• Source: Cantellated 6-simplexes

In six-dimensional geometry, a cantellated 6-simplex is a convex uniform 6-polytope, being a cantellation of the regular 6-simplex.
There are unique 4 degrees of cantellation for the 6-simplex, including truncations.




Cantellated 6-simplex






= Alternate names

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Small rhombated heptapeton (Acronym: sril) (Jonathan Bowers)




= Coordinates

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The vertices of the cantellated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,0,0,1,1,2). This construction is based on facets of the cantellated 7-orthoplex.




= Images

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Bicantellated 6-simplex






= Alternate names

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Small prismated heptapeton (Acronym: sabril) (Jonathan Bowers)




= Coordinates

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The vertices of the bicantellated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,0,1,1,2,2). This construction is based on facets of the bicantellated 7-orthoplex.




= Images

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Cantitruncated 6-simplex






= Alternate names

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Great rhombated heptapeton (Acronym: gril) (Jonathan Bowers)




= Coordinates

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The vertices of the cantitruncated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,0,0,1,2,3). This construction is based on facets of the cantitruncated 7-orthoplex.




= Images

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Bicantitruncated 6-simplex






= Alternate names

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Great birhombated heptapeton (Acronym: gabril) (Jonathan Bowers)




= Coordinates

=
The vertices of the bicantitruncated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,0,1,2,3,3). This construction is based on facets of the bicantitruncated 7-orthoplex.




= Images

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Related uniform 6-polytopes


The truncated 6-simplex is one of 35 uniform 6-polytopes based on the [3,3,3,3,3] Coxeter group, all shown here in A6 Coxeter plane orthographic projections.




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, ISBN 978-0-471-01003-6 [1]
(Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380–407, MR 2,10]
(Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
Norman Johnson Uniform Polytopes, Manuscript (1991)
N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D.
Klitzing, Richard. "6D uniform polytopes (polypeta)". x3o3x3o3o3o - sril, o3x3o3x3o3o - sabril, x3x3x3o3o3o - gril, o3x3x3x3o3o - gabril




External links


Polytopes of Various Dimensions
Multi-dimensional Glossary

Kata Kunci Pencarian:

• Cantellated 6-simplexes
• Cantellated 7-simplexes
• Cantellated 5-simplexes
• Cantellated 8-simplexes
• 4 21 polytope
• Triangular prism
• Stericated 8-simplexes
• Rectified 5-cell
• 120-cell
• Truncated 5-cell