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Truncated 7 simplexes

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Truncated 7-simplexes

In seven-dimensional geometry, a truncated 7-simplex is a convex uniform 7-polytope, being a truncation of the regular 7-simplex.

Contents

There are unique 3 degrees of truncation. Vertices of the truncation 7-simplex are located as pairs on the edge of the 7-simplex. Vertices of the bitruncated 7-simplex are located on the triangular faces of the 7-simplex. Vertices of the tritruncated 7-simplex are located inside the tetrahedral cells of the 7-simplex.

Truncated 7-simplex

In seven-dimensional geometry, a truncated 7-simplex is a convex uniform 7-polytope, being a truncation of the regular 7-simplex.

Alternate names

  • Truncated octaexon (Acronym: toc) (Jonathan Bowers)

    • Coordinates

    The vertices of the truncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,0,0,1,2). This construction is based on facets of the truncated 8-orthoplex.

    Alternate names

  • Bitruncated octaexon (acronym: bittoc) (Jonathan Bowers)

    • Coordinates

    The vertices of the bitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,0,1,2,2). This construction is based on facets of the bitruncated 8-orthoplex.

    Alternate names

  • Tritruncated octaexon (acronym: tattoc) (Jonathan Bowers)

    • Coordinates

    The vertices of the tritruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,1,2,2,2). This construction is based on facets of the tritruncated 8-orthoplex.

    These three polytopes are from a set of 71 uniform 7-polytopes with A7 symmetry.

    References

    Truncated 7-simplexes Wikipedia
    (Text) CC BY-SA