In seven-dimensional geometry, a runcinated 7-cube is a convex uniform 7-polytope with 3rd order truncations (runcination) of the regular 7-cube.

More information Orthogonal projections in B7 Coxeter plane ...

7-cube

Runcinated 7-cube

Biruncinated 7-cube

Runcitruncated 7-cube

Biruncitruncated 7-cube

Runcicantellated 7-cube

Biruncicantellated 7-cube

Runcicantitruncated 7-cube

Biruncicantitruncated 7-cube
Orthogonal projections in B7 Coxeter plane
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There are 16 unique runcinations of the 7-cube with permutations of truncations, and cantellations. 8 are more simply constructed from the 7-orthoplex.

These polytopes are among 127 uniform 7-polytopes with B7 symmetry.

Runcinated 7-cube

Runcinated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,3{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges33600
Vertices4480
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex

Alternate names

  • Small prismated hepteract (acronym: spesa) (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

Biruncinated 7-cube

More information Biruncinated 7-cube ...
Biruncinated 7-cube
Typeuniform 7-polytope
Schläfli symbolt1,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges67200
Vertices8960
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Small biprismated hepteract (Acronym sibposa) (Jonathan Bowers)[2]

Images

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

Runcitruncated 7-cube

More information Runcitruncated 7-cube ...
Runcitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,1,3{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges73920
Vertices13440
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Prismatotruncated hepteract (acronym: petsa) (Jonathan Bowers)[3]

Images

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

Biruncitruncated 7-cube

More information Biruncitruncated 7-cube ...
Biruncitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt1,2,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges134400
Vertices26880
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Biprismatotruncated hepteract (acronym: biptesa) (Jonathan Bowers)[4]

Images

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

Runcicantellated 7-cube

More information Runcicantellated 7-cube ...
Runcicantellated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,2,3{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges53760
Vertices13440
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Prismatorhombated hepteract (acronym: parsa) (Jonathan Bowers)[5]

Images

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

Biruncicantellated 7-cube

More information biruncicantellated 7-cube ...
biruncicantellated 7-cube
Typeuniform 7-polytope
Schläfli symbolt1,3,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges120960
Vertices26880
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Biprismatorhombated hepteract (acronym: bopresa) (Jonathan Bowers)[6]

Images

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

Runcicantitruncated 7-cube

More information Runcicantitruncated 7-cube ...
Runcicantitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,1,2,3{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges94080
Vertices26880
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Great prismated hepteract (acronym: gapsa) (Jonathan Bowers)[7]

Images

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

Biruncicantitruncated 7-cube

More information biruncicantitruncated 7-cube ...
biruncicantitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt1,2,3,4{4,35}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges188160
Vertices53760
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Great biprismated hepteract (acronym: gibposa) (Jonathan Bowers)[8]

Images

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

Notes

References

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