- Source: Stericated 6-orthoplexes
In six-dimensional geometry, a stericated 6-orthoplex is a convex uniform 6-polytope, 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.
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)
= 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 [32,1,1,1]+ or [4,(3,3,3,3)+], and constructed from 12 snub 5-demicubes, 64 snub 5-simplexes, 60 snub 24-cell antiprisms, 160 3-s{3,4} duoantiprisms, 240 2-sr{3,3} duoantiprisms, and 11520 irregular 5-simplexes filling the gaps at the deleted vertices.
Related polytopes
These polytopes are from a set of 63 uniform 6-polytopes generated from the B6 Coxeter plane, 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, 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
