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Stericated 7-orthoplexes#Steritruncated 7-orthoplex

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colspan=3|Orthogonal projections in B6 Coxeter plane
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7-orthoplex
{{CDD|node_1|3|node|3|node|3|node|3|node|3|node|4|node}}

|160px
Stericated 7-orthoplex
{{CDD|node_1|3|node|3|node|3|node|3|node_1|3|node|4|node}}

|160px
Steritruncated 7-orthoplex
{{CDD|node_1|3|node_1|3|node|3|node|3|node_1|3|node|4|node}}

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|160px
Bisteritruncated 7-orthoplex
{{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node_1|4|node}}

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Stericantellated 7-orthoplex
{{CDD|node_1|3|node|3|node_1|3|node|3|node_1|3|node|4|node}}

|160px
Stericantitruncated 7-orthoplex
{{CDD|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node|4|node}}

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|160px
Bistericantitruncated 7-orthoplex
{{CDD|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|4|node}}

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Steriruncinated 7-orthoplex
{{CDD|node_1|3|node|3|node|3|node_1|3|node_1|3|node|4|node}}

|160px
Steriruncitruncated 7-orthoplex
{{CDD|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|4|node}}

align=center

|160px
Steriruncicantellated 7-orthoplex
{{CDD|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|4|node}}

|160px
Bisteriruncitruncated 7-orthoplex
{{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|4|node}}

|160px
Steriruncicantitruncated 7-orthoplex
{{CDD|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node|4|node}}

In seven-dimensional geometry, a stericated 7-orthoplex is a convex uniform 7-polytope with 4th order truncations (sterication) of the regular 7-orthoplex.

There are 24 unique sterication for the 7-orthoplex with permutations of truncations, cantellations, and runcinations. 14 are more simply constructed from the 7-cube.

This polytope is one of 127 uniform 7-polytopes with B7 symmetry.

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Stericated 7-orthoplex

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! style="background:#e7dcc3;" colspan="2"|Stericated 7-orthoplex

style="background:#e7dcc3;"|Typeuniform 7-polytope
style="background:#e7dcc3;"|Schläfli symbolt0,4{35,4}
style="background:#e7dcc3;"|Coxeter-Dynkin diagrams{{CDD|node_1|3|node|3|node|3|node|3|node_1|3|node|4|node}}
{{CDD|node_1|3|node|3|node|3|node|3|node_1|split1|nodes}}
style="background:#e7dcc3;"|6-faces
style="background:#e7dcc3;"|5-faces
style="background:#e7dcc3;"|4-faces
style="background:#e7dcc3;"|Cells
style="background:#e7dcc3;"|Faces
style="background:#e7dcc3;"|Edges
style="background:#e7dcc3;"|Vertices
style="background:#e7dcc3;"|Vertex figure
style="background:#e7dcc3;"|Coxeter groupsB7, [4,35]
style="background:#e7dcc3;"|Propertiesconvex

= Alternate names=

  • Small cellated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)Klitizing, (x3o3o3o3x3o4o - )

= Images =

{{7-cube Coxeter plane graphs|t26|150}}

Steritruncated 7-orthoplex

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! style="background:#e7dcc3;" colspan="2"|steritruncated 7-orthoplex

style="background:#e7dcc3;"|Typeuniform 7-polytope
style="background:#e7dcc3;"|Schläfli symbolt0,1,4{35,4}
style="background:#e7dcc3;"|Coxeter-Dynkin diagrams{{CDD|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node|4|node}}
{{CDD|node_1|3|node_1|3|node_1|3|node|3|node_1|split1|nodes}}
style="background:#e7dcc3;"|6-faces
style="background:#e7dcc3;"|5-faces
style="background:#e7dcc3;"|4-faces
style="background:#e7dcc3;"|Cells
style="background:#e7dcc3;"|Faces
style="background:#e7dcc3;"|Edges
style="background:#e7dcc3;"|Vertices
style="background:#e7dcc3;"|Vertex figure
style="background:#e7dcc3;"|Coxeter groupsB7, [4,35]
style="background:#e7dcc3;"|Propertiesconvex

= Alternate names=

  • Cellitruncated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)Klitizing, (x3x3o3o3x3o4o - )

= Images =

{{7-cube Coxeter plane graphs|t256|150}}

Bisteritruncated 7-orthoplex

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! style="background:#e7dcc3;" colspan="2"|bisteritruncated 7-orthoplex

style="background:#e7dcc3;"|Typeuniform 7-polytope
style="background:#e7dcc3;"|Schläfli symbolt1,2,5{35,4}
style="background:#e7dcc3;"|Coxeter-Dynkin diagrams{{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node_1|4|node}}
{{CDD|node|3|node_1|3|node_1|3|node|3|node|split1|nodes_11}}
style="background:#e7dcc3;"|6-faces
style="background:#e7dcc3;"|5-faces
style="background:#e7dcc3;"|4-faces
style="background:#e7dcc3;"|Cells
style="background:#e7dcc3;"|Faces
style="background:#e7dcc3;"|Edges
style="background:#e7dcc3;"|Vertices
style="background:#e7dcc3;"|Vertex figure
style="background:#e7dcc3;"|Coxeter groupsB7, [4,35]
style="background:#e7dcc3;"|Propertiesconvex

= Alternate names=

  • Bicellitruncated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)Klitizing, (o3x3x3o3o3x4o - )

= Images =

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

Stericantellated 7-orthoplex

class="wikitable" align="right" style="margin-left:10px" width="320"

! style="background:#e7dcc3;" colspan="2"|Stericantellated 7-orthoplex

style="background:#e7dcc3;"|Typeuniform 7-polytope
style="background:#e7dcc3;"|Schläfli symbolt0,2,4{35,4}
style="background:#e7dcc3;"|Coxeter-Dynkin diagrams{{CDD|node_1|3|node|3|node_1|3|node|3|node_1|3|node|4|node}}
{{CDD|node_1|3|node|3|node_1|3|node|3|node_1|split1|nodes}}
style="background:#e7dcc3;"|6-faces
style="background:#e7dcc3;"|5-faces
style="background:#e7dcc3;"|4-faces
style="background:#e7dcc3;"|Cells
style="background:#e7dcc3;"|Faces
style="background:#e7dcc3;"|Edges
style="background:#e7dcc3;"|Vertices
style="background:#e7dcc3;"|Vertex figure
style="background:#e7dcc3;"|Coxeter groupsB7, [4,35]
style="background:#e7dcc3;"|Propertiesconvex

= Alternate names=

  • Cellirhombated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)Klitizing, (x3o3x3o3x3o4o - )

= Images =

{{7-cube Coxeter plane graphs|t246|150}}

Stericantitruncated 7-orthoplex

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! style="background:#e7dcc3;" colspan="2"|stericantitruncated 7-orthoplex

style="background:#e7dcc3;"|Typeuniform 7-polytope
style="background:#e7dcc3;"|Schläfli symbolt0,1,2,4{35,4}
style="background:#e7dcc3;"|Coxeter-Dynkin diagrams{{CDD|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node|4|node}}
{{CDD|node_1|3|node_1|3|node_1|3|node|3|node_1|split1|nodes}}
style="background:#e7dcc3;"|6-faces
style="background:#e7dcc3;"|5-faces
style="background:#e7dcc3;"|4-faces
style="background:#e7dcc3;"|Cells
style="background:#e7dcc3;"|Faces
style="background:#e7dcc3;"|Edges
style="background:#e7dcc3;"|Vertices
style="background:#e7dcc3;"|Vertex figure
style="background:#e7dcc3;"|Coxeter groupsB7, [4,35]
style="background:#e7dcc3;"|Propertiesconvex

= Alternate names=

  • Celligreatorhombated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)Klitizing, (x3x3x3o3x3o4o - )

= Images =

{{7-cube Coxeter plane graphs|t2456|150}}

Bistericantitruncated 7-orthoplex

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! style="background:#e7dcc3;" colspan="2"|bistericantitruncated 7-orthoplex

style="background:#e7dcc3;"|Typeuniform 7-polytope
style="background:#e7dcc3;"|Schläfli symbolt1,2,3,5{35,4}
style="background:#e7dcc3;"|Coxeter-Dynkin diagrams{{CDD|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|4|node}}
{{CDD|node|3|node_1|3|node_1|3|node_1|3|node|split1|nodes_11}}
style="background:#e7dcc3;"|6-faces
style="background:#e7dcc3;"|5-faces
style="background:#e7dcc3;"|4-faces
style="background:#e7dcc3;"|Cells
style="background:#e7dcc3;"|Faces
style="background:#e7dcc3;"|Edges
style="background:#e7dcc3;"|Vertices
style="background:#e7dcc3;"|Vertex figure
style="background:#e7dcc3;"|Coxeter groupsB7, [4,35]
style="background:#e7dcc3;"|Propertiesconvex

= Alternate names=

  • Bicelligreatorhombated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)Klitizing, (o3x3x3x3o3x4o - )

= Images =

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

Steriruncinated 7-orthoplex

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! style="background:#e7dcc3;" colspan="2"|Steriruncinated 7-orthoplex

style="background:#e7dcc3;"|Typeuniform 7-polytope
style="background:#e7dcc3;"|Schläfli symbolt0,3,4{35,4}
style="background:#e7dcc3;"|Coxeter-Dynkin diagrams{{CDD|node_1|3|node|3|node|3|node_1|3|node_1|3|node|4|node}}
{{CDD|node_1|3|node|3|node|3|node_1|3|node_1|split1|nodes}}
style="background:#e7dcc3;"|6-faces
style="background:#e7dcc3;"|5-faces
style="background:#e7dcc3;"|4-faces
style="background:#e7dcc3;"|Cells
style="background:#e7dcc3;"|Faces
style="background:#e7dcc3;"|Edges
style="background:#e7dcc3;"|Vertices
style="background:#e7dcc3;"|Vertex figure
style="background:#e7dcc3;"|Coxeter groupsB7, [4,35]
style="background:#e7dcc3;"|Propertiesconvex

= Alternate names=

  • Celliprismated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)Klitizing, (x3o3o3x3x3o4o - )

= Images =

{{7-cube Coxeter plane graphs|t236|150|NOB7A6}}

Steriruncitruncated 7-orthoplex

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! style="background:#e7dcc3;" colspan="2"|steriruncitruncated 7-orthoplex

style="background:#e7dcc3;"|Typeuniform 7-polytope
style="background:#e7dcc3;"|Schläfli symbolt0,1,3,4{35,4}
style="background:#e7dcc3;"|Coxeter-Dynkin diagrams{{CDD|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|4|node}}
{{CDD|node_1|3|node_1|3|node|3|node_1|3|node_1|split1|nodes}}
style="background:#e7dcc3;"|6-faces
style="background:#e7dcc3;"|5-faces
style="background:#e7dcc3;"|4-faces
style="background:#e7dcc3;"|Cells
style="background:#e7dcc3;"|Faces
style="background:#e7dcc3;"|Edges
style="background:#e7dcc3;"|Vertices
style="background:#e7dcc3;"|Vertex figure
style="background:#e7dcc3;"|Coxeter groupsB7, [4,35]
style="background:#e7dcc3;"|Propertiesconvex

= Alternate names=

  • Celliprismatotruncated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)Klitizing, (x3x3x3o3x3o4o - )

= Images =

{{7-cube Coxeter plane graphs|t2356|150}}

Steriruncicantellated 7-orthoplex

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! style="background:#e7dcc3;" colspan="2"|steriruncicantellated 7-orthoplex

style="background:#e7dcc3;"|Typeuniform 7-polytope
style="background:#e7dcc3;"|Schläfli symbolt0,2,3,4{35,4}
style="background:#e7dcc3;"|Coxeter-Dynkin diagrams{{CDD|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|4|node}}
{{CDD|node_1|3|node|3|node_1|3|node_1|3|node_1|split1|nodes}}
style="background:#e7dcc3;"|6-faces
style="background:#e7dcc3;"|5-faces
style="background:#e7dcc3;"|4-faces
style="background:#e7dcc3;"|Cells
style="background:#e7dcc3;"|Faces
style="background:#e7dcc3;"|Edges
style="background:#e7dcc3;"|Vertices
style="background:#e7dcc3;"|Vertex figure
style="background:#e7dcc3;"|Coxeter groupsB7, [4,35]
style="background:#e7dcc3;"|Propertiesconvex

= Alternate names=

  • Celliprismatorhombated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)Klitizing, (x3o3x3x3x3o4o - )

= Images =

{{7-cube Coxeter plane graphs|t2346|150}}

Steriruncicantitruncated 7-orthoplex

class="wikitable" align="right" style="margin-left:10px" width="320"

! style="background:#e7dcc3;" colspan="2"|steriruncicantitruncated 7-orthoplex

style="background:#e7dcc3;"|Typeuniform 7-polytope
style="background:#e7dcc3;"|Schläfli symbolt0,1,2,3,4{35,4}
style="background:#e7dcc3;"|Coxeter-Dynkin diagrams{{CDD|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node|4|node}}
{{CDD|node_1|3|node_1|3|node_1|3|node_1|3|node_1|split1|nodes}}
style="background:#e7dcc3;"|6-faces
style="background:#e7dcc3;"|5-faces
style="background:#e7dcc3;"|4-faces
style="background:#e7dcc3;"|Cells
style="background:#e7dcc3;"|Faces
style="background:#e7dcc3;"|Edges
style="background:#e7dcc3;"|Vertices
style="background:#e7dcc3;"|Vertex figure
style="background:#e7dcc3;"|Coxeter groupsB7, [4,35]
style="background:#e7dcc3;"|Propertiesconvex

= Alternate names=

  • Great cellated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)Klitizing, (x3x3x3x3x3o4o - )

= Images =

{{7-cube Coxeter plane graphs|t23456|150}}

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, [https://www.wiley.com/en-us/Kaleidoscopes-p-9780471010036 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|polyexa.htm|7D|uniform polytopes (polyexa)}}

External links

  • [http://www.polytope.net/hedrondude/topes.htm Polytopes of Various Dimensions]
  • [http://tetraspace.alkaline.org/glossary.htm Multi-dimensional Glossary]

{{Polytopes}}

Category:7-polytopes