Rectified dischiliahecatonhexaconta-myriaheptachiliadiacosioctaconta-zetton

The rectified dischiliahecatonhexaconta-myriaheptachiliadiacosioctaconta-zetton, 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, small rhombated diacosipentacontahexazetton, small triprismated octadecazetton, exirhombated enneazetton, small terated hecatonicosihexapentacosiheptacontihexaexal prism, hexagonal-birectified hexeractic duoprism, triangular-demified icosiheptaheptacontadipetal duoprism, decachoral-small prismatodecachoral duoprism, truncated pentachoral-small rhombated pentachoral duoprism, rectified tesseractic duoprism, hexadecachoral-truncated hexadecachoral duoprism, cuboctahedral-rectified penteractic duoprism, octahedral-truncated triacontaditeral duoprism, truncated octahedral-triacontaditeral duoprism, tetrahedral-small rhombated demipenteractic duoprism, truncated tetrahedral-small prismated demipenteractic duoprism, square-truncated hexacontatetrapetal duoprism, square-rectified hexeractic duoprism, petitruncated octaexal prism, small birhombated octaexal prism, hexagonal-truncated hexateral duoprismatic prism, and triangular-bitruncated hexateral duoprismatic prism.

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 These are the coordinates of a birectified octeract, small rhombated diacosipentacontahexazetton, and small teridemiocteract, respectively.
 * $$\left(±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0,\,0\right),$$
 * $$\left(±\sqrt2,\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0,\,0,\,0,\,0,\,0\right),$$
 * $$\left(\frac{3\sqrt{2}}{4},\,\frac{3\sqrt{2}}{4},\,\frac{\sqrt{2}}{4},\,\frac{\sqrt{2}}{4},\,\frac{\sqrt{2}}{4},\,\frac{\sqrt{2}}{4},\,\frac{\sqrt{2}}{4},\,\frac{\sqrt{2}}{4}\right).$$