Rectified hexacosichoron

{{Infobox polytope The rectified hexacosichoron, or rit, is a convex uniform polychoron that consists of 600 regular octahedra and 120 regular icosahedra. Two icosahedra and 5 icosahedra join at each pentagonal prismatic vertex. As the name suggests, it can be obtained by rectifying the hexacosichoron.
 * type=Uniform
 * dim = 4
 * img=SRectified_600-cell_schlegel_halfsolid.png
 * obsa = Rox
 * cells = 600 octahedra, 120 icosahedra
 * faces = 1200+2400 triangles
 * edges = 3600
 * vertices = 720
 * verf = Pentagonal prism, edge length 1)
 * coxeter = o5o3x3o
 * army=Rox
 * reg=Rox
 * symmetry = H4
 * circum = $\sqrt{5+2√5}$ ≈ 3.07768
 * hypervolume = 25(31+15$\sqrt{5}$)/4 ≈ 403.38137
 * dich= Oct–3–oct: acos(–(1+3$\sqrt{5}$)/8) ≈ 164.47751º
 * dich2= Ike–3–oct: acos(–{{radic{7+3$\sqrt{5}$}}/4) ≈ 157.76124°
 * dual = Pentagonal-bipyramidal heptacosicosachoron
 * conjugate=Rectified grand hexacosichoron
 * conv = Yes
 * orientable=Yes
 * nat=Tame}}

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+)/2, ±(3+$\sqrt{5}$)/2)
 * (±1/2, ±1/2, ±(2+$\sqrt{5}$)/2, ±·2+$\sqrt{5}$)/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)