Truncated hecatonicosihexapentacosiheptacontahexaexon

The truncated hecatonicosihexapentacosiheptacontahexaexon, or tanq, also called the truncated 321 polytope, is a convex uniform polyexon. It has 56 icosiheptaheptacontadipeta, 126 truncated hexacontatetrapeta, and 576 rectified heptapeta. 1 icosiheptaheptacontadipeton, 10 truncated hexacontatetrapeta and 16 truncated heptapeta join at each vertex. As the name suggests, it is the truncation of the hecatonicosihexapentacosiheptacontahexaexon.

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


 * $$\left(±\sqrt2,\,±\frac{\sqrt2}{2},\,0,\,0,\,0,\,0,\,±\frac32\right)$$ and all permutations of first 6 coordinates,
 * $$\left(\frac{5\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,±1\right)$$ and all even sign changes and all permutations of the first 6 coordinates,
 * $$\left(\sqrt2,\,\frac{\sqrt2}{2},\,\frac{\sqrt2}{2},\,\frac{\sqrt2}{2},\,\frac{\sqrt2}{2},\,\frac{\sqrt2}{2},\,±\frac12\right)$$ and all even sign changes and all permutations of the first 6 coordinates,
 * $$\left(±\frac{3\sqrt2}{2},\,0,\,0,\,0,\,0,\,0,\,±\frac12\right)$$ and all permutations of first 6 coordinates,
 * $$\left(\frac{3\sqrt2}{4},\,\frac{3\sqrt2}{4},\,\frac{3\sqrt2}{4},\,\frac{3\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,0\right)$$ and all even sign changes and all permutations of the first 6 coordinates.

Representations
A rectified hecatonicosihexapentacosiheptacontahexaexon has the following Coxeter diagrams:


 * o3o3o3o *c3o3x3o (full symmetry)
 * xuxuxooo3ooxooooo3oooooooo3oooooxoo3oooxuxux *c3oooooooo&#xt (E6 axial, icosiheptaheptacontadipeton-first)
 * ox(uo)x(ou)xo3oo(oo)x(oo)oo3oo(oo)o(oo)oo *b3oo(oo)o(oo)oo3xo(oo)o(oo)ox3xu(ud)o(du)ux&#xt (D6 axial, truncated hexacontatetrapeton-first)
 * xooo3xuxo3xooo3oooo3ooox3oxux3ooox&#zx (A7 symmetry)