Rectified hecatonicosihexapentacosiheptacontahexaexon

The rectified hecatonicosihexapentacosiheptacontahexaexon, or ranq, also called the rectified 321 polytope, is a convex uniform polyexon. It has 56 icosiheptaheptacontadipeta, 126 rectified hexacontatetrapeta, and 576 rectified heptapeta. 2 icosiheptaheptacontadipeta, 10 rectified hexacontatetrapeta and 16 rectified heptapeta join at each demipenteractic prismatic vertex. As the name suggests, it is the rectification of the hecatonicosihexapentacosiheptacontahexaexon.

Vertex coordinates
The vertices of a rectified hecatonicosihexapentacosiheptacontahexaexon of edge length 1, centered at the origin, are given by:


 * $$\left(±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0,\,0,\,0,\,0,\,±1\right)$$ and all permutations of first 6 coordinates
 * $$\left(\frac{3\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,±\frac12\right)$$ and all even sign changes and all permutations of the first 6 coordinates
 * $$\left(±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0,\,0,\,0\right)$$ and all permutations of first 6 coordinates
 * $$\left(±\sqrt2,\,0,\,0,\,0,\,0,\,0,\,0\right)$$ and all permutations of first 6 coordinates

Representations
A rectified hecatonicosihexapentacosiheptacontahexaexon has the following Coxeter diagrams:


 * o3o3o3o *c3o3x3o (full symmetry)
 * xoxoo3oxooo3ooooo3oooxo3ooxox *c3ooooo&#xt (E6 axial, icosiheptaheptacontadipeton-first)
 * ox(oo)xo3oo(xo)oo3oo(oo)oo *b3oo(oo)oo3xo(oo)ox3ox(ou)xo&#xt (D6 axial, rectified hexacontatetrapeton-first)