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Runcinated 7 simplexes

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Runcinated 7-simplexes

In seven-dimensional geometry, a runcinated 7-simplex is a convex uniform 7-polytope with 3rd order truncations (runcination) of the regular 7-simplex.

Contents

There are 8 unique runcinations of the 7-simplex with permutations of truncations, and cantellations.

Alternate names

  • Small prismated octaexon (acronym: spo) (Jonathan Bowers)

    • Coordinates

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

    Alternate names

  • Small biprismated octaexon (sibpo) (Jonathan Bowers)

    • Coordinates

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

    Alternate names

  • Prismatotruncated octaexon (acronym: patto) (Jonathan Bowers)

    • Coordinates

    The vertices of the runcitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,1,1,2,3). This construction is based on facets of the runcitruncated 8-orthoplex.

    Alternate names

  • Biprismatotruncated octaexon (acronym: bipto) (Jonathan Bowers)

    • Coordinates

    The vertices of the biruncitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,1,1,2,3,3). This construction is based on facets of the biruncitruncated 8-orthoplex.

    Alternate names

  • Prismatorhombated octaexon (acronym: paro) (Jonathan Bowers)

    • Coordinates

    The vertices of the runcicantellated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,1,2,2,3). This construction is based on facets of the runcicantellated 8-orthoplex.

    Alternate names

  • Biprismatorhombated octaexon (acronym: bipro) (Jonathan Bowers)

    • Coordinates

    The vertices of the biruncicantellated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,1,2,2,3,3). This construction is based on facets of the biruncicantellated 8-orthoplex.

    Alternate names

  • Great prismated octaexon (acronym: gapo) (Jonathan Bowers)

    • Coordinates

    The vertices of the runcicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,1,2,3,4). This construction is based on facets of the runcicantitruncated 8-orthoplex.

    Alternate names

  • Great biprismated octaexon (acronym: gibpo) (Jonathan Bowers)

    • Coordinates

    The vertices of the biruncicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,1,2,3,4,4). This construction is based on facets of the biruncicantitruncated 8-orthoplex.

    These polytopes are among 71 uniform 7-polytopes with A7 symmetry.

    References

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