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6-cube
Stericated 6-cube
Steritruncated 6-cube
Stericantellated 6-cube
Stericantitruncated 6-cube
Steriruncinated 6-cube
Steriruncitruncated 6-cube
Steriruncicantellated 6-cube
Steriruncicantitruncated 6-cube
Orthogonal projections in B6 Coxeter plane
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, cantellations, and runcinations.
Small cellated hexeract (Acronym: scox) (Jonathan Bowers)[ 1]
Steritruncated 6-cube [ edit ]
Steritruncated 6-cube
Type
uniform 6-polytope
Schläfli symbol
t0,1,4 {4,3,3,3,3}
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
Cellirhombated hexeract (Acronym: catax) (Jonathan Bowers)[ 2]
Stericantellated 6-cube [ edit ]
Cellirhombated hexeract (Acronym: crax) (Jonathan Bowers)[ 3]
Stericantitruncated 6-cube [ edit ]
stericantitruncated 6-cube
Type
uniform 6-polytope
Schläfli symbol
t0,1,2,4 {4,3,3,3,3}
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
Celligreatorhombated hexeract (Acronym: cagorx) (Jonathan Bowers)[ 4]
Steriruncinated 6-cube [ edit ]
steriruncinated 6-cube
Type
uniform 6-polytope
Schläfli symbol
t0,3,4 {4,3,3,3,3}
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
Celliprismated hexeract (Acronym: copox) (Jonathan Bowers)[ 5]
Steriruncitruncated 6-cube [ edit ]
Celliprismatotruncated hexeract (Acronym: captix) (Jonathan Bowers)[ 6]
Steriruncicantellated 6-cube [ edit ]
steriruncicantellated 6-cube
Type
uniform 6-polytope
Schläfli symbol
t0,2,3,4 {4,3,3,3,3}
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
Celliprismatorhombated hexeract (Acronym: coprix) (Jonathan Bowers)[ 7]
Steriruncicantitruncated 6-cube [ edit ]
Great cellated hexeract (Acronym: gocax) (Jonathan Bowers)[ 8]
These polytopes are from a set of 63 uniform 6-polytopes generated from the B6 Coxeter plane , including the regular 6-cube or 6-orthoplex .
B6 polytopes
β べーた 6
t1 β べーた 6
t2 β べーた 6
t2 γ がんま 6
t1 γ がんま 6
γ がんま 6
t0,1 β べーた 6
t0,2 β べーた 6
t1,2 β べーた 6
t0,3 β べーた 6
t1,3 β べーた 6
t2,3 γ がんま 6
t0,4 β べーた 6
t1,4 γ がんま 6
t1,3 γ がんま 6
t1,2 γ がんま 6
t0,5 γ がんま 6
t0,4 γ がんま 6
t0,3 γ がんま 6
t0,2 γ がんま 6
t0,1 γ がんま 6
t0,1,2 β べーた 6
t0,1,3 β べーた 6
t0,2,3 β べーた 6
t1,2,3 β べーた 6
t0,1,4 β べーた 6
t0,2,4 β べーた 6
t1,2,4 β べーた 6
t0,3,4 β べーた 6
t1,2,4 γ がんま 6
t1,2,3 γ がんま 6
t0,1,5 β べーた 6
t0,2,5 β べーた 6
t0,3,4 γ がんま 6
t0,2,5 γ がんま 6
t0,2,4 γ がんま 6
t0,2,3 γ がんま 6
t0,1,5 γ がんま 6
t0,1,4 γ がんま 6
t0,1,3 γ がんま 6
t0,1,2 γ がんま 6
t0,1,2,3 β べーた 6
t0,1,2,4 β べーた 6
t0,1,3,4 β べーた 6
t0,2,3,4 β べーた 6
t1,2,3,4 γ がんま 6
t0,1,2,5 β べーた 6
t0,1,3,5 β べーた 6
t0,2,3,5 γ がんま 6
t0,2,3,4 γ がんま 6
t0,1,4,5 γ がんま 6
t0,1,3,5 γ がんま 6
t0,1,3,4 γ がんま 6
t0,1,2,5 γ がんま 6
t0,1,2,4 γ がんま 6
t0,1,2,3 γ がんま 6
t0,1,2,3,4 β べーた 6
t0,1,2,3,5 β べーた 6
t0,1,2,4,5 β べーた 6
t0,1,2,4,5 γ がんま 6
t0,1,2,3,5 γ がんま 6
t0,1,2,3,4 γ がんま 6
t0,1,2,3,4,5 γ がんま 6
^ Klitzing, (x4o3o3o3x3o - scox)
^ Klitzing, (x4x3o3o3x3o - catax)
^ Klitzing, (x4o3x3o3x3o - crax)
^ Klitzing, (x4x3x3o3x3o - cagorx)
^ Klitzing, (x4o3o3x3x3o - copox))
^ Klitzing, (x4x3o3x3x3o - captix)
^ Klitzing, (x4o3x3x3x3o - coprix)
^ Klitzing, (x4x3x3x3x3o - gocax)
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)" .