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Stericated 8-simplexes

Class of eight-dimensional polytopes From Wikipedia, the free encyclopedia

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In eight-dimensional geometry, a stericated 8-simplex is a convex uniform 8-polytope with 4th order truncations (sterication) of the regular 8-simplex. There are 16 unique sterications for the 8-simplex including permutations of truncation, cantellation, and runcination.

More information Orthogonal projections in A8 Coxeter plane ...
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Stericated 8-simplex

Stericated 8-simplex
Typeuniform 8-polytope
Schläfli symbolt0,4{3,3,3,3,3,3,3}
Coxeter-Dynkin diagrams
7-faces
6-faces
5-faces
4-faces
Cells
Faces
Edges6300
Vertices630
Vertex figure
Coxeter groupA8, [37], order 362880
Propertiesconvex

Acronym: secane (Jonathan Bowers)[1]

Coordinates

The Cartesian coordinates of the vertices of the stericated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,1,1,1,1,2). This construction is based on facets of the stericated 9-orthoplex.

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Bistericated 8-simplex

More information Bistericated 8-simplex ...

Acronym: sobcane (Jonathan Bowers)[2]

Coordinates

The Cartesian coordinates of the vertices of the bistericated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,1,1,1,1,2,2). This construction is based on facets of the bistericated 9-orthoplex.

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Steritruncated 8-simplex

More information Steritruncated 8-simplex ...

Acronym: catene (Jonathan Bowers)[3]

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Bisteritruncated 8-simplex

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Acronym: bictane (Jonathan Bowers)[4]

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Stericantellated 8-simplex

Acronym: crane (Jonathan Bowers)[5]

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Bistericantellated 8-simplex

Acronym: bocrane (Jonathan Bowers)[6]

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Stericantitruncated 8-simplex

Acronym: cograne (Jonathan Bowers)[7]

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Bistericantitruncated 8-simplex

Acronym: bocagrane (Jonathan Bowers)[8]

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Steriruncinated 8-simplex

Acronym: capene (Jonathan Bowers)[9]

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Bisteriruncinated 8-simplex

Acronym: bacpane (Jonathan Bowers)[10]

Images

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Steriruncitruncated 8-simplex

Acronym: coptane (Jonathan Bowers)[11]

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Bisteriruncitruncated 8-simplex

Acronym: bicpotane (Jonathan Bowers)[12]

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Steriruncicantellated 8-simplex

Acronym: coprene (Jonathan Bowers)[13]

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Bisteriruncicantellated 8-simplex

Acronym: bicprene (Jonathan Bowers)[14]

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Steriruncicantitruncated 8-simplex

Acronym: gacene (Jonathan Bowers)[15]

Images

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Bisteriruncicantitruncated 8-simplex

Acronym: gobcane (Jonathan Bowers)[16]

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The 16 presented polytopes are in the family of 135 uniform 8-polytopes with A8 symmetry.

More information A8 polytopes ...

Notes

References

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