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Runcinated 6-simplexes
From Wikipedia, the free encyclopedia
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In six-dimensional geometry, a runcinated 6-simplex is a convex uniform 6-polytope constructed as a runcination (3rd order truncations) of the regular 6-simplex.
There are 8 unique runcinations of the 6-simplex with permutations of truncations, and cantellations.
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Runcinated 6-simplex
Runcinated 6-simplex | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | t0,3{3,3,3,3,3} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5-faces | 70 |
4-faces | 455 |
Cells | 1330 |
Faces | 1610 |
Edges | 840 |
Vertices | 140 |
Vertex figure | |
Coxeter group | A6, [35], order 5040 |
Properties | convex |
Alternate names
- Small prismated heptapeton (Acronym: spil) (Jonathan Bowers)[1]
Coordinates
The vertices of the runcinated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,0,1,1,1,2). This construction is based on facets of the runcinated 7-orthoplex.
Images
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Biruncinated 6-simplex
Alternate names
- Small biprismated tetradecapeton (Acronym: sibpof) (Jonathan Bowers)[2]
Coordinates
The vertices of the biruncinated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,1,1,1,2,2). This construction is based on facets of the biruncinated 7-orthoplex.
Images
- Note: (*) Symmetry doubled for Ak graphs with even k due to symmetrically-ringed Coxeter-Dynkin diagram.
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Runcitruncated 6-simplex
Alternate names
- Prismatotruncated heptapeton (Acronym: patal) (Jonathan Bowers)[3]
Coordinates
The vertices of the runcitruncated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,0,1,1,2,3). This construction is based on facets of the runcitruncated 7-orthoplex.
Images
Biruncitruncated 6-simplex
Alternate names
- Biprismatorhombated heptapeton (Acronym: bapril) (Jonathan Bowers)[4]
Coordinates
The vertices of the biruncitruncated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,1,1,2,3,3). This construction is based on facets of the biruncitruncated 7-orthoplex.
Images
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Runcicantellated 6-simplex
Alternate names
- Prismatorhombated heptapeton (Acronym: pril) (Jonathan Bowers)[5]
Coordinates
The vertices of the runcicantellated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,0,1,2,2,3). This construction is based on facets of the runcicantellated 7-orthoplex.
Images
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Runcicantitruncated 6-simplex
Alternate names
- Runcicantitruncated heptapeton
- Great prismated heptapeton (Acronym: gapil) (Jonathan Bowers)[6]
Coordinates
The vertices of the runcicantitruncated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,0,1,2,3,4). This construction is based on facets of the runcicantitruncated 7-orthoplex.
Images
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Biruncicantitruncated 6-simplex
Alternate names
- Biruncicantitruncated heptapeton
- Great biprismated tetradecapeton (Acronym: gibpof) (Jonathan Bowers)[7]
Coordinates
The vertices of the biruncicantittruncated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,1,2,3,4,4). This construction is based on facets of the biruncicantitruncated 7-orthoplex.
Images
- Note: (*) Symmetry doubled for Ak graphs with even k due to symmetrically-ringed Coxeter-Dynkin diagram.
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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.
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Notes
References
External links
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