In six-dimensional
geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
, a stericated 6-orthoplex is a convex
uniform 6-polytope
In six-dimensional geometry, a uniform 6-polytope is a six-dimensional uniform polytope. A uniform polypeton is vertex-transitive, and all facets are uniform 5-polytopes.
The complete set of convex uniform 6-polytopes has not been determined, ...
, constructed as a
sterication (4th order truncation) of the regular
6-orthoplex.
There are 16 unique sterications for the 6-orthoplex with permutations of truncations, cantellations, and runcinations. Eight are better represented from the
stericated 6-cube
In six-dimensional geometry, a stericated 6-cube is a convex uniform 6-polytope, constructed as a sterication (4th order truncation) of the regular 6-cube.
There are 8 unique sterications for the 6-cube with permutations of truncations, cantellati ...
.
Stericated 6-orthoplex
Alternate names
* Small cellated hexacontatetrapeton (Acronym: scag) (Jonathan Bowers)
Images
Steritruncated 6-orthoplex
Alternate names
* Cellitruncated hexacontatetrapeton (Acronym: catog) (Jonathan Bowers)
Images
Stericantellated 6-orthoplex
Alternate names
* Cellirhombated hexacontatetrapeton (Acronym: crag) (Jonathan Bowers)
Images
Stericantitruncated 6-orthoplex
Alternate names
* Celligreatorhombated hexacontatetrapeton (Acronym: cagorg) (Jonathan Bowers)
Images
Steriruncinated 6-orthoplex
Alternate names
* Celliprismated hexacontatetrapeton (Acronym: copog) (Jonathan Bowers)
Images
Steriruncitruncated 6-orthoplex
Alternate names
* Celliprismatotruncated hexacontatetrapeton (Acronym: captog) (Jonathan Bowers)
Images
Steriruncicantellated 6-orthoplex
Alternate names
* Celliprismatorhombated hexacontatetrapeton (Acronym: coprag) (Jonathan Bowers)
Images
Steriruncicantitruncated 6-orthoplex
Alternate names
* Great cellated hexacontatetrapeton (Acronym: gocog) (Jonathan Bowers)
[Klitzing, (x3x3x3x3x4o - gocog)]
Images
Snub 6-demicube
The snub 6-demicube defined as an
alternation of the omnitruncated 6-demicube is not uniform, but it can be given Coxeter diagram or and
symmetry 2,1,1,1sup>+ or
,(3,3,3,3)+ and constructed from 12
snub 5-demicubes, 64
snub 5-simplexes, 60 snub 24-cell antiprisms, 160 3-s duoantiprisms, 240 2-sr duoantiprisms, and 11520 irregular
5-simplex
In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope. It has six vertices, 15 edges, 20 triangle faces, 15 tetrahedral cells, and 6 5-cell facets. It has a dihedral angle of cos−1(), or approximately 78.46°.
The 5-s ...
es filling the gaps at the deleted vertices.
Related polytopes
These polytopes are from a set of 63
uniform 6-polytope
In six-dimensional geometry, a uniform 6-polytope is a six-dimensional uniform polytope. A uniform polypeton is vertex-transitive, and all facets are uniform 5-polytopes.
The complete set of convex uniform 6-polytopes has not been determined, ...
s generated from the B
6 Coxeter plane
In mathematics, the Coxeter number ''h'' is the order of a Coxeter element of an irreducible Coxeter group. It is named after H.S.M. Coxeter.
Definitions
Note that this article assumes a finite Coxeter group. For infinite Coxeter groups, there a ...
, including the regular
6-orthoplex or
6-orthoplex.
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,
*** (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.
*
External links
Polytopes of Various Dimensions
{{Polytopes
6-polytopes