Hexicated 7-cubes

Shape in seven dimensional geometry From Wikipedia, the free encyclopedia

Hexicated 7-cubes

In seven-dimensional geometry, a hexicated 7-cube is a convex uniform 7-polytope, including 6th-order truncations (hexication) from the regular 7-cube.

More information Orthogonal projections in B4 Coxeter plane ...
Orthogonal projections in B4 Coxeter plane

7-cube

Hexicated 7-cube

Hexitruncated 7-cube

Hexicantellated 7-cube

Hexiruncinated 7-cube

Hexicantitruncated 7-cube

Hexiruncitruncated 7-cube

Hexiruncicantellated 7-cube

Hexisteritruncated 7-cube

Hexistericantellated 7-cube

Hexipentitruncated 7-cube

Hexiruncicantitruncated 7-cube

Hexistericantitruncated 7-cube

Hexisteriruncitruncated 7-cube

Hexisteriruncicantellated 7-cube

Hexipenticantitruncated 7-cube

Hexipentiruncitruncated 7-cube

Hexisteriruncicantitruncated 7-cube

Hexipentiruncicantitruncated 7-cube

Hexipentistericantitruncated 7-cube

Hexipentisteriruncicantitruncated 7-cube
(Omnitruncated 7-cube)
Close

There are 32 hexications for the 7-cube, including all permutations of truncations, cantellations, runcinations, sterications, and pentellations. 20 are represented here, while 12 are more easily constructed from the 7-orthoplex.

The simple hexicated 7-cube is also called an expanded 7-cube, with only the first and last nodes ringed, is constructed by an expansion operation applied to the regular 7-cube. The highest form, the hexipentisteriruncicantitruncated 7-cube is more simply called a omnitruncated 7-cube with all of the nodes ringed.

These polytope are among a family of 127 uniform 7-polytopes with B7 symmetry.

Hexicated 7-cube

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

In seven-dimensional geometry, a hexicated 7-cube is a convex uniform 7-polytope, a hexication (6th order truncation) of the regular 7-cube, or alternately can be seen as an expansion operation.

Alternate names

  • Small petated hepteract (acronym: ) (Jonathan Bowers)

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

Hexitruncated 7-cube

More information hexitruncated 7-cube ...
hexitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,1,6{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

  • Petitruncated hepteract (acronym: ) (Jonathan Bowers)

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

Hexicantellated 7-cube

More information Hexicantellated 7-cube ...
Hexicantellated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,2,6{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

  • Petirhombated hepteract (acronym: ) (Jonathan Bowers)

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

Hexiruncinated 7-cube

More information Hexiruncinated 7-cube ...
Hexiruncinated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,3,6{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

  • Petiprismated hepteract (acronym: ) (Jonathan Bowers)

Images

More information Coxeter plane, B7 / A6 ...
orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph too complex 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

Hexicantitruncated 7-cube

More information Hexicantitruncated 7-cube ...
Hexicantitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,1,2,6{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

  • Petigreatorhombated hepteract (acronym: ) (Jonathan Bowers)

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

Hexiruncitruncated 7-cube

More information Hexiruncitruncated 7-cube ...
Hexiruncitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,1,3,6{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

  • Petiprismatotruncated hepteract (acronym: ) (Jonathan Bowers)

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

Hexiruncicantellated 7-cube

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

In seven-dimensional geometry, a hexiruncicantellated 7-cube is a uniform 7-polytope.

Alternate names

  • Petiprismatorhombated hepteract (acronym: ) (Jonathan Bowers)

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

Hexisteritruncated 7-cube

More information hexisteritruncated 7-cube ...
hexisteritruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,1,4,6{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

  • Peticellitruncated hepteract (acronym: ) (Jonathan Bowers)

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

Hexistericantellated 7-cube

More information hexistericantellated 7-cube ...
hexistericantellated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,2,4,6{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

  • Peticellirhombihepteract (acronym: ) (Jonathan Bowers)

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

Hexipentitruncated 7-cube

More information Hexipentitruncated 7-cube ...
Hexipentitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,1,5,6{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

  • Petiteritruncated hepteract (acronym: ) (Jonathan Bowers)

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

Hexiruncicantitruncated 7-cube

More information Hexiruncicantitruncated 7-cube ...
Hexiruncicantitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,1,2,3,6{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

  • Petigreatoprismated hepteract (acronym: ) (Jonathan Bowers)

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 too complex too complex
Dihedral symmetry [6] [4]
Close

Hexistericantitruncated 7-cube

More information Hexistericantitruncated 7-cube ...
Hexistericantitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,1,2,4,6{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

  • Peticelligreatorhombated hepteract (acronym: ) (Jonathan Bowers)

Images

More information Coxeter plane, B7 / A6 ...
orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph too complex 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

Hexisteriruncitruncated 7-cube

More information Hexisteriruncitruncated 7-cube ...
Hexisteriruncitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,1,3,4,6{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

  • Peticelliprismatotruncated hepteract (acronym: ) (Jonathan Bowers)

Images

More information Coxeter plane, B7 / A6 ...
orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph too complex 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

Hexisteriruncicantellated 7-cube

More information Hexisteriruncitruncated 7-cube ...
Hexisteriruncitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,2,3,4,6{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

  • Peticelliprismatorhombihepteract (acronym: ) (Jonathan Bowers)

Images

More information Coxeter plane, B7 / A6 ...
orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph too complex 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

Hexipenticantitruncated 7-cube

More information hexipenticantitruncated 7-cube ...
hexipenticantitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,1,2,5,6{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

  • Petiterigreatorhombated hepteract (acronym: ) (Jonathan Bowers)

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

Hexipentiruncitruncated 7-cube

More information Hexisteriruncicantitruncated 7-cube ...
Hexisteriruncicantitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,1,2,3,4,6{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 petacellated hepteract (acronym: ) (Jonathan Bowers)

Images

More information Coxeter plane, B7 / A6 ...
orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph too complex 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

Hexisteriruncicantitruncated 7-cube

More information Hexisteriruncicantitruncated 7-cube ...
Hexisteriruncicantitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,1,2,3,4,6{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 petacellated hepteract (acronym: ) (Jonathan Bowers)

Images

More information Coxeter plane, B7 / A6 ...
orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph too complex 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

Hexipentiruncicantitruncated 7-cube

More information Hexipentiruncicantitruncated 7-cube ...
Hexipentiruncicantitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,1,2,3,5,6{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

  • Petiterigreatoprismated hepteract (acronym: ) (Jonathan Bowers)

Images

More information Coxeter plane, B7 / A6 ...
orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph too complex 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

Hexipentistericantitruncated 7-cube

More information Hexipentistericantitruncated 7-cube ...
Hexipentistericantitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,1,2,4,5,6{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

  • Petitericelligreatorhombihepteract (acronym: putcagroh) (Jonathan Bowers)

Images

More information Coxeter plane, B7 / A6 ...
orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph too complex 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

Omnitruncated 7-cube

More information Omnitruncated 7-cube ...
Omnitruncated 7-cube
Typeuniform 7-polytope
Schläfli symbolt0,1,2,3,4,5,6{36}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

The omnitruncated 7-cube is the largest uniform 7-polytope in the B7 symmetry of the regular 7-cube. It can also be called the hexipentisteriruncicantitruncated 7-cube which is the long name for the omnitruncation for 7 dimensions, with all reflective mirrors active.

Alternate names

  • Great petated hepteract (Acronym: ) (Jonathan Bowers)

Images

More information Coxeter plane, B7 / A6 ...
orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph too complex 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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