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.

Blending 10 rectified hexacosichora results in the small disnub dishexacosichoron, which is uniform.

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.

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Icosahedron (120): Hexacosichoron
 * Octahedron (600): Hecatonicosachoron
 * Triangle (1200): Rectified hecatonicosachoron
 * Triangle (2400): Semi-uniform small disprismatotesseractihexadecachoron
 * Edge (3600): Small rhombated hexacosichoron