2 41 polytope
2 41 polytope | |
---|---|
Rank | 8 |
Type | Uniform |
Notation | |
Bowers style acronym | Bay |
Coxeter diagram | x3o3o3o *c3o3o3o3o () |
Elements | |
Zetta | 17280 octaexa, 240 pentacontahexapentacosiheptacontahexaexa |
Exa | 138240 heptapeta, 6720 icosiheptaheptacontadipeta |
Peta | 483840 hexatera, 60480 triacontaditera |
Tera | 241920+967680 pentachora |
Cells | 1209600 tetrahedra |
Faces | 483840 triangles |
Edges | 69120 |
Vertices | 2160 |
Vertex figure | Demihepteract, edge length 1 |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Dizettal angles | Laq–hop–oca: |
Laq–jak–laq: 120° | |
Central density | 1 |
Number of external pieces | 17520 |
Level of complexity | 5 |
Related polytopes | |
Army | Bay |
Regiment | Bay |
Conjugate | None |
Abstract & topological properties | |
Flag count | 3483648000 |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | E8, order 696729600 |
Convex | Yes |
Nature | Tame |
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]
- Klitzing, Richard. "bay".
- Wikipedia contributors. "241 polytope".