Small terademified pentacontahexapentacosiheptacontahexaexon

The small terademified pentacontahexapentacosiheptacontahexaexon, or sethalq, also called the small teridemified 231 polytope, is a convex uniform polyexon. It has 56, 756 small prismatodemipenteractic prisms, 4032 triangular-small prismatodecachoric prisms, 576 , 10080 triangular-tetrahedral duoprismatic prisms, 2016 small cellidodecateric prisms, and 126 small cellidemihexeracts. 1 demified icosiheptaheptacontadipeton, 5 small prismatodemipenteractic prisms, 10 triangular-small prismatodecachoric prisms, 1 small teritetradecapeton, 10 triangular-tetrahedral duoprismatic prisms, 5 small cellidodecateric prisms, and 1 small cellidemihexeract join at each vertex.

Vertex coordinates
The vertices of a small terademified pentacontahexapentacosiheptacontahexaexon 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
 * $$\left(±\sqrt2,\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0,\,±2\right),$$
 * $$\left(±\frac{3\sqrt2}{2},\,±\sqrt2,\,±\frac{\sqrt2}{2},\,0,\,0,\,0,\,±1\right),$$
 * $$\left(±\sqrt2,\,±\sqrt2,\,±\sqrt2,\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0,\,±1\right),$$
 * $$\left(±\frac{3\sqrt2}{2},\,±\sqrt2,\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0,\,0\right),$$
 * $$\left(\frac{3\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,±\frac52\right),$$
 * $$\left(\frac{3\sqrt2}{4},\,\frac{3\sqrt2}{4},\,\frac{3\sqrt2}{4},\,\frac{3\sqrt2}{4},\,\frac{3\sqrt2}{4},\,\frac{\sqrt2}{4},\,±\frac32\right),$$
 * $$\left(\frac{5\sqrt2}{4},\,\frac{5\sqrt2}{4},\,\frac{3\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,±\frac12\right),$$
 * $$\left(\frac{5\sqrt2}{4},\,\frac{3\sqrt2}{4},\,\frac{3\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,±\frac32\right),$$
 * $$\left(\frac{3\sqrt2}{2},\,\frac{\sqrt2}{2},\,\frac{\sqrt2}{2},\,\frac{\sqrt2}{2},\,\frac{\sqrt2}{2},\,\frac{\sqrt2}{2},\,±1\right),$$
 * $$\left(\frac{7\sqrt2}{4},\,\frac{3\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,±\frac12\right),$$
 * $$\left(\frac{5\sqrt2}{4},\,\frac{3\sqrt2}{4},\,\frac{3\sqrt2}{4},\,\frac{3\sqrt2}{4},\,\frac{3\sqrt2}{4},\,\frac{\sqrt2}{4},\,±\frac12\right).$$