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.
Stericated 8-simplex
Acronym: secane (Jonathan Bowers)
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
Bistericated 8-simplex
Acronym: sobcane (Jonathan Bowers)
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
Steritruncated 8-simplex
Acronym: catene (Jonathan Bowers)
Images
Bisteritruncated 8-simplex
Acronym: bictane (Jonathan Bowers)
Images
Stericantellated 8-simplex
Acronym: crane (Jonathan Bowers)
Images
Bistericantellated 8-simplex
Acronym: bocrane (Jonathan Bowers)
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Stericantitruncated 8-simplex
Acronym: cograne (Jonathan Bowers)
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Bistericantitruncated 8-simplex
Acronym: bocagrane (Jonathan Bowers)
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Steriruncinated 8-simplex
Acronym: capene (Jonathan Bowers)
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Bisteriruncinated 8-simplex
Acronym: bacpane (Jonathan Bowers)
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Steriruncitruncated 8-simplex
Acronym: coptane (Jonathan Bowers)
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Bisteriruncitruncated 8-simplex
Acronym: bicpotane (Jonathan Bowers)
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Steriruncicantellated 8-simplex
Acronym: coprene (Jonathan Bowers)
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Bisteriruncicantellated 8-simplex
Acronym: bicprene (Jonathan Bowers)
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Steriruncicantitruncated 8-simplex
Acronym: gacene (Jonathan Bowers)
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Bisteriruncicantitruncated 8-simplex
Acronym: gobcane (Jonathan Bowers)
Images
Related polytopes
The 16 presented polytopes are in the family of 135 uniform 8-polytopes with A<sub>8</sub> symmetry.
Notes
References
- H.S.M. Coxeter:
- H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
- Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, wiley.com,
- (Paper 22) H.S.M. Coxeter, Regular and Semi-Regular Polytopes I, [Math. Zeit. 46 (1940) 380âÂÂ407, MR 2,10]
- (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559âÂÂ591]
- (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3âÂÂ45]
- Norman Johnson Uniform Polytopes, Manuscript (1991)
- N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D.
- x3o3o3o3x3o3o3o - secane, o3x3o3o3o3x3o3o - sobcane, x3x3o3o3x3o3o3o - catene, o3x3x3o3o3x3o3o - bictane, x3o3x3o3x3o3o3o - crane, o3x3o3x3o3x3o3o - bocrane, x3x3x3o3x3o3o3o - cograne, o3x3x3x3ox3o3o3 - bocagrane, x3o3o3x3x3o3o3o - capene, o3x3o3o3x3x3o3o - bacpane, x3x3o3x3x3o3o3o - coptane, o3x3x3o3x3x3o3o - bicpotane, x3o3x3x3x3o3o3o - coprene, o3x3o3x3x3x3o3o - bicprene, x3x3x3x3x3o3o3o - gacene, o3x3x3x3x3x3o3o - gobcane
External links