left(\frac{7\sqrt{10}}{20},\,-\frac{5\sqrt6}{12},\,\frac{\sqrt3}{6},\,±\frac12,\,±\frac12\right),$$
 * $$\left(\frac{7\sqrt{10}}{20},\,-\frac{5\sqrt6}{12},\,-\frac{\sqrt3}{3},\,0,\,±\frac12\right),$$
 * $$\left(-\frac{3\sqrt{10}}{20},\,\frac{\sqrt6}{12},\,\frac{\sqrt3}{6},\,±\frac32,\,±\frac12\right),$$
 * $$\left(-\frac{3\sqrt{10}}{20},\,\frac{\sqrt6}{12},\,\frac{2\sqrt3}{3},\,±1,\,±\frac12\right),$$
 * $$\left(-\frac{3\sqrt{10}}{20},\,\frac{\sqrt6}{12},\,-\frac{5\sqrt3}{6},\,±\frac12,\,±\frac12\right),$$
 * $$\left(-\frac{3\sqrt{10}}{20},\,\frac{5\sqrt6}{12},\,\frac{\sqrt3}{3},\,±1,\,±\frac12\right),$$
 * $$\left(-\frac{3\sqrt{10}}{20},\,\frac{5\sqrt6}{12},\,-\frac{2\sqrt3}{3},\,0,\,±\frac12\right),$$
 * $$\left(-\frac{3\sqrt{10}}{20},\,-\frac{7\sqrt6}{12},\,-\frac{\sqrt3}{6},\,±\frac12,\,±\frac12\right),$$
 * $$\left(-\frac{3\sqrt{10}}{20},\,-\frac{7\sqrt6}{12},\,\frac{\sqrt3}{3},\,0,\,±\frac12\right),$$
 * $$\left(-\frac{2\sqrt{10}}{5},\,0,\,0,\,±1,\,±\frac12\right),$$
 * $$\left(-\frac{2\sqrt{10}}{5},\,0,\,±\frac{\sqrt3}{2},\,±\frac12,\,±\frac12\right),$$
 * $$\left(-\frac{2\sqrt{10}}{5},\,-\frac{\sqrt6}{3},\,-\frac{\sqrt3}{6},\,±\frac12,\,±\frac12\right),$$
 * $$\left(-\frac{2\sqrt{10}}{5},\,\frac{\sqrt6}{3},\,\frac{\sqrt3}{6},\,±\frac12,\,±\frac12\right),$$
 * $$\left(-\frac{2\sqrt{10}}{5},\,-\frac{\sqrt6}{3},\,\frac{\sqrt3}{3},\,0,\,±\frac12\right),$$
 * $$\left(-\frac{2\sqrt{10}}{5},\,\frac{\sqrt6}{3},\,-\frac{\sqrt3}{3},\,0,\,±\frac12\right).$$