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.
Stericated 6-cube Alternate names Small cellated hexeract (Acronym: scox) (Jonathan Bowers)[ 1] Images Steritruncated 6-cube
Steritruncated 6-cube
Type
uniform 6-polytope
Schläfli symbol t0,1,4 {4,3,3,3,3}
Coxeter-Dynkin diagrams File:CDel node 1.png File:CDel 4.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 3.png File:CDel node 1.png File:CDel 3.png File:CDel node.png
5-faces
4-faces
Cells
Faces
Edges
19200
Vertices
3840
Vertex figure
Coxeter groups B6 , [4,3,3,3,3]
Properties
convex
Alternate names Cellirhombated hexeract (Acronym: catax) (Jonathan Bowers)[ 2] Images Stericantellated 6-cube Alternate names Cellirhombated hexeract (Acronym: crax) (Jonathan Bowers)[ 3] Images Stericantitruncated 6-cube
stericantitruncated 6-cube
Type
uniform 6-polytope
Schläfli symbol t0,1,2,4 {4,3,3,3,3}
Coxeter-Dynkin diagrams File:CDel node 1.png File:CDel 4.png File:CDel node 1.png File:CDel 3.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 3.png File:CDel node 1.png
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 hexeract (Acronym: cagorx) (Jonathan Bowers)[ 4] Images Steriruncinated 6-cube
steriruncinated 6-cube
Type
uniform 6-polytope
Schläfli symbol t0,3,4 {4,3,3,3,3}
Coxeter-Dynkin diagrams File:CDel node 1.png File:CDel 4.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 3.png File:CDel node 1.png File:CDel 3.png File:CDel node 1.png File:CDel 3.png File:CDel node.png
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 hexeract (Acronym: copox) (Jonathan Bowers)[ 5] Images Steriruncitruncated 6-cube Alternate names Celliprismatotruncated hexeract (Acronym: captix) (Jonathan Bowers)[ 6] Images Steriruncicantellated 6-cube
steriruncicantellated 6-cube
Type
uniform 6-polytope
Schläfli symbol t0,2,3,4 {4,3,3,3,3}
Coxeter-Dynkin diagrams File:CDel node 1.png File:CDel 4.png File:CDel node.png File:CDel 3.png File:CDel node 1.png File:CDel 3.png File:CDel node 1.png File:CDel 3.png File:CDel node 1.png File:CDel 3.png File:CDel node.png
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 hexeract (Acronym: coprix) (Jonathan Bowers)[ 7] Images Steriruncicantitruncated 6-cube Alternate names Great cellated hexeract (Acronym: gocax) (Jonathan Bowers)[ 8] Images Related polytopes 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
File:6-cube t5.svg β6
File:6-cube t4.svg t1 β6
File:6-cube t3.svg t2 β6
File:6-cube t2.svg t2 γ6
File:6-cube t1.svg t1 γ6
File:6-cube t0.svg γ6
File:6-cube t45.svg t0,1 β6
File:6-cube t35.svg t0,2 β6
File:6-cube t34.svg t1,2 β6
File:6-cube t25.svg t0,3 β6
File:6-cube t24.svg t1,3 β6
File:6-cube t23.svg t2,3 γ6
File:6-cube t15.svg t0,4 β6
File:6-cube t14.svg t1,4 γ6
File:6-cube t13.svg t1,3 γ6
File:6-cube t12.svg t1,2 γ6
File:6-cube t05.svg t0,5 γ6
File:6-cube t04.svg t0,4 γ6
File:6-cube t03.svg t0,3 γ6
File:6-cube t02.svg t0,2 γ6
File:6-cube t01.svg t0,1 γ6
File:6-cube t345.svg t0,1,2 β6
File:6-cube t245.svg t0,1,3 β6
File:6-cube t235.svg t0,2,3 β6
File:6-cube t234.svg t1,2,3 β6
File:6-cube t145.svg t0,1,4 β6
File:6-cube t135.svg t0,2,4 β6
File:6-cube t134.svg t1,2,4 β6
File:6-cube t125.svg t0,3,4 β6
File:6-cube t124.svg t1,2,4 γ6
File:6-cube t123.svg t1,2,3 γ6
File:6-cube t045.svg t0,1,5 β6
File:6-cube t035.svg t0,2,5 β6
File:6-cube t034.svg t0,3,4 γ6
File:6-cube t025.svg t0,2,5 γ6
File:6-cube t024.svg t0,2,4 γ6
File:6-cube t023.svg t0,2,3 γ6
File:6-cube t015.svg t0,1,5 γ6
File:6-cube t014.svg t0,1,4 γ6
File:6-cube t013.svg t0,1,3 γ6
File:6-cube t012.svg t0,1,2 γ6
File:6-cube t2345.svg t0,1,2,3 β6
File:6-cube t1345.svg t0,1,2,4 β6
File:6-cube t1245.svg t0,1,3,4 β6
File:6-cube t1235.svg t0,2,3,4 β6
File:6-cube t1234.svg t1,2,3,4 γ6
File:6-cube t0345.svg t0,1,2,5 β6
File:6-cube t0245.svg t0,1,3,5 β6
File:6-cube t0235.svg t0,2,3,5 γ6
File:6-cube t0234.svg t0,2,3,4 γ6
File:6-cube t0145.svg t0,1,4,5 γ6
File:6-cube t0135.svg t0,1,3,5 γ6
File:6-cube t0134.svg t0,1,3,4 γ6
File:6-cube t0125.svg t0,1,2,5 γ6
File:6-cube t0124.svg t0,1,2,4 γ6
File:6-cube t0123.svg t0,1,2,3 γ6
File:6-cube t12345.svg t0,1,2,3,4 β6
File:6-cube t02345.svg t0,1,2,3,5 β6
File:6-cube t01345.svg t0,1,2,4,5 β6
File:6-cube t01245.svg t0,1,2,4,5 γ6
File:6-cube t01235.svg t0,1,2,3,5 γ6
File:6-cube t01234.svg t0,1,2,3,4 γ6
File:6-cube t012345.svg t0,1,2,3,4,5 γ6
Notes
↑ Klitzing, (x4o3o3o3x3o - scox)
↑ Klitzing, (x4x3o3o3x3o - catax)
↑ Klitzing, (x4o3x3o3x3o - crax)
↑ Klitzing, (x4x3x3o3x3o - cagorx)
↑ Klitzing, (x4o3o3x3x3o - copox))
↑ Klitzing, (x4x3o3x3x3o - captix)
↑ Klitzing, (x4o3x3x3x3o - coprix)
↑ Klitzing, (x4x3x3x3x3o - gocax)
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
