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Cantellated 8 simplexes

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Cantellated 8-simplexes

In eight-dimensional geometry, a cantellated 8-simplex is a convex uniform 8-polytope, being a cantellation of the regular 8-simplex.

Contents

There are six unique cantellations for the 8-simplex, including permutations of truncation.

Alternate names

  • Small rhombated enneazetton (acronym: srene) (Jonathan Bowers)

    • Coordinates

    The Cartesian coordinates of the vertices of the cantellated 8-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,0,0,1,1,2). This construction is based on facets of the cantellated 9-orthoplex.

    Alternate names

  • Small birhombated enneazetton (acronym: sabrene) (Jonathan Bowers)

    • Coordinates

    The Cartesian coordinates of the vertices of the bicantellated 8-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,0,1,1,2,2). This construction is based on facets of the bicantellated 9-orthoplex.

    Alternate names

  • Small trirhombihexadecaexon (acronym: satrene) (Jonathan Bowers)

    • Coordinates

    The Cartesian coordinates of the vertices of the tricantellated 8-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,0,1,1,2,2). This construction is based on facets of the tricantellated 9-orthoplex.

    Alternate names

  • Great rhombated enneazetton (acronym: grene) (Jonathan Bowers)

    • Coordinates

    The Cartesian coordinates of the vertices of the cantitruncated 8-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,0,0,1,2,3). This construction is based on facets of the bicantitruncated 9-orthoplex.

    Alternate names

  • Great birhombated enneazetton (acronym: gabrene) (Jonathan Bowers)

    • Coordinates

    The Cartesian coordinates of the vertices of the bicantitruncated 8-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,0,1,2,3,3). This construction is based on facets of the bicantitruncated 9-orthoplex.

    Tricantitruncated 8-simplex

  • Great trirhombated enneazetton (acronym: gatrene) (Jonathan Bowers)

    • Coordinates

    The Cartesian coordinates of the vertices of the tricantitruncated 8-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,1,2,3,3,3). This construction is based on facets of the bicantitruncated 9-orthoplex.

    This polytope is one of 135 uniform 8-polytopes with A8 symmetry.

    References

    Cantellated 8-simplexes Wikipedia
    (Text) CC BY-SA