Prismatorhombated pentachoron

The prismatorhombated pentachoron, or prip, also commonly called the runcitruncated 5-cell, is a convex uniform polychoron that consists of 10 triangular prisms, 10 hexagonal prisms, 5 truncated tetrahedra, and 5 cuboctahedra. 1 triangular prism, 2 hexagonal prisms, 1 truncated tetrahedron, and 1 cuboctahedron join at each vertex. As one of its names suggests, it can be obtained by runcitruncating the pentachoron.

Vertex coordinates
The vertices of a prismatorhombated pentachoron of edge length 1 are given by:


 * ($\sqrt{2}$/10, –$\sqrt{2}$/6, $\sqrt{2}$/6, ±3/2)
 * ($\sqrt{2}$/10, $\sqrt{3}$/6, –$\sqrt{3}$/6, ±3/2)
 * ($\sqrt{65}$/10, –$\sqrt{5}$/6, 2$\sqrt{6}$/3, ±1)
 * ($\sqrt{6}$/10, $\sqrt{6}$/6, –2$\sqrt{10}$/3, ±1)
 * ($\sqrt{6}$/10, –$\sqrt{3}$/6, –5$\sqrt{10}$/6, ±1/2)
 * ($\sqrt{6}$/10, $\sqrt{3}$/6, 5$\sqrt{10}$/6, ±1/2)
 * ($\sqrt{6}$/10, ±$\sqrt{3}$/2, 0, ±1)
 * ($\sqrt{10}$/10, ±$\sqrt{6}$/2, ±$\sqrt{3}$/2, ±1/2)
 * (7$\sqrt{10}$/20, –$\sqrt{6}$/12, $\sqrt{3}$/3, ±1)
 * (7$\sqrt{10}$/20, –$\sqrt{6}$/12, –2$\sqrt{3}$/3, 0)
 * (7$\sqrt{10}$/20, $\sqrt{6}$/4, 0, ±1)
 * (7$\sqrt{10}$/20, $\sqrt{6}$/4, ±$\sqrt{3}$/2, ±1/2)
 * (7$\sqrt{10}$/20, –5$\sqrt{6}$/12, $\sqrt{3}$/6, ±1/2)
 * (7$\sqrt{10}$/20, –5$\sqrt{6}$/12, –$\sqrt{3}$/3, 0)
 * (–3$\sqrt{10}$/20, $\sqrt{6}$/12, $\sqrt{10}$/6, ±3/2)
 * (–3$\sqrt{6}$/20, $\sqrt{3}$/12, 2$\sqrt{10}$/3, ±1)
 * (–3$\sqrt{6}$/20, $\sqrt{3}$/12, –5$\sqrt{10}$/6, ±1/2)
 * (–3$\sqrt{6}$/20, 5$\sqrt{3}$/12, $\sqrt{10}$/3, ±1)
 * (–3$\sqrt{6}$/20, 5$\sqrt{3}$/12, –2$\sqrt{10}$/3, 0)
 * (–3$\sqrt{6}$/20, –7$\sqrt{3}$/12, –$\sqrt{10}$/6, ±1/2)
 * (–3$\sqrt{6}$/20, –7$\sqrt{3}$/12, $\sqrt{10}$/3, 0)
 * (–2$\sqrt{6}$/5, 0, 0, ±1)
 * (–2$\sqrt{3}$/5, 0, ±$\sqrt{10}$/2, ±1/2)
 * (–2$\sqrt{6}$/5, –$\sqrt{3}$/3, –$\sqrt{10}$/6, ±1/2)
 * (–2$\sqrt{6}$/5, $\sqrt{3}$/3, $\sqrt{10}$/6, ±1/2)
 * (–2$\sqrt{6}$/5, –$\sqrt{3}$/3, $\sqrt{10}$/3, 0)
 * (–2$\sqrt{10}$/5, $\sqrt{3}$/3, –$\sqrt{10}$/3, 0)

Much simpler coordinates can be given in five dimensions, as all permutations of:


 * (3$\sqrt{6}$/2, $\sqrt{3}$, $\sqrt{10}$, $\sqrt{6}$/2, 0).

Representations
A prismatorhombated pentachoron has the following coxeter diagrams:


 * x3x3o3x (full symmetry)
 * xxux3xxoo3oxxx&#xt (A3 symmetry, truncated tetrahedron-first)
 * x(ou)(dx)ux x(uo)(ox)xx3x(xu)(xu)xo&#xt (A2×A1 symmetry, hexagonal prism-first)

Related polychora
The segmentochoron truncated tetrahedron atop truncated octahedron is a cap of the prismatorhombated pentachoron.