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Stericated 7-cubes#Steriruncicantellated 7-cube

class=wikitable style="float:right; margin-left:8px; width:480px"
colspan=3|Orthogonal projections in B6 Coxeter plane
align=center

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

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

|160px
Bistericated 7-cube
{{CDD|node|4|node_1|3|node|3|node|3|node|3|node_1|3|node}}

align=center

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

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

|160px
Stericantellated 7-cube
{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node|3|node}}

align=center

|160px
Bistericantellated 7-cube
{{CDD|node|4|node_1|3|node|3|node_1|3|node|3|node_1|3|node}}

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

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

align=center

|160px
Steriruncinated 7-cube
{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node|3|node}}

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

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

align=center

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

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

|160px
Bisteriruncicantitruncated 7-cube
{{CDD|node|4|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}

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

There are 24 unique sterication for the 7-cube with permutations of truncations, cantellations, and runcinations. 10 are more simply constructed from the 7-orthoplex.

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

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Stericated 7-cube

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

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

style="background:#e7dcc3;"|Typeuniform 7-polytope
style="background:#e7dcc3;"|Schläfli symbolt0,4{4,35}
style="background:#e7dcc3;"|Coxeter-Dynkin diagrams{{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node|3|node}}
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 hepteract (acronym: ) (Jonathan Bowers)Klitizing, (x3o3o3o3x3o4o - )

= Images =

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

Bistericated 7-cube

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

! style="background:#e7dcc3;" colspan="2"|bistericated 7-cube

style="background:#e7dcc3;"|Typeuniform 7-polytope
style="background:#e7dcc3;"|Schläfli symbolt1,5{4,35}
style="background:#e7dcc3;"|Coxeter-Dynkin diagrams{{CDD|node|4|node_1|3|node|3|node|3|node|3|node_1|3|node}}
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 bicellated hepteractihecatonicosoctaexon (acronym: ) (Jonathan Bowers)Klitizing, (x3o3x3o3x3o4o - )

= Images =

{{B7 Coxeter plane graphs|t15|150}}

Steritruncated 7-cube

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

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

style="background:#e7dcc3;"|Typeuniform 7-polytope
style="background:#e7dcc3;"|Schläfli symbolt0,1,4{4,35}
style="background:#e7dcc3;"|Coxeter-Dynkin diagrams{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1|3|node|3|node}}
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 hepteract (acronym: ) (Jonathan Bowers)Klitizing, (x3x3o3o3x3o4o - )

= Images =

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

Bisteritruncated 7-cube

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

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

style="background:#e7dcc3;"|Typeuniform 7-polytope
style="background:#e7dcc3;"|Schläfli symbolt1,2,5{4,35}
style="background:#e7dcc3;"|Coxeter-Dynkin diagrams{{CDD|node|4|node_1|3|node_1|3|node|3|node|3|node_1|3|node}}
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 hepteract (acronym: ) (Jonathan Bowers)Klitizing, (o3x3x3o3o3x4o - )

= Images =

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

Stericantellated 7-cube

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

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

style="background:#e7dcc3;"|Typeuniform 7-polytope
style="background:#e7dcc3;"|Schläfli symbolt0,2,4{4,35}
style="background:#e7dcc3;"|Coxeter-Dynkin diagrams{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node|3|node}}
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 hepteract (acronym: ) (Jonathan Bowers)Klitizing, (x3o3x3o3x3o4o - )

= Images =

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

Bistericantellated 7-cube

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

! style="background:#e7dcc3;" colspan="2"|Bistericantellated 7-cube

style="background:#e7dcc3;"|Typeuniform 7-polytope
style="background:#e7dcc3;"|Schläfli symbolt1,3,5{4,35}
style="background:#e7dcc3;"|Coxeter-Dynkin diagrams{{CDD|node|4|node_1|3|node|3|node_1|3|node|3|node_1|3|node}}
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=

  • Bicellirhombihepteract (acronym: ) (Jonathan Bowers)Klitizing, (o3x3o3x3o3x4o - )

= Images =

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

Stericantitruncated 7-cube

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

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

style="background:#e7dcc3;"|Typeuniform 7-polytope
style="background:#e7dcc3;"|Schläfli symbolt0,1,2,4{4,35}
style="background:#e7dcc3;"|Coxeter-Dynkin diagrams{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1|3|node|3|node}}
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 hepteract (acronym: ) (Jonathan Bowers)Klitizing, (x3x3x3o3x3o4o - )

= Images =

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

Bistericantitruncated 7-cube

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

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

style="background:#e7dcc3;"|Typeuniform 7-polytope
style="background:#e7dcc3;"|Schläfli symbolt1,2,3,5{4,35}
style="background:#e7dcc3;"|Coxeter-Dynkin diagrams{{CDD|node|4|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node}}
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 hepteract (acronym: ) (Jonathan Bowers)Klitizing, (o3x3x3x3o3x4o - )

= Images =

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

Steriruncinated 7-cube

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

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

style="background:#e7dcc3;"|Typeuniform 7-polytope
style="background:#e7dcc3;"|Schläfli symbolt0,3,4{4,35}
style="background:#e7dcc3;"|Coxeter-Dynkin diagrams{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node|3|node}}
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 hepteract (acronym: ) (Jonathan Bowers)Klitizing, (x3o3o3x3x3o4o - )

= Images =

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

Steriruncitruncated 7-cube

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

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

style="background:#e7dcc3;"|Typeuniform 7-polytope
style="background:#e7dcc3;"|Schläfli symbolt0,1,3,4{4,35}
style="background:#e7dcc3;"|Coxeter-Dynkin diagrams{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1|3|node|3|node}}
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 hepteract (acronym: ) (Jonathan Bowers)Klitizing, (x3x3x3o3x3o4o - )

= Images =

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

Steriruncicantellated 7-cube

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

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

style="background:#e7dcc3;"|Typeuniform 7-polytope
style="background:#e7dcc3;"|Schläfli symbolt0,2,3,4{4,35}
style="background:#e7dcc3;"|Coxeter-Dynkin diagrams{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node}}
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 hepteract (acronym: ) (Jonathan Bowers)Klitizing, (x3o3x3x3x3o4o - )

= Images =

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

Bisteriruncitruncated 7-cube

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

! style="background:#e7dcc3;" colspan="2"|bisteriruncitruncated 7-cube

style="background:#e7dcc3;"|Typeuniform 7-polytope
style="background:#e7dcc3;"|Schläfli symbolt1,2,4,5{4,35}
style="background:#e7dcc3;"|Coxeter-Dynkin diagrams{{CDD|node|4|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node}}
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=

  • Bicelliprismatotruncated hepteractihecatonicosoctaexon (acronym: ) (Jonathan Bowers)Klitizing, (o3x3x3o3x3x4o - )

= Images =

{{B7 Coxeter plane graphs|t1245|150}}

==Steriruncicantitruncated 7-cube==

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

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

style="background:#e7dcc3;"|Typeuniform 7-polytope
style="background:#e7dcc3;"|Schläfli symbolt0,1,2,3,4{4,35}
style="background:#e7dcc3;"|Coxeter-Dynkin diagrams{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node}}
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 hepteract (acronym: ) (Jonathan Bowers)Klitizing, (x3x3x3x3x3o4o - )

= Images =

{{7-cube Coxeter plane graphs|t01234|150||NOA5orA3}}

Bisteriruncicantitruncated 7-cube

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

! style="background:#e7dcc3;" colspan="2"|bisteriruncicantitruncated 7-cube

style="background:#e7dcc3;"|Typeuniform 7-polytope
style="background:#e7dcc3;"|Schläfli symbolt1,2,3,4,5{4,35}
style="background:#e7dcc3;"|Coxeter-Dynkin diagrams{{CDD|node|4|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}
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 bicellated hepteractihecatonicosoctaexon (Acronym ) (Jonathan Bowers) Klitizing, (o3x3x3x3x3x4o - )

= Images =

{{B7 Coxeter plane graphs|t12345|150|NOB7A6}}

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, {{ISBN|978-0-471-01003-6}} [http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html]
  • (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)}} x3o3o3o3x3o4o - , x3o3x3o3x3o4o - , x3x3o3o3x3o4o - , o3x3x3o3o3x4o - , x3o3x3o3x3o4o - , o3x3o3x3o3x4o - , x3x3x3o3x3o4o - , o3x3x3x3o3x4o - , x3o3o3x3x3o4o - , x3x3x3o3x3o4o - , x3o3x3x3x3o4o - , o3x3x3o3x3x4o - , x3x3x3x3x3o4o - , o3x3x3x3x3x4o -

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