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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.

Contents

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.

Alternate names

  • Truncated hexeract (Acronym: tox) (Jonathan Bowers)

    • Construction and coordinates

    The truncated 6-cube may be constructed by truncating the vertices of the 6-cube at 1 / ( 2 + 2 ) 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:

    ( ± 1 ,   ± ( 1 + 2 ) ,   ± ( 1 + 2 ) ,   ± ( 1 + 2 ) ,   ± ( 1 + 2 ) ,   ± ( 1 + 2 ) )

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

    Alternate names

  • Bitruncated hexeract (Acronym: botox) (Jonathan Bowers)

    • Construction and coordinates

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

    ( 0 ,   ± 1 ,   ± 2 ,   ± 2 ,   ± 2 ,   ± 2 )

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

    Alternate names

  • Tritruncated hexeract (Acronym: xog) (Jonathan Bowers)

    • Construction and coordinates

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

    ( 0 ,   0 ,   ± 1 ,   ± 2 ,   ± 2 ,   ± 2 )

    These polytopes are from a set of 63 Uniform 6-polytopes generated from the B6 Coxeter plane, including the regular 6-cube or 6-orthoplex.

    References

    Truncated 6-cubes Wikipedia
    (Text) CC BY-SA


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