Small rhombated pentachoron

The small rhombated pentachoron, or srip, also commonly called the cantellated 5-cell, is a convex uniform polychoron that consists of 5 regular octahedra, 10 triangular prisms, and 5 cuboctahedra. 1 octahedron, 2 triangular prisms, and 2 cuboctahedra join at each vertex. As one of its names suggests, it can be obtained by cantellating the pentachoron.

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


 * ($\sqrt{2}$/5, 0, 0, ±1),
 * ($\sqrt{35}$/5, 0, ±$\sqrt{5}$/2, ±1/2),
 * ($\sqrt{6}$/5, –$\sqrt{6}$/3, $\sqrt{10}$/3, 0),
 * ($\sqrt{10}$/5, $\sqrt{3}$/3, –$\sqrt{10}$/3, 0),
 * ($\sqrt{6}$/5, –$\sqrt{3}$/3, –$\sqrt{10}$/6, ±1/2),
 * ($\sqrt{6}$/5, $\sqrt{3}$/3, $\sqrt{10}$/6, ±1/2),
 * (–3$\sqrt{6}$/10, –$\sqrt{3}$/6, –$\sqrt{10}$/3, 0),
 * (–3$\sqrt{6}$/10, $\sqrt{3}$/6, $\sqrt{10}$/3, 0),
 * (–$\sqrt{6}$/20, –$\sqrt{3}$/12, –2$\sqrt{10}$/3, 0),
 * (–$\sqrt{6}$/20, –5$\sqrt{3}$/12, –$\sqrt{10}$/3, 0),
 * (–$\sqrt{6}$/20, $\sqrt{3}$/4, 0, ±1),
 * (–$\sqrt{10}$/20, –$\sqrt{6}$/12, $\sqrt{3}$/3, ±1),
 * (–$\sqrt{10}$/20, –5$\sqrt{6}$/12, $\sqrt{10}$/6, ±1/2),
 * (–$\sqrt{6}$/20, $\sqrt{3}$/4, ±$\sqrt{10}$/2, ±1/2),
 * (–3$\sqrt{6}$/10, –$\sqrt{3}$/6, $\sqrt{10}$/6, ±1/2),
 * (–3$\sqrt{6}$/20, $\sqrt{3}$/6, –$\sqrt{10}$/6, ±1/2).

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


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

Representations
A small rhombated pentachoron has the following Coxeter diagrams:


 * x3o3x3o (full symmetry)
 * oxx3xxo3oox&#xt (A3 axial, octahedron-first)
 * x(uo)xo x(ou)xx3o(xo)xo&#xt (A2×A1 axial, triangular prism-first)

Related polychora
When viewed in A3 axial symmetry, the small rhombated pentachoron can be cut into 2 segmentochora, namely cuboctahedron atop truncated tetrahedron and octahedron atop truncated tetrahedron, join at the truncated tetrahedral bases.

The triangular pucofastegium occurs as the triangle-first cap of the small rhombated pentachoron.