Stericated 6-orthoplexes
6-orthoplex Stericated 6-orthoplex Steritruncated 6-orthoplex
Stericantellated 6-orthoplex Stericantitruncated 6-orthoplex Steriruncinated 6-orthoplex
Steriruncitruncated 6-orthoplex Steriruncicantellated 6-orthoplex Steriruncicantitruncated 6-orthoplex
Orthogonal projections in B6 Coxeter plane
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)[ 1]
Images
Steritruncated 6-orthoplex
Steritruncated 6-orthoplex
Type
uniform 6-polytope
Schläfli symbol t0,1,4 {3,3,3,3,4}
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges
19200
Vertices
3840
Vertex figure
Coxeter groups B6 , [4,3,3,3,3]
Properties
convex
Alternate names
Cellitruncated hexacontatetrapeton (Acronym: catog) (Jonathan Bowers)[ 2]
Images
Stericantellated 6-orthoplex
Stericantellated 6-orthoplex
Type
uniform 6-polytope
Schläfli symbols t0,2,4 {34 ,4}
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges
28800
Vertices
5760
Vertex figure
Coxeter groups B6 , [4,3,3,3,3]
Properties
convex
Alternate names
Cellirhombated hexacontatetrapeton (Acronym: crag) (Jonathan Bowers)[ 3]
Images
Stericantitruncated 6-orthoplex
Stericantitruncated 6-orthoplex
Type
uniform 6-polytope
Schläfli symbol t0,1,2,4 {3,3,3,3,4}
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges
46080
Vertices
11520
Vertex figure
Coxeter groups B6 , [4,3,3,3,3]
Properties
convex
Alternate names
Celligreatorhombated hexacontatetrapeton (Acronym: cagorg) (Jonathan Bowers)[ 4]
Images
Steriruncinated 6-orthoplex
Steriruncinated 6-orthoplex
Type
uniform 6-polytope
Schläfli symbol t0,3,4 {3,3,3,3,4}
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges
15360
Vertices
3840
Vertex figure
Coxeter groups B6 , [4,3,3,3,3]
Properties
convex
Alternate names
Celliprismated hexacontatetrapeton (Acronym: copog) (Jonathan Bowers)[ 5]
Images
Steriruncitruncated 6-orthoplex
Alternate names
Celliprismatotruncated hexacontatetrapeton (Acronym: captog) (Jonathan Bowers)[ 6]
Images
Steriruncicantellated 6-orthoplex
Steriruncicantellated 6-orthoplex
Type
uniform 6-polytope
Schläfli symbol t0,2,3,4 {3,3,3,3,4}
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges
40320
Vertices
11520
Vertex figure
Coxeter groups B6 , [4,3,3,3,3]
Properties
convex
Alternate names
Celliprismatorhombated hexacontatetrapeton (Acronym: coprag) (Jonathan Bowers)[ 7]
Images
Steriruncicantitruncated 6-orthoplex
Steriuncicantitruncated 6-orthoplex
Type
uniform 6-polytope
Schläfli symbols t0,1,2,3,4 {34 ,4}
Coxeter-Dynkin diagrams
5-faces
536:t0,1,2,3 {3,3,3,4} 0,1,2 {3,3,4} 0,1,2 {3,3} 0,1,2 {3,3} t0,1,2,3,4 {34 }
4-faces
8216
Cells
38400
Faces
76800
Edges
69120
Vertices
23040
Vertex figure irregular 5-simplex
Coxeter groups B6 , [4,3,3,3,3]
Properties
convex
Alternate names
Great cellated hexacontatetrapeton (Acronym: gocog) (Jonathan Bowers)[ 8]
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 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.
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 .
B6 polytopes
β6
t1 β6
t2 β6
t2 γ6
t1 γ6
γ6
t0,1 β6
t0,2 β6
t1,2 β6
t0,3 β6
t1,3 β6
t2,3 γ6
t0,4 β6
t1,4 γ6
t1,3 γ6
t1,2 γ6
t0,5 γ6
t0,4 γ6
t0,3 γ6
t0,2 γ6
t0,1 γ6
t0,1,2 β6
t0,1,3 β6
t0,2,3 β6
t1,2,3 β6
t0,1,4 β6
t0,2,4 β6
t1,2,4 β6
t0,3,4 β6
t1,2,4 γ6
t1,2,3 γ6
t0,1,5 β6
t0,2,5 β6
t0,3,4 γ6
t0,2,5 γ6
t0,2,4 γ6
t0,2,3 γ6
t0,1,5 γ6
t0,1,4 γ6
t0,1,3 γ6
t0,1,2 γ6
t0,1,2,3 β6
t0,1,2,4 β6
t0,1,3,4 β6
t0,2,3,4 β6
t1,2,3,4 γ6
t0,1,2,5 β6
t0,1,3,5 β6
t0,2,3,5 γ6
t0,2,3,4 γ6
t0,1,4,5 γ6
t0,1,3,5 γ6
t0,1,3,4 γ6
t0,1,2,5 γ6
t0,1,2,4 γ6
t0,1,2,3 γ6
t0,1,2,3,4 β6
t0,1,2,3,5 β6
t0,1,2,4,5 β6
t0,1,2,4,5 γ6
t0,1,2,3,5 γ6
t0,1,2,3,4 γ6
t0,1,2,3,4,5 γ6
Notes
^ Klitzing, (x3o3o3o3x4o - scag)
^ Klitzing, (x3x3o3o3x4o - catog)
^ Klitzing, (x3o3x3o3x4o - crag)
^ Klitzing, (x3x3x3o3x4o - cagorg)
^ Klitzing, (x3o3o3x3x4o - copog)
^ Klitzing, (x3x3o3x3x4o - captog)
^ Klitzing, (x3o3x3x3x4o - coprag)
^ Klitzing, (x3x3x3x3x4o - gocog)
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
