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
* Small rhombated heptapeton (Acronym: sril) (Jonathan Bowers)
Coordinates
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
In seven-dimensional geometry, a cantellated 7-orthoplex is a convex uniform 7-polytope, being a cantellation of the regular 7-orthoplex.
There are ten degrees of cantellation for the 7-orthoplex, including truncations. Six are most simply const ...
.
Images
Bicantellated 6-simplex
Alternate names
* Small prismated heptapeton (Acronym: sabril) (Jonathan Bowers)
Coordinates
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
In seven-dimensional geometry, a cantellated 7-orthoplex is a convex uniform 7-polytope, being a cantellation of the regular 7-orthoplex.
There are ten degrees of cantellation for the 7-orthoplex, including truncations. Six are most simply cons ...
.
Images
Cantitruncated 6-simplex
Alternate names
* Great rhombated heptapeton (Acronym: gril) (Jonathan Bowers)
Coordinates
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
In seven-dimensional geometry, a cantellated 7-orthoplex is a convex uniform 7-polytope, being a cantellation of the regular 7-orthoplex.
There are ten degrees of cantellation for the 7-orthoplex, including truncations. Six are most simply cons ...
.
Images
Bicantitruncated 6-simplex
Alternate names
* Great birhombated heptapeton (Acronym: gabril) (Jonathan Bowers)
[Klitzing, (o3x3x3x3o3o - gabril)]
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
In seven-dimensional geometry, a cantellated 7-orthoplex is a convex uniform 7-polytope, being a cantellation of the regular 7-orthoplex.
There are ten degrees of cantellation for the 7-orthoplex, including truncations. Six are most simply cons ...
.
Images
Related uniform 6-polytopes
The truncated 6-simplex is one of 35
uniform 6-polytopes based on the
,3,3,3,3 Coxeter group, all shown here in A
6 Coxeter plane orthographic projection
Orthographic projection (also orthogonal projection and analemma) is a means of representing Three-dimensional space, three-dimensional objects in Two-dimensional space, two dimensions. Orthographic projection is a form of parallel projection in ...
s.
Notes
References
*
H.S.M. Coxeter
Harold Scott MacDonald "Donald" Coxeter, (9 February 1907 – 31 March 2003) was a British and later also Canadian geometer. He is regarded as one of the greatest geometers of the 20th century.
Biography
Coxeter was born in Kensington t ...
:
** 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,
*** (Paper 22) H.S.M. Coxeter, ''Regular and Semi Regular Polytopes I'',
ath. Zeit. 46 (1940) 380-407, MR 2,10*** (Paper 23) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes II'',
ath. Zeit. 188 (1985) 559-591*** (Paper 24) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes III'',
ath. Zeit. 200 (1988) 3-45*
Norman Johnson ''Uniform Polytopes'', Manuscript (1991)
** N.W. Johnson: ''The Theory of Uniform Polytopes and Honeycombs'', Ph.D.
* x3o3x3o3o3o - sril, o3x3o3x3o3o - sabril, x3x3x3o3o3o - gril, o3x3x3x3o3o - gabril
External links
Polytopes of Various Dimensions
{{Polytopes
6-polytopes