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.
Stericated 6-cube [ edit ] Alternate names [ edit ] 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
Alternate names [ edit ] Cellirhombated hexeract (Acronym: catax) (Jonathan Bowers)[2] Stericantellated 6-cube [ edit ] Alternate names [ 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
Alternate names [ edit ] 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
Alternate names [ edit ] Celliprismated hexeract (Acronym: copox) (Jonathan Bowers)[5] Steriruncitruncated 6-cube [ edit ] Alternate names [ 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
Alternate names [ edit ] Celliprismatorhombated hexeract (Acronym: coprix) (Jonathan Bowers)[7] Steriruncicantitruncated 6-cube [ edit ] Alternate names [ edit ] Great cellated hexeract (Acronym: gocax) (Jonathan Bowers)[8] Related polytopes [ edit ] 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 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
^ 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 [ edit ] 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 [ edit ]