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Truncated 6-cubes

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In six-dimensional geometry, a truncated 6-cube (or truncated hexeract) is a convex uniform 6-polytope, being a truncation of the regular 6-cube.

More information Orthogonal projections in B6 Coxeter plane ...

There are 5 truncations for the 6-cube. Vertices of the truncated 6-cube are located as pairs on the edge of the 6-cube. Vertices of the bitruncated 6-cube are located on the square faces of the 6-cube. Vertices of the tritruncated 6-cube are located inside the cubic cells of the 6-cube.

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Truncated 6-cube

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Truncated 6-cube
Typeuniform 6-polytope
ClassB6 polytope
Schläfli symbolt{4,3,3,3,3}
Coxeter-Dynkin diagrams
5-faces76
4-faces464
Cells1120
Faces1520
Edges1152
Vertices384
Vertex figureThumb
( )v{3,3,3}
Coxeter groupsB6, [3,3,3,3,4]
Propertiesconvex

Alternate names

  • Truncated hexeract (Acronym: tox) (Jonathan Bowers)[1]

Construction and coordinates

The truncated 6-cube may be constructed by truncating the vertices of the 6-cube at of the edge length. A regular 5-simplex replaces each original vertex.

The Cartesian coordinates of the vertices of a truncated 6-cube having edge length 2 are the permutations of:

Images

More information Coxeter plane, B6 ...

The truncated 6-cube, is fifth in a sequence of truncated hypercubes:

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Bitruncated 6-cube

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More information Bitruncated 6-cube ...

Alternate names

  • Bitruncated hexeract (Acronym: botox) (Jonathan Bowers)[2]

Construction and coordinates

The Cartesian coordinates of the vertices of a bitruncated 6-cube having edge length 2 are the permutations of:

Images

More information Coxeter plane, B6 ...

The bitruncated 6-cube is fourth in a sequence of bitruncated hypercubes:

More information Image, Name ...
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Tritruncated 6-cube

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More information Tritruncated 6-cube ...

Alternate names

  • Tritruncated hexeract (Acronym: xog) (Jonathan Bowers)[4]

Construction and coordinates

The Cartesian coordinates of the vertices of a tritruncated 6-cube having edge length 2 are the permutations of:

Images

More information Coxeter plane, B6 ...
More information Dim., n ...

The table below contains a set of 63 Uniform 6-polytopes generated from the B6 Coxeter plane, including the regular 6-cube or 6-orthoplex.

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Notes

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References

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