Diacositetraconta-myriaheptachiliadiacosioctaconta-zetton

The diacositetraconta-myriaheptachiliadiacosioctaconta-zetton, abbreviated as 240-17280-zetton, also known as bay or the 241 polytope, is a uniform polyzetton. It consists of 17280 octaexa and 240 pentacontahexapentacosiheptacontahexaexa, with 14 pentacontahexapentacosiheptacontahexaexa and 64 octaexa joining at each vertex forming a demihepteract as the vertex figure.

The diacositetraconta-myriaheptachiliadiacosioctaconta-zetton contains the vertices and edges of the truncated enneazetton, small cellated enneazetton, small biterioctadecazetton, trirectified diacosipentacontahexazetton, small petidemiocteract, pentacontahexahecatonicosihexaexic prism, triangular-rectified icosiheptaheptacontidipetic duoprism, hexagonal-pentacontatetrapetic duoprism, pentachoric-truncated pentachoric duoprism, rectified pentachoric-small rhombated pentachoric duoprism, small prismatodecachoric duoprism, square-birectified hexacontatetrapetic duoprism, octahedral-penteractitriacontiditeric duoprism, cuboctahedral-rectified triacontiditeric duoprism, hexadecachoric-rectified tesseractic duoprism, icositetrachoric duoprism, tetrahedral-small prismated demipenteractic duoprism, truncated tetrahedral-demipenteractic duoprism, small cellated octaexic prism, triangular-small prismated hexateric duoprismatic prism, hexagonal-dodecateric duoprismatic prism, triangular-triangular-triangular-hexagonal tetraprism, tesseractic-icositetrachoric duoprism, square-octahedral-cuboctahedral duoprism, and the octeract.

Vertex coordinates
Coordinates for a diacositetraconta-myriaheptachiliadiacosioctaconta-zetton with edge length 1 are given by all permutations of all permutations of and all permutations and odd sign changes of
 * $$\left(±\sqrt2,\,0,\,0,\,0,\,0,\,0,\,0,\,0\right),$$
 * $$\left(±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0,\,0,\,0,\,0\right),$$
 * $$\left(\frac{3\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4}\right).$$

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


 * x3o3o3o *c3o3o3o3o (full symmetry)
 * xooox3ooooo3ooooo3oxoxo *c3ooooo3ooxoo3ooooo&#xt (E7 axial, pentacontahexapentacosiheptacontahexaexon-first)
 * oxo3ooo3ooo *b3ooo3xoo3ooo3ooo3oxu&#zx (D8 subsymmetry)
 * xxooo3xoxoo3ooooo3oooxo3oxooo3ooooo3ooxox3oooxx&#zx (A8 subsymmetry)