- Source: Stericated 6-simplexes
In six-dimensional geometry, a stericated 6-simplex is a convex uniform 6-polytope with 4th order truncations (sterication) of the regular 6-simplex.
There are 8 unique sterications for the 6-simplex with permutations of truncations, cantellations, and runcinations.
Stericated 6-simplex
= Alternate names
=Small cellated heptapeton (Acronym: scal) (Jonathan Bowers)
= Coordinates
=The vertices of the stericated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,1,1,1,1,2). This construction is based on facets of the stericated 7-orthoplex.
= Images
=Steritruncated 6-simplex
= Alternate names
=Cellitruncated heptapeton (Acronym: catal) (Jonathan Bowers)
= Coordinates
=The vertices of the steritruncated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,1,1,1,2,3). This construction is based on facets of the steritruncated 7-orthoplex.
= Images
=Stericantellated 6-simplex
= Alternate names
=Cellirhombated heptapeton (Acronym: cral) (Jonathan Bowers)
= Coordinates
=The vertices of the stericantellated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,1,1,2,2,3). This construction is based on facets of the stericantellated 7-orthoplex.
= Images
=Stericantitruncated 6-simplex
= Alternate names
=Celligreatorhombated heptapeton (Acronym: cagral) (Jonathan Bowers)
= Coordinates
=The vertices of the stericanttruncated 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 stericantitruncated 7-orthoplex.
= Images
=Steriruncinated 6-simplex
= Alternate names
=Celliprismated heptapeton (Acronym: copal) (Jonathan Bowers)
= Coordinates
=The vertices of the steriruncinated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,1,2,2,3,3). This construction is based on facets of the steriruncinated 7-orthoplex.
= Images
=Steriruncitruncated 6-simplex
= Alternate names
=Celliprismatotruncated heptapeton (Acronym: captal) (Jonathan Bowers)
= Coordinates
=The vertices of the steriruncittruncated 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 steriruncitruncated 7-orthoplex.
= Images
=Steriruncicantellated 6-simplex
= Alternate names
=Bistericantitruncated 6-simplex as t1,2,3,5{3,3,3,3,3}
Celliprismatorhombated heptapeton (Acronym: copril) (Jonathan Bowers)
= Coordinates
=The vertices of the steriruncitcantellated 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 steriruncicantellated 7-orthoplex.
= Images
=Steriruncicantitruncated 6-simplex
= Alternate names
=Great cellated heptapeton (Acronym: gacal) (Jonathan Bowers)
= Coordinates
=The vertices of the steriruncicantittruncated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,1,2,3,4,5). This construction is based on facets of the steriruncicantitruncated 7-orthoplex.
= Images
=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)".
External links
Polytopes of Various Dimensions
Multi-dimensional Glossary
Kata Kunci Pencarian:
- Stericated 6-simplexes
- Stericated 7-simplexes
- Pentellated 6-simplexes
- Stericated 6-orthoplexes
- Stericated 8-simplexes
- Stericated 5-simplexes
- 5-simplex honeycomb
