2 41 polytope

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2 41 polytope
Rank8
TypeUniform
Notation
Bowers style acronymBay
Coxeter diagramx3o3o3o *c3o3o3o3o ()
Elements
Zetta17280 octaexa, 240 pentacontahexapentacosiheptacontahexaexa
Exa138240 heptapeta, 6720 icosiheptaheptacontadipeta
Peta483840 hexatera, 60480 triacontaditera
Tera241920+967680 pentachora
Cells1209600 tetrahedra
Faces483840 triangles
Edges69120
Vertices2160
Vertex figureDemihepteract, edge length 1
Measures (edge length 1)
Circumradius
Hypervolume
Dizettal anglesLaq–hop–oca:
 Laq–jak–laq: 120°
Central density1
Number of external pieces17520
Level of complexity5
Related polytopes
ArmyBay
RegimentBay
ConjugateNone
Abstract & topological properties
Flag count3483648000
Euler characteristic0
OrientableYes
Properties
SymmetryE8, order 696729600
ConvexYes
NatureTame

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 trioprism, and the octeract.

Vertex coordinates[edit | edit source]

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

Representations[edit | edit source]

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)

External links[edit | edit source]