Octadiminished hecatonicosihexapentacosiheptacontahexaexon

The octadiminished hecatonicosihexapentacosiheptacontahexaexon or odinaq, also known as the tridiminished icosiheptaheptacontadipetic alterprism, is a convex scaliform polyexon, with and 8 tridiminished icosiheptaheptacontadipeta, 24 hexacontatetrapeta, 96 hexadecachoric scalenes, and 192 heptapeta 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 icosiheptaheptacontadipeton atop alternate tridiminished 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.
 * $$\left(0,0,0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)$$
 * $$\left(0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},0,0\right)$$
 * $$\left(0,\frac{1}{2},0,\frac{1}{2},0,\frac{1}{2},0\right)$$
 * $$\left(0,\frac{1}{2},\frac{1}{2},0,0,0,\frac{1}{2}\right)$$
 * $$\left(\frac{1}{2},0,0,\frac{1}{2},0,0,\frac{1}{2}\right)$$
 * $$\left(\frac{1}{2},0,\frac{1}{2},0,0,\frac{1}{2},0\right)$$