Rectified dischiliahecatonhexaconta-myriaheptachiliadiacosioctaconta-zetton

The rectified dischiliahecatonhexaconta-myriaheptachiliadiacosioctaconta-zetton, or riffy, also called the rectified 421 polytope, is a convex uniform polyzetton. It has 240 hecatonicosihexapentacosiheptacontahexaexa, 2160 rectified hecatonicosoctaexa, and 17280 rectified octaexa. 2 hecatonicosihexapentacosiheptacontahexaexa, 27 rectified hecatonicosoctaexa, and 72 rectified octaexa join at each icosiheptaheptacontadipetic prismatic vertex. As the name suggests, it is the rectification of the dischiliahecatonhexaconta-myriaheptachiliadiacosioctaconta-zetton.

The rectified dischiliahecatonhexaconta-myriaheptachiliadiacosioctaconta-zetton contains the vertices and edges of a birectified octeract, small teridemiocteract, and small rhombated diacosipentacontahexazetton.

Vertex coordinates
Coordinates for the vertices of a rectified dischiliahecatonhexaconta-myriaheptachiliadiacosioctaconta-zetton with edge length 1 are given by all permutations and sign changes of as well as all permutations and even sign changes of
 * $$\left(±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0,\,0\right),$$
 * $$\left(±\sqrt2,\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0,\,0,\,0,\,0,\,0\right),$$
 * $$\left(\frac{3\sqrt{2}}{4},\,\frac{3\sqrt{2}}{4},\,\frac{\sqrt{2}}{4},\,\frac{\sqrt{2}}{4},\,\frac{\sqrt{2}}{4},\,\frac{\sqrt{2}}{4},\,\frac{\sqrt{2}}{4},\,\frac{\sqrt{2}}{4}\right).$$