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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.
This article's lead section may be too short to adequately summarize the key points. (September 2024) |
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Stericated 8-simplex
Stericated 8-simplex | |
---|---|
Type | uniform 8-polytope |
Schläfli symbol | t0,4{3,3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7-faces | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 6300 |
Vertices | 630 |
Vertex figure | |
Coxeter group | A8, [37], order 362880 |
Properties | convex |
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.
Images
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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.
Images
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Steritruncated 8-simplex
Acronym: catene (Jonathan Bowers)[3]
Images
Bisteritruncated 8-simplex
Acronym: bictane (Jonathan Bowers)[4]
Images
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Stericantellated 8-simplex
Acronym: crane (Jonathan Bowers)[5]
Images
Bistericantellated 8-simplex
Acronym: bocrane (Jonathan Bowers)[6]
Images
Stericantitruncated 8-simplex
Acronym: cograne (Jonathan Bowers)[7]
Images
Bistericantitruncated 8-simplex
Acronym: bocagrane (Jonathan Bowers)[8]
Images
Steriruncinated 8-simplex
Acronym: capene (Jonathan Bowers)[9]
Images
Bisteriruncinated 8-simplex
Acronym: bacpane (Jonathan Bowers)[10]
Images
Steriruncitruncated 8-simplex
Acronym: coptane (Jonathan Bowers)[11]
Images
Bisteriruncitruncated 8-simplex
Acronym: bicpotane (Jonathan Bowers)[12]
Images
Steriruncicantellated 8-simplex
Acronym: coprene (Jonathan Bowers)[13]
Images
Bisteriruncicantellated 8-simplex
Acronym: bicprene (Jonathan Bowers)[14]
Images
Steriruncicantitruncated 8-simplex
Acronym: gacene (Jonathan Bowers)[15]
Images
Bisteriruncicantitruncated 8-simplex
Acronym: gobcane (Jonathan Bowers)[16]
Images
Related polytopes
The 16 presented polytopes are in the family of 135 uniform 8-polytopes with A8 symmetry.
Notes
References
External links
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