6-orthoplexStericated 6-orthoplexSteritruncated 6-orthoplexStericantellated 6-orthoplexStericantitruncated 6-orthoplexSteriruncinated 6-orthoplexSteriruncitruncated 6-orthoplexSteriruncicantellated 6-orthoplexSteriruncicantitruncated 6-orthoplexOrthogonal 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-cubes.
Stericated 6-orthoplex Stericated 6-orthoplexTypeuniform 6-polytopeSchläfli symbol 2r2r{3,3,3,3,4}Coxeter-Dynkin diagrams5-faces4-facesCells Faces Edges5760Vertices960Vertex figureCoxeter groupsB6, [4,3,3,3,3]Propertiesconvex
Alternate names Small cellated hexacontatetrapeton (Acronym: scag) (Jonathan Bowers)
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Steritruncated 6-orthoplex Steritruncated 6-orthoplexTypeuniform 6-polytopeSchläfli symbol t0,1,4{3,3,3,3,4}Coxeter-Dynkin diagrams5-faces4-faces Cells Faces Edges19200Vertices3840Vertex figureCoxeter groupsB6, [4,3,3,3,3]Propertiesconvex
Alternate names Cellitruncated hexacontatetrapeton (Acronym: catog) (Jonathan Bowers)
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Stericantellated 6-orthoplex Stericantellated 6-orthoplexTypeuniform 6-polytopeSchläfli symbolst0,2,4{34,4}rr2r{3,3,3,3,4}Coxeter-Dynkin diagrams5-faces 4-facesCellsFaces Edges28800Vertices5760Vertex figureCoxeter groupsB6, [4,3,3,3,3]Propertiesconvex
Alternate names Cellirhombated hexacontatetrapeton (Acronym: crag) (Jonathan Bowers)
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Stericantitruncated 6-orthoplex Stericantitruncated 6-orthoplexTypeuniform 6-polytopeSchläfli symbol t0,1,2,4{3,3,3,3,4}Coxeter-Dynkin diagrams5-faces4-facesCells FacesEdges46080 Vertices11520Vertex figureCoxeter groupsB6, [4,3,3,3,3]Propertiesconvex
Alternate names Celligreatorhombated hexacontatetrapeton (Acronym: cagorg) (Jonathan Bowers)
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Steriruncinated 6-orthoplex Steriruncinated 6-orthoplexTypeuniform 6-polytopeSchläfli symbol t0,3,4{3,3,3,3,4}Coxeter-Dynkin diagrams5-faces4-facesCellsFacesEdges15360Vertices3840Vertex figureCoxeter groupsB6, [4,3,3,3,3]Propertiesconvex
Alternate names Celliprismated hexacontatetrapeton (Acronym: copog) (Jonathan Bowers)
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Steriruncitruncated 6-orthoplex Steriruncitruncated 6-orthoplexTypeuniform 6-polytopeSchläfli symbol 2t2r{3,3,3,3,4}Coxeter-Dynkin diagrams5-faces4-facesCellsFacesEdges40320Vertices11520Vertex figureCoxeter groupsB6, [4,3,3,3,3]Propertiesconvex
Alternate names Celliprismatotruncated hexacontatetrapeton (Acronym: captog) (Jonathan Bowers)
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Steriruncicantellated 6-orthoplex Steriruncicantellated 6-orthoplexTypeuniform 6-polytopeSchläfli symbol t0,2,3,4{3,3,3,3,4}Coxeter-Dynkin diagrams5-faces4-facesCells FacesEdges40320Vertices11520Vertex figureCoxeter groupsB6, [4,3,3,3,3]Propertiesconvex
Alternate names Celliprismatorhombated hexacontatetrapeton (Acronym: coprag) (Jonathan Bowers)
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Steriruncicantitruncated 6-orthoplex Steriuncicantitruncated 6-orthoplexTypeuniform 6-polytopeSchläfli symbolst0,1,2,3,4{34,4}tr2r{3,3,3,3,4}Coxeter-Dynkin diagrams5-faces536:12 t0,1,2,3{3,3,3,4}60 {}×t0,1,2{3,3,4} ×160 {6}×t0,1,2{3,3} ×240 {4}×t0,1,2{3,3} ×64 t0,1,2,3,4{34}4-faces8216Cells38400Faces76800Edges69120Vertices23040Vertex figureirregular 5-simplexCoxeter groupsB6, [4,3,3,3,3]Propertiesconvex
Alternate names Great cellated hexacontatetrapeton (Acronym: gocog) (Jonathan Bowers)
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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 or and 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.
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