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Stericated 6-cubes#Steriruncicantitruncated 6-cube

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6-cube
{{CDD|node_1|4|node|3|node|3|node|3|node|3|node}}

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Stericated 6-cube
{{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node}}

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Steritruncated 6-cube
{{CDD|node_1|4|node_1|3|node|3|node|3|node_1|3|node}}

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Stericantellated 6-cube
{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node}}

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Stericantitruncated 6-cube
{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1|3|node}}

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Steriruncinated 6-cube
{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node}}

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Steriruncitruncated 6-cube
{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1|3|node}}

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Steriruncicantellated 6-cube
{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node}}

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Steriruncicantitruncated 6-cube
{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node}}

colspan=3|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

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!bgcolor=#e7dcc3 colspan=2|Stericated 6-cube

bgcolor=#e7dcc3|Typeuniform 6-polytope
bgcolor=#e7dcc3|Schläfli symbol2r2r{4,3,3,3,3}
bgcolor=#e7dcc3|Coxeter-Dynkin diagrams{{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node}}
{{CDD|node|split1|nodes|3a4b|nodes_11|3a|nodea}}
bgcolor=#e7dcc3|5-faces
bgcolor=#e7dcc3|4-faces
bgcolor=#e7dcc3|Cells
bgcolor=#e7dcc3|Faces
bgcolor=#e7dcc3|Edges5760
bgcolor=#e7dcc3|Vertices960
bgcolor=#e7dcc3|Vertex figure
bgcolor=#e7dcc3|Coxeter groupsB6, [4,3,3,3,3]
bgcolor=#e7dcc3|Propertiesconvex

= Alternate names =

  • Small cellated hexeract (Acronym: scox) (Jonathan Bowers){{sfn|Klitzing|at=[https://bendwavy.org/klitzing/incmats/scox.htm (x4o3o3o3x3o - scox)]}}

= Images =

{{6-cube Coxeter plane graphs|t04|150}}

Steritruncated 6-cube

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!bgcolor=#e7dcc3 colspan=2|Steritruncated 6-cube

bgcolor=#e7dcc3|Typeuniform 6-polytope
bgcolor=#e7dcc3|Schläfli symbolt0,1,4{4,3,3,3,3}
bgcolor=#e7dcc3|Coxeter-Dynkin diagrams{{CDD|node_1|4|node_1|3|node|3|node|3|node_1|3|node}}
bgcolor=#e7dcc3|5-faces
bgcolor=#e7dcc3|4-faces
bgcolor=#e7dcc3|Cells
bgcolor=#e7dcc3|Faces
bgcolor=#e7dcc3|Edges19200
bgcolor=#e7dcc3|Vertices3840
bgcolor=#e7dcc3|Vertex figure
bgcolor=#e7dcc3|Coxeter groupsB6, [4,3,3,3,3]
bgcolor=#e7dcc3|Propertiesconvex

= Alternate names =

  • Cellirhombated hexeract (Acronym: catax) (Jonathan Bowers){{sfn|Klitzing|at=[https://bendwavy.org/klitzing/incmats/catax.htm (x4x3o3o3x3o - catax)]}}

= Images =

{{6-cube Coxeter plane graphs|t014|150}}

== Stericantellated 6-cube ==

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!bgcolor=#e7dcc3 colspan=2|Stericantellated 6-cube

bgcolor=#e7dcc3|Typeuniform 6-polytope
bgcolor=#e7dcc3|Schläfli symbol2r2r{4,3,3,3,3}
bgcolor=#e7dcc3|Coxeter-Dynkin diagrams{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node}}
{{CDD|node_1|split1|nodes|3a4b|nodes_11|3a|nodea}}
bgcolor=#e7dcc3|5-faces
bgcolor=#e7dcc3|4-faces
bgcolor=#e7dcc3|Cells
bgcolor=#e7dcc3|Faces
bgcolor=#e7dcc3|Edges28800
bgcolor=#e7dcc3|Vertices5760
bgcolor=#e7dcc3|Vertex figure
bgcolor=#e7dcc3|Coxeter groupsB6, [4,3,3,3,3]
bgcolor=#e7dcc3|Propertiesconvex

= Alternate names =

  • Cellirhombated hexeract (Acronym: crax) (Jonathan Bowers){{sfn|Klitzing|at=[https://bendwavy.org/klitzing/incmats/crax.htm (x4o3x3o3x3o - crax)]}}

= Images =

{{6-cube Coxeter plane graphs|t024|150}}

Stericantitruncated 6-cube

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!bgcolor=#e7dcc3 colspan=2|stericantitruncated 6-cube

bgcolor=#e7dcc3|Typeuniform 6-polytope
bgcolor=#e7dcc3|Schläfli symbolt0,1,2,4{4,3,3,3,3}
bgcolor=#e7dcc3|Coxeter-Dynkin diagrams{{CDD|node_1|4|node_1|3|node_1|3|node|3|node|3|node_1}}
bgcolor=#e7dcc3|5-faces
bgcolor=#e7dcc3|4-faces
bgcolor=#e7dcc3|Cells
bgcolor=#e7dcc3|Faces
bgcolor=#e7dcc3|Edges46080
bgcolor=#e7dcc3|Vertices11520
bgcolor=#e7dcc3|Vertex figure
bgcolor=#e7dcc3|Coxeter groupsB6, [4,3,3,3,3]
bgcolor=#e7dcc3|Propertiesconvex

= Alternate names =

  • Celligreatorhombated hexeract (Acronym: cagorx) (Jonathan Bowers)Klitzing, (x4x3x3o3x3o - cagorx)

= Images =

{{6-cube Coxeter plane graphs|t0124|150}}

Steriruncinated 6-cube

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!bgcolor=#e7dcc3 colspan=2|steriruncinated 6-cube

bgcolor=#e7dcc3|Typeuniform 6-polytope
bgcolor=#e7dcc3|Schläfli symbolt0,3,4{4,3,3,3,3}
bgcolor=#e7dcc3|Coxeter-Dynkin diagrams{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node}}
bgcolor=#e7dcc3|5-faces
bgcolor=#e7dcc3|4-faces
bgcolor=#e7dcc3|Cells
bgcolor=#e7dcc3|Faces
bgcolor=#e7dcc3|Edges15360
bgcolor=#e7dcc3|Vertices3840
bgcolor=#e7dcc3|Vertex figure
bgcolor=#e7dcc3|Coxeter groupsB6, [4,3,3,3,3]
bgcolor=#e7dcc3|Propertiesconvex

= Alternate names =

  • Celliprismated hexeract (Acronym: copox) (Jonathan Bowers){{sfn|Klitzing|at=[https://bendwavy.org/klitzing/incmats/copox.htm (x4o3o3x3x3o - copox)]}}

= Images =

{{6-cube Coxeter plane graphs|t034|150}}

Steriruncitruncated 6-cube

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!bgcolor=#e7dcc3 colspan=2|steriruncitruncated 6-cube

bgcolor=#e7dcc3|Typeuniform 6-polytope
bgcolor=#e7dcc3|Schläfli symbol2t2r{4,3,3,3,3}
bgcolor=#e7dcc3|Coxeter-Dynkin diagrams{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1|3|node}}
{{CDD|node|split1|nodes_11|3a4b|nodes_11|3a|nodea}}
bgcolor=#e7dcc3|5-faces
bgcolor=#e7dcc3|4-faces
bgcolor=#e7dcc3|Cells
bgcolor=#e7dcc3|Faces
bgcolor=#e7dcc3|Edges40320
bgcolor=#e7dcc3|Vertices11520
bgcolor=#e7dcc3|Vertex figure
bgcolor=#e7dcc3|Coxeter groupsB6, [4,3,3,3,3]
bgcolor=#e7dcc3|Propertiesconvex

= Alternate names =

  • Celliprismatotruncated hexeract (Acronym: captix) (Jonathan Bowers)Klitzing, (x4x3o3x3x3o - captix)

= Images =

{{6-cube Coxeter plane graphs|t0134|150}}

Steriruncicantellated 6-cube

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!bgcolor=#e7dcc3 colspan=2|steriruncicantellated 6-cube

bgcolor=#e7dcc3|Typeuniform 6-polytope
bgcolor=#e7dcc3|Schläfli symbolt0,2,3,4{4,3,3,3,3}
bgcolor=#e7dcc3|Coxeter-Dynkin diagrams{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node}}
bgcolor=#e7dcc3|5-faces
bgcolor=#e7dcc3|4-faces
bgcolor=#e7dcc3|Cells
bgcolor=#e7dcc3|Faces
bgcolor=#e7dcc3|Edges40320
bgcolor=#e7dcc3|Vertices11520
bgcolor=#e7dcc3|Vertex figure
bgcolor=#e7dcc3|Coxeter groupsB6, [4,3,3,3,3]
bgcolor=#e7dcc3|Propertiesconvex

= Alternate names =

  • Celliprismatorhombated hexeract (Acronym: coprix) (Jonathan Bowers){{sfn|Klitzing|at=[https://bendwavy.org/klitzing/incmats/coprix.htm (x4o3x3x3x3o - coprix)]}}

= Images =

{{6-cube Coxeter plane graphs|t0234|150}}

Steriruncicantitruncated 6-cube

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!bgcolor=#e7dcc3 colspan=2|Steriuncicantitruncated 6-cube

bgcolor=#e7dcc3|Typeuniform 6-polytope
bgcolor=#e7dcc3|Schläfli symboltr2r{4,3,3,3,3}
bgcolor=#e7dcc3|Coxeter-Dynkin diagrams{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node}}
{{CDD|node_1|split1|nodes_11|3a4b|nodes_11|3a|nodea}}
bgcolor=#e7dcc3|5-faces
bgcolor=#e7dcc3|4-faces
bgcolor=#e7dcc3|Cells
bgcolor=#e7dcc3|Faces
bgcolor=#e7dcc3|Edges69120
bgcolor=#e7dcc3|Vertices23040
bgcolor=#e7dcc3|Vertex figure
bgcolor=#e7dcc3|Coxeter groupsB6, [4,3,3,3,3]
bgcolor=#e7dcc3|Propertiesconvex

= Alternate names =

  • Great cellated hexeract (Acronym: gocax) (Jonathan Bowers)Klitzing, (x4x3x3x3x3o - gocax)

= Images =

{{6-cube Coxeter plane graphs|t01234|150}}

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.

{{Hexeract family}}

Notes

{{reflist}}

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, [http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html wiley.com], {{isbn|978-0-471-01003-6}}
  • (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.
  • {{KlitzingPolytopes|polypeta.htm|6D uniform polytopes (polypeta) with acronyms}}{{sfn whitelist|CITEREFKlitzing}}

External links

  • [https://web.archive.org/web/20070310205351/http://members.cox.net/hedrondude/topes.htm Polytopes of Various Dimensions]
  • [http://tetraspace.alkaline.org/glossary.htm Multi-dimensional Glossary]

{{Polytopes}}

Category:6-polytopes