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Stericated 6-orthoplexes#Stericated 6-orthoplex

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|160px
6-orthoplex
{{CDD|node_1|3|node|3|node|3|node|3|node|4|node}}

|160px
Stericated 6-orthoplex
{{CDD|node_1|3|node|3|node|3|node|3|node_1|4|node}}

|160px
Steritruncated 6-orthoplex
{{CDD|node_1|3|node_1|3|node|3|node|3|node_1|4|node}}

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|160px
Stericantellated 6-orthoplex
{{CDD|node_1|3|node|3|node_1|3|node|3|node_1|4|node}}

|160px
Stericantitruncated 6-orthoplex
{{CDD|node_1|3|node_1|3|node_1|3|node|3|node_1|4|node}}

|160px
Steriruncinated 6-orthoplex
{{CDD|node_1|3|node|3|node|3|node_1|3|node_1|4|node}}

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|160px
Steriruncitruncated 6-orthoplex
{{CDD|node_1|3|node_1|3|node|3|node_1|3|node_1|4|node}}

|160px
Steriruncicantellated 6-orthoplex
{{CDD|node_1|3|node|3|node_1|3|node_1|3|node_1|4|node}}

|160px
Steriruncicantitruncated 6-orthoplex
{{CDD|node_1|3|node_1|3|node_1|3|node_1|3|node_1|4|node}}

colspan=3|Orthogonal 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

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

bgcolor=#e7dcc3|Typeuniform 6-polytope
bgcolor=#e7dcc3|Schläfli symbol2r2r{3,3,3,3,4}
bgcolor=#e7dcc3|Coxeter-Dynkin diagrams{{CDD|node_1|3|node|3|node|3|node|3|node_1|4|node}}
{{CDD|node|split1|nodes|3ab|nodes_11|4a|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 hexacontatetrapeton (Acronym: scag) (Jonathan Bowers){{sfn|Klitzing|at=[https://bendwavy.org/klitzing/incmats/scag.htm (x3o3o3o3x4o - scag)]}}

= Images =

{{6-cube Coxeter plane graphs|t15|150}}

Steritruncated 6-orthoplex

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

bgcolor=#e7dcc3|Typeuniform 6-polytope
bgcolor=#e7dcc3|Schläfli symbolt0,1,4{3,3,3,3,4}
bgcolor=#e7dcc3|Coxeter-Dynkin diagrams{{CDD|node_1|3|node_1|3|node|3|node|3|node_1|4|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 =

  • Cellitruncated hexacontatetrapeton (Acronym: catog) (Jonathan Bowers){{sfn|Klitzing|at=[https://bendwavy.org/klitzing/incmats/catog.htm (x3x3o3o3x4o - catog)]}}

= Images =

{{6-cube Coxeter plane graphs|t145|150}}

Stericantellated 6-orthoplex

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

bgcolor=#e7dcc3|Typeuniform 6-polytope
bgcolor=#e7dcc3|Schläfli symbolst0,2,4{34,4}
rr2r{3,3,3,3,4}
bgcolor=#e7dcc3|Coxeter-Dynkin diagrams{{CDD|node_1|3|node|3|node_1|3|node|3|node_1|4|node}}{{CDD|node_1|split1|nodes|3ab|nodes_11|4a|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 hexacontatetrapeton (Acronym: crag) (Jonathan Bowers){{sfn|Klitzing|at=[https://bendwavy.org/klitzing/incmats/scrag.htm (x3o3x3o3x4o - crag)]}}

= Images =

{{6-cube Coxeter plane graphs|t135|150}}

Stericantitruncated 6-orthoplex

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!bgcolor=#e7dcc3 colspan=2|Stericantitruncated 6-orthoplex

bgcolor=#e7dcc3|Typeuniform 6-polytope
bgcolor=#e7dcc3|Schläfli symbolt0,1,2,4{3,3,3,3,4}
bgcolor=#e7dcc3|Coxeter-Dynkin diagrams{{CDD|node_1|3|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 hexacontatetrapeton (Acronym: cagorg) (Jonathan Bowers) {{sfn|Klitzing|at=[https://bendwavy.org/klitzing/incmats/cagorg.htm (x3x3x3o3x4o - cagorg)]}}

= Images =

{{6-cube Coxeter plane graphs|t1345|150}}

Steriruncinated 6-orthoplex

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!bgcolor=#e7dcc3 colspan=2|Steriruncinated 6-orthoplex

bgcolor=#e7dcc3|Typeuniform 6-polytope
bgcolor=#e7dcc3|Schläfli symbolt0,3,4{3,3,3,3,4}
bgcolor=#e7dcc3|Coxeter-Dynkin diagrams{{CDD|node_1|3|node|3|node|3|node_1|3|node_1|4|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 hexacontatetrapeton (Acronym: copog) (Jonathan Bowers){{sfn|Klitzing|at=[https://bendwavy.org/klitzing/incmats/copog.htm (x3o3o3x3x4o - copog)]}}

= Images =

{{6-cube Coxeter plane graphs|t125|150}}

Steriruncitruncated 6-orthoplex

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!bgcolor=#e7dcc3 colspan=2|Steriruncitruncated 6-orthoplex

bgcolor=#e7dcc3|Typeuniform 6-polytope
bgcolor=#e7dcc3|Schläfli symbol2t2r{3,3,3,3,4}
bgcolor=#e7dcc3|Coxeter-Dynkin diagrams{{CDD|node_1|3|node_1|3|node|3|node_1|3|node_1|4|node}}
{{CDD|node|split1|nodes_11|3ab|nodes_11|4a|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 hexacontatetrapeton (Acronym: captog) (Jonathan Bowers){{sfn|Klitzing|at=[https://bendwavy.org/klitzing/incmats/captog.htm (x3x3o3x3x4o - captog)]}}

= Images =

{{6-cube Coxeter plane graphs|t1245|150}}

Steriruncicantellated 6-orthoplex

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!bgcolor=#e7dcc3 colspan=2|Steriruncicantellated 6-orthoplex

bgcolor=#e7dcc3|Typeuniform 6-polytope
bgcolor=#e7dcc3|Schläfli symbolt0,2,3,4{3,3,3,3,4}
bgcolor=#e7dcc3|Coxeter-Dynkin diagrams{{CDD|node_1|3|node|3|node_1|3|node_1|3|node_1|4|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 hexacontatetrapeton (Acronym: coprag) (Jonathan Bowers){{sfn|Klitzing|at=[https://bendwavy.org/klitzing/incmats/coprag.htm (x3o3x3x3x4o - coprag)]}}

= Images =

{{6-cube Coxeter plane graphs|t1235|150}}

Steriruncicantitruncated 6-orthoplex

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

bgcolor=#e7dcc3|Typeuniform 6-polytope
bgcolor=#e7dcc3|Schläfli symbolst0,1,2,3,4{34,4}
tr2r{3,3,3,3,4}
bgcolor=#e7dcc3|Coxeter-Dynkin diagrams{{CDD|node_1|3|node_1|3|node_1|3|node_1|3|node_1|4|node}}{{CDD|node_1|split1|nodes_11|3ab|nodes_11|4a|nodea}}
bgcolor=#e7dcc3|5-faces536:
12 t0,1,2,3{3,3,3,4}40px
60 {}×t0,1,2{3,3,4} 40px×40px
160 {6}×t0,1,2{3,3} 40px×40px
240 {4}×t0,1,2{3,3} 40px×40px
64 t0,1,2,3,4{34}40px
bgcolor=#e7dcc3|4-faces8216
bgcolor=#e7dcc3|Cells38400
bgcolor=#e7dcc3|Faces76800
bgcolor=#e7dcc3|Edges69120
bgcolor=#e7dcc3|Vertices23040
bgcolor=#e7dcc3|Vertex figureirregular 5-simplex
bgcolor=#e7dcc3|Coxeter groupsB6, [4,3,3,3,3]
bgcolor=#e7dcc3|Propertiesconvex

= Alternate names =

  • Great cellated hexacontatetrapeton (Acronym: gocog) (Jonathan Bowers){{sfn|Klitzing|at=[https://bendwavy.org/klitzing/incmats/gocog.htm (x3x3x3x3x4o - gocog)]}}

= Images =

{{6-cube Coxeter plane graphs|t12345|150}}

= 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 {{CDD|nodes_hh|split2|node_h|3|node_h|3|node_h|3|node_h}} or {{CDD|node|4|node_h|3|node_h|3|node_h|3|node_h|3|node_h}} 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-orthoplex 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