Dischiliahecatonhexaconta-myriaheptachiliadiacosioctaconta-zetton

The dischiliahecatonhexaconta-myriaheptachiliadiacosioctaconta-zetton, abbreviated as 2160-17280-zetton, also known as fy, the E8 polytope, or the 421 polytope, is a uniform polyzetton. It consists of 2160 hecatonicosoctaexa and 17280 octaexa as facets, with 126 hecatonicosoctaexa and 576 octaexa as facets forming a hecatonicosihexapentacosiheptacontahexaexon as the vertex figure.

The dischiliahecatonhexaconta-myriaheptachiliadiacosioctaconta-zetton contains the vertices and edges of the birectified enneazetton, small exioctadecazetton, demiocteract, rectified diacosipentacontahexazetton, hecatonicosihexapentacosiheptacontahexaexic prism, triangular-icosiheptaheptacontidipetic duoprism, pentachoric-rectified pentachoric duoprism, tetrahedral-demipenteractic duoprism, hexadecachoric duoprism, octahedral-triacontiditeric duoprism, square-hexacontatetrapetic duoprism, rectified octaexic prism, and triangular-hexateric duoprismatic prism.

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

Representations
A dischiliahecatonhexaconta-myriaheptachiliadiacosioctaconta-zetton has the following Coxeter diagrams:


 * o3o3o3o *c3o3o3o3x (full symmetry)
 * ooxoo3ooooo3ooooo3ooooo *c3ooooo3ooooo3oxoxo&#xt (E7 axial, vertex-first)
 * oxooo3ooooo3oooxo *b3ooooo3ooooo3ooxoo3xooox&#xt (D7 axial, hecatonicosoctaexon-first)
 * xo3oo3oo *b3oo3oo3oo3ox3oo&#zx (D8 subsymmetry)
 * oxo3ooo3xoo3ooo3ooo3oox3ooo3oxo&#zx (A8 subsymmetry)
 * xooxooo3oooooxo3ooxoooo3ooooooo3ooooxoo3oxooooo3oooxoox&#xt (A7 axial, octaexon-first)
 * xoxooo3ooooxo3ooooox3xooxoo oxooox3ooxooo3oooxoo3oxooxo&#zx (A4×A4 subsymmetry)
 * ooxoo3xoooo3oooxo *b3oooox ooxoo3oxooo3oooxo *f3oooox&#zx (D4×D4 subsymmetry)
 * xoxo3xoox ooxo3oooo3oooo3oooo3ooox *e3oxoo&#zx (A6×A2 subsymmetry)