Stericated 7-cubes

From Wikipedia, the free encyclopedia

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

More information Orthogonal projections in B6 Coxeter plane ...
Orthogonal projections in B6 Coxeter plane

7-cube
Stericated 7-cube
Bistericated 7-cube

Steritruncated 7-cube
Bisteritruncated 7-cube
Stericantellated 7-cube

Bistericantellated 7-cube
Stericantitruncated 7-cube
Bistericantitruncated 7-cube

Steriruncinated 7-cube
Steriruncitruncated 7-cube
Steriruncicantellated 7-cube

Bisteriruncitruncated 7-cube
Steriruncicantitruncated 7-cube
Bisteriruncicantitruncated 7-cube
Close

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.

Stericated 7-cube

Stericated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex

Alternate names

  • Small cellated hepteract (acronym: scosa) (Jonathan Bowers)[1]

Images

More information Coxeter plane, B7 / A6 ...
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]
Close

Bistericated 7-cube

More information Bistericated 7-cube ...
Bistericated 7-cube
Typeuniform 7-polytope
Schläfli symbolt1,5{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Small bicellated hepteractihecatonicosaoctaexon (acronym: sabcosaz) (Jonathan Bowers)[2]

Images

More information Coxeter plane, B7 / A6 ...
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]
Close

Steritruncated 7-cube

More information Steritruncated 7-cube ...
Steritruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,1,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Cellitruncated hepteract (acronym: catsa) (Jonathan Bowers)[3]

Images

More information Coxeter plane, B7 / A6 ...
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]
Close

Bisteritruncated 7-cube

More information Bisteritruncated 7-cube ...
Bisteritruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt1,2,5{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Bicellitruncated hepteract (acronym: bactasa) (Jonathan Bowers)[4]

Images

More information Coxeter plane, B7 / A6 ...
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]
Close

Stericantellated 7-cube

More information Stericantellated 7-cube ...
Stericantellated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,2,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Cellirhombated hepteract (acronym: carsa) (Jonathan Bowers)[5]

Images

More information Coxeter plane, B7 / A6 ...
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]
Close

Bistericantellated 7-cube

More information Bistericantellated 7-cube ...
Bistericantellated 7-cube
Typeuniform 7-polytope
Schläfli symbolt1,3,5{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Bicellirhombihepteract (acronym: bacresaz) (Jonathan Bowers)[6]

Images

More information Coxeter plane, B7 / A6 ...
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]
Close

Stericantitruncated 7-cube

More information Stericantitruncated 7-cube ...
Stericantitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,1,2,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Celligreatorhombated hepteract (acronym: cogarsa) (Jonathan Bowers)[7]

Images

More information Coxeter plane, B7 / A6 ...
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]
Close

Bistericantitruncated 7-cube

More information Bistericantitruncated 7-cube ...
Bistericantitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt1,2,3,5{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Bicelligreatorhombated hepteract (acronym: becgresa) (Jonathan Bowers)[8]

Images

More information Coxeter plane, B7 / A6 ...
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]
Close

Steriruncinated 7-cube

More information Steriruncinated 7-cube ...
Steriruncinated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,3,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Celliprismated hepteract (acronym: capsa) (Jonathan Bowers)[9]

Images

More information Coxeter plane, B7 / A6 ...
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]
Close

Steriruncitruncated 7-cube

More information Steriruncitruncated 7-cube ...
Steriruncitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,1,3,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Celliprismatotruncated hepteract (acronym: captesa) (Jonathan Bowers)[10]

Images

More information Coxeter plane, B7 / A6 ...
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]
Close

Steriruncicantellated 7-cube

More information Steriruncicantellated 7-cube ...
Steriruncicantellated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,2,3,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Celliprismatorhombated hepteract (acronym: copresa) (Jonathan Bowers)[11]

Images

More information Coxeter plane, B7 / A6 ...
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]
Close

Bisteriruncitruncated 7-cube

More information Bisteriruncitruncated 7-cube ...
Bisteriruncitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt1,2,4,5{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Bicelliprismatotruncated hepteractihecatonicosaoctaexon (acronym: bocaptosaz) (Jonathan Bowers)[12]

Images

More information Coxeter plane, B7 / A6 ...
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]
Close

Steriruncicantitruncated 7-cube

More information Steriruncicantitruncated 7-cube ...
Steriruncicantitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,1,2,3,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Great cellated hepteract (acronym: gacosa) (Jonathan Bowers)[13]

Images

More information Coxeter plane, B7 / A6 ...
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph too complex too complex
Dihedral symmetry [6] [4]
Close

Bisteriruncicantitruncated 7-cube

More information Bisteriruncicantitruncated 7-cube ...
Bisteriruncicantitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt1,2,3,4,5{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Great bicellated hepteractihecatonicosaoctaexon (acronym: gabcosaz) (Jonathan Bowers) [14]

Images

More information Coxeter plane, B7 / A6 ...
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph too complex
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]
Close

Notes

References

External links

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