Octadiminished hecatonicosihexapentacosiheptacontahexaexon

The octadiminished hecatonicosihexapentacosiheptacontahexaexon, or odinaq, is a convex scaliform polyexon, with 24 hexacontatetrapeta, 192 heptapeta, 96 hexadecachoric scalenes, and 8 tridiminished icosiheptaheptacontadipeta as facets. As its name suggests, the octadiminished hecatonicosihexapentacosiheptacontahexaexon is formed by removing 8 vertices (corresponding to a cube) from a hecatonicosihexapentacosiheptacontahexaexon.

It is a convex segmentotoexon, as a tridiminished rectified icosiheptaheptacontadipeton atop alternate tridiminished rectified icosiheptaheptacontadipeton.

Just as the hecatonicosihexapentacosiheptacontahexaexon is the convex hull of two alternate rectified octaexa, the octadiminished hecatonicosihexapentacosiheptacontahexaexon is the hull of two alternate tetradiminished rectified octaexa.

Vertex coordinates
The vertices of an octadiminished hecatonicosihexapentacosiheptacontahexaexon of edge length 1, centered at the origin, are given by: Alternatively, the vertices are given by all sign changes of the following:
 * $$\left(±\frac{\sqrt2}{2},\,0,\,0,\,0,\,0,\,0,\,±\frac12\right)$$ and all permutations of the first 4 coordinates,
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,0\right)$$ and all even sign changes of the first 6 coordinates.
 * $$\left(0,0,0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)$$
 * $$\left(0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},0,0\right)$$
 * $$\left(0,\frac{1}{2},0,\frac{1}{2},0,\frac{1}{2},0\right)$$
 * $$\left(0,\frac{1}{2},\frac{1}{2},0,0,0,\frac{1}{2}\right)$$
 * $$\left(\frac{1}{2},0,0,\frac{1}{2},0,0,\frac{1}{2}\right)$$
 * $$\left(\frac{1}{2},0,\frac{1}{2},0,0,\frac{1}{2},0\right)$$