6-cubeStericated 6-cubeSteritruncated 6-cubeStericantellated 6-cubeStericantitruncated 6-cubeSteriruncinated 6-cubeSteriruncitruncated 6-cubeSteriruncicantellated 6-cubeSteriruncicantitruncated 6-cubeOrthogonal 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 Stericated 6-cubeTypeuniform 6-polytopeSchläfli symbol 2r2r{4,3,3,3,3}Coxeter-Dynkin diagrams5-faces4-facesCells Faces Edges5760Vertices960Vertex figureCoxeter groupsB6, [4,3,3,3,3]Propertiesconvex
Alternate names Small cellated hexeract (Acronym: scox) (Jonathan Bowers)
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Steritruncated 6-cube Steritruncated 6-cubeTypeuniform 6-polytopeSchläfli symbol t0,1,4{4,3,3,3,3}Coxeter-Dynkin diagrams5-faces4-faces Cells Faces Edges19200Vertices3840Vertex figureCoxeter groupsB6, [4,3,3,3,3]Propertiesconvex
Alternate names Cellirhombated hexeract (Acronym: catax) (Jonathan Bowers)
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Stericantellated 6-cube Stericantellated 6-cubeTypeuniform 6-polytopeSchläfli symbol 2r2r{4,3,3,3,3}Coxeter-Dynkin diagrams5-faces 4-facesCellsFacesEdges28800Vertices5760Vertex figureCoxeter groupsB6, [4,3,3,3,3]Propertiesconvex
Alternate names Cellirhombated hexeract (Acronym: crax) (Jonathan Bowers)
Images
Stericantitruncated 6-cube Stericantitruncated 6-cubeTypeuniform 6-polytopeSchläfli symbol t0,1,2,4{4,3,3,3,3}Coxeter-Dynkin diagrams5-faces4-facesCells FacesEdges46080Vertices11520Vertex figureCoxeter groupsB6, [4,3,3,3,3]Propertiesconvex
Alternate names Celligreatorhombated hexeract (Acronym: cagorx) (Jonathan Bowers)
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Steriruncinated 6-cube Steriruncinated 6-cubeTypeuniform 6-polytopeSchläfli symbol t0,3,4{4,3,3,3,3}Coxeter-Dynkin diagrams5-faces4-facesCellsFacesEdges15360Vertices3840Vertex figureCoxeter groupsB6, [4,3,3,3,3]Propertiesconvex
Alternate names Celliprismated hexeract (Acronym: copox) (Jonathan Bowers)
Images
Steriruncitruncated 6-cube Steriruncitruncated 6-cubeTypeuniform 6-polytopeSchläfli symbol 2t2r{4,3,3,3,3}Coxeter-Dynkin diagrams5-faces4-facesCellsFacesEdges40320Vertices11520Vertex figureCoxeter groupsB6, [4,3,3,3,3]Propertiesconvex
Alternate names Celliprismatotruncated hexeract (Acronym: captix) (Jonathan Bowers)
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Steriruncicantellated 6-cube Steriruncicantellated 6-cubeTypeuniform 6-polytopeSchläfli symbol t0,2,3,4{4,3,3,3,3}Coxeter-Dynkin diagrams5-faces4-facesCells FacesEdges40320Vertices11520Vertex figureCoxeter groupsB6, [4,3,3,3,3]Propertiesconvex
Alternate names Celliprismatorhombated hexeract (Acronym: coprix) (Jonathan Bowers)
Images
Steriruncicantitruncated 6-cube Steriuncicantitruncated 6-cubeTypeuniform 6-polytopeSchläfli symbol tr2r{4,3,3,3,3}Coxeter-Dynkin diagrams5-faces 4-faces Cells Faces Edges69120Vertices23040Vertex figureCoxeter groupsB6, [4,3,3,3,3]Propertiesconvex
Alternate names Great cellated hexeract (Acronym: gocax) (Jonathan Bowers)
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 and 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 Ivić Weiss, Wiley-Interscience Publication, 1995, wiley.com, (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.
External links Polytopes of Various Dimensions Multi-dimensional Glossary