Rectified hexacosichoron

The rectified hexacosichoron, or rox, also commonly called the rectified 600-cell or the snub tetrahedral hecatonicosachoron, is a convex uniform polychoron that consists of 600 regular octahedra and 120 regular icosahedra. Two icosahedra and 5 octahedra join at each pentagonal prismatic vertex. As the name suggests, it can be obtained by rectifying the hexacosichoron.

Vertex coordinates
The vertices of a rectified hexacosichoron of edge length 1 are given by all permutations of: along with even permutations of:
 * (0, 0, ±(1+$\sqrt{5+2√5}$)/2, ±(3+$\sqrt{5}$)/2),
 * (±1/2, ±1/2, ±(2+$\sqrt{5}$)/2, ±(2+$\sqrt{7+3√5}$)/2),
 * (0, ±1/2, ±(1+$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/4),
 * (0, ±(3+$\sqrt{5}$)/4, ±(2+$\sqrt{5}$)/2, +·5+$\sqrt{5}$)/4),
 * (±1/2, ±(1+$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2, ±·3+$\sqrt{5}$)/4),
 * (±(1+$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/4, ±·1+$\sqrt{5}$)/2, ±(2+$\sqrt{5}$)/2).

Representations
A rectified hexacosichoron has the following Coxeter diagrams:


 * o5o3x3o (full symmetry)
 * DCBAVFfxoo ooxooxxoof5oxoofoxxoo3xoxFofofVx5&#zx (H3×A1 symmetry)
 * AoooFxoxVofoFofxxf5oAooxFxooVofoFxfxf ooAoxoFxofVoxfFofx5oooAoxxFfooVfxoFfx&#zx (H2×H2 symmetry)
 * ooxooxxo(of)oxxooxoo5oxoofoxx(oo)xxofooxo3xoxFofof(Vx)fofoFxox&#xt (H3 axial, icosahedron-first)

Related polychora
The segmentochoron icosahedron atop icosidodecahedron can be obtained as a cap of the rectified hexacosichoron in icosahedron-first orientation; the second segment in this orientation is [[icosidodecahedron atop small rhombicosidodecahedron.