Cantellated 7-cube

Orthogonal projections in BC₆ Coxeter plane
7-cube	Cantellated 7-cube	Bicantellated 7-cube	Tricantellated 7-cube
Birectified 7-cube	Cantitruncated 7-cube	Bicantitruncated 7-cube	Tricantitruncated 7-cube
Cantellated 7-orthoplex Cantellated 7-orthoplex In seven-dimensional geometry, a cantellated 7-orthoplex is a convex uniform 7-polytope, being a cantellation of the regular 7-orthoplex.There are ten degrees of cantellation for the 7-orthoplex, including truncations...	Bicantellated 7-orthoplex	Cantitruncated 7-orthoplex	Bicantitruncated 7-orthoplex

In seven-dimensional geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

, a cantellated 7-cube is a convex uniform 7-polytope, being a cantellation of the regular 7-cube.

There are 10 degrees of cantellation for the 7-cube, including truncations. 4 are most simply constructable from the dual 7-orthoplex.

Cantellated 7-cube
Type	uniform polyexon
Schläfli symbol	t_0,2{4,3,3,3,3,3}
Coxeter-Dynkin diagram Coxeter-Dynkin diagram In geometry, a Coxeter–Dynkin diagram is a graph with numerically labeled edges representing the spatial relations between a collection of mirrors...
6-faces
5-faces
4-faces
Cells
Faces
Edges	16128
Vertices	2688
Vertex figure Vertex figure In geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.-Definitions - theme and variations:...
Coxeter group Coxeter group In mathematics, a Coxeter group, named after H.S.M. Coxeter, is an abstract group that admits a formal description in terms of mirror symmetries. Indeed, the finite Coxeter groups are precisely the finite Euclidean reflection groups; the symmetry groups of regular polyhedra are an example... s	BC₇, [4,3,3,3,3,3]
Properties	convex Convex polytope A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn...

Bicantellated 7-cube

Bicantellated 7-cube
Type	uniform polyexon
Schläfli symbol	t_1,3{4,3,3,3,3,3}
Coxeter-Dynkin diagram Coxeter-Dynkin diagram In geometry, a Coxeter–Dynkin diagram is a graph with numerically labeled edges representing the spatial relations between a collection of mirrors... s
6-faces
5-faces
4-faces
Cells
Faces
Edges	40320
Vertices	6720
Vertex figure Vertex figure In geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.-Definitions - theme and variations:...
Coxeter group Coxeter group In mathematics, a Coxeter group, named after H.S.M. Coxeter, is an abstract group that admits a formal description in terms of mirror symmetries. Indeed, the finite Coxeter groups are precisely the finite Euclidean reflection groups; the symmetry groups of regular polyhedra are an example... s	BC₇, [4,3,3,3,3,3]
Properties	convex Convex polytope A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn...

Tricantellated 7-cube

Tricantellated 7-cube
Type	uniform polyexon
Schläfli symbol	t_2,4{4,3,3,3,3,3}
Coxeter-Dynkin diagram Coxeter-Dynkin diagram In geometry, a Coxeter–Dynkin diagram is a graph with numerically labeled edges representing the spatial relations between a collection of mirrors... s
6-faces
5-faces
4-faces
Cells
Faces
Edges	47040
Vertices	6720
Vertex figure Vertex figure In geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.-Definitions - theme and variations:...
Coxeter group Coxeter group In mathematics, a Coxeter group, named after H.S.M. Coxeter, is an abstract group that admits a formal description in terms of mirror symmetries. Indeed, the finite Coxeter groups are precisely the finite Euclidean reflection groups; the symmetry groups of regular polyhedra are an example... s	BC₇, [4,3,3,3,3,3]
Properties	convex Convex polytope A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn...

Alternate names

Small trirhombihepteractihecatonicosoctaexon (acronym: strasaz) (Jonathan Bowers)

Cantitruncated 7-cube

Cantitruncated 7-cube
Type	uniform polyexon
Schläfli symbol	t_0,1,2{4,3,3,3,3,3}
Coxeter-Dynkin diagram Coxeter-Dynkin diagram In geometry, a Coxeter–Dynkin diagram is a graph with numerically labeled edges representing the spatial relations between a collection of mirrors... s
6-faces
5-faces
4-faces
Cells
Faces
Edges	18816
Vertices	5376
Vertex figure Vertex figure In geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.-Definitions - theme and variations:...
Coxeter group Coxeter group In mathematics, a Coxeter group, named after H.S.M. Coxeter, is an abstract group that admits a formal description in terms of mirror symmetries. Indeed, the finite Coxeter groups are precisely the finite Euclidean reflection groups; the symmetry groups of regular polyhedra are an example... s	BC₇, [4,3,3,3,3,3]
Properties	convex Convex polytope A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn...

Bicantitruncated 7-cube

Bicantitruncated 7-cube
Type	uniform polyexon
Schläfli symbol	t_1,2,3{4,3,3,3,3,3}
Coxeter-Dynkin diagram Coxeter-Dynkin diagram In geometry, a Coxeter–Dynkin diagram is a graph with numerically labeled edges representing the spatial relations between a collection of mirrors... s
6-faces
5-faces
4-faces
Cells
Faces
Edges	47040
Vertices	13440
Vertex figure Vertex figure In geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.-Definitions - theme and variations:...
Coxeter group Coxeter group In mathematics, a Coxeter group, named after H.S.M. Coxeter, is an abstract group that admits a formal description in terms of mirror symmetries. Indeed, the finite Coxeter groups are precisely the finite Euclidean reflection groups; the symmetry groups of regular polyhedra are an example... s	BC₇, [4,3,3,3,3,3]
Properties	convex Convex polytope A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn...

Tricantitruncated 7-cube

Tricantitruncated 7-cube
Type	uniform polyexon
Schläfli symbol	t_2,3,4{4,3,3,3,3,3}
Coxeter-Dynkin diagram Coxeter-Dynkin diagram In geometry, a Coxeter–Dynkin diagram is a graph with numerically labeled edges representing the spatial relations between a collection of mirrors... s
6-faces
5-faces
4-faces
Cells
Faces
Edges	53760
Vertices	13440
Vertex figure Vertex figure In geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.-Definitions - theme and variations:...
Coxeter group Coxeter group In mathematics, a Coxeter group, named after H.S.M. Coxeter, is an abstract group that admits a formal description in terms of mirror symmetries. Indeed, the finite Coxeter groups are precisely the finite Euclidean reflection groups; the symmetry groups of regular polyhedra are an example... s	BC₇, [4,3,3,3,3,3]
Properties	convex Convex polytope A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn...

Alternate names

Great trirhombihepteractihecatonicosoctaexon (acronym: gotrasaz) (Jonathan Bowers)

Related polytopes

These polytopes are from a family of 127 uniform 7-polytopes with BC₇ symmetry.

External links

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