Bitruncated hecatonicosihexapentacosiheptacontahexaexon

The bitruncated hecatonicosihexapentacosiheptacontahexaexon, or botnaq, also called the bitruncated 321 polytope, is a convex uniform polyexon. It has 56, 576 , and 126. 2 truncated icosiheptaheptacontadipeta, 5 bitruncated heptapeta, and 5 bitruncated hexacontatetrapeta join at each vertex. As the name suggests, it is the bitruncation of the hecatonicosihexapentacosiheptacontahexaexon.

Vertex coordinates
The vertices of a bitruncated hecatonicosihexapentacosiheptacontahexaexon of edge length 1, centered at the origin, are given by all permutations of first 6 coordinates of all permutations and even sign changes of the first 6 coordinates of and all permutations and odd sign changes of the first 6 coordinates of
 * $$\left(±\sqrt2,\,±\sqrt2,\,±\frac{\sqrt2}{2},\,0,\,0,\,0,\,±\frac52\right),$$
 * $$\left(±\frac{3\sqrt2}{2},\,±\sqrt2,\,±\sqrt2,\,±\sqrt2,\,0,\,0,\,±\frac12\right),$$
 * $$\left(\frac{5\sqrt2}{4},\,\frac{5\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,±2\right),$$
 * $$\left(\frac{3\sqrt2}{2},\,\sqrt2,\,\frac{\sqrt2}{2},\,\frac{\sqrt2}{2},\,\frac{\sqrt2}{2},\,\frac{\sqrt2}{2},\,±\frac32\right),$$
 * $$\left(\frac{7\sqrt2}{4},\,\frac{3\sqrt2}{4},\,\frac{3\sqrt2}{4},\,\frac{3\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,±1\right),$$
 * $$\left(2\sqrt2,\,\frac{\sqrt2}{2},\,\frac{\sqrt2}{2},\,\frac{\sqrt2}{2},\,\frac{\sqrt2}{2},\,\frac{\sqrt2}{2},\,±\frac12\right),$$
 * $$\left(\frac{5\sqrt2}{4},\,\frac{5\sqrt2}{4},\,\frac{5\sqrt2}{4},\,\frac{3\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,0\right).$$