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Stericated 7 simplexes

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Stericated 7-simplexes

In seven-dimensional geometry, a stericated 7-simplex is a convex uniform 7-polytope with 4th order truncations (sterication) of the regular 7-simplex.

Contents

There are 14 unique sterication for the 7-simplex with permutations of truncations, cantellations, and runcinations.

Alternate names

  • Small cellated octaexon (acronym: sco) (Jonathan Bowers)

    • Coordinates

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

    Alternate names

  • Small bicellated hexadecaexon (acronym: sabach) (Jonathan Bowers)

    • Coordinates

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

    Alternate names

  • Cellitruncated octaexon (acronym: cato) (Jonathan Bowers)

    • Coordinates

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

    Alternate names

  • Bicellitruncated octaexon (acronym: bacto) (Jonathan Bowers)

    • Coordinates

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

    Alternate names

  • Cellirhombated octaexon (acronym: caro) (Jonathan Bowers)

    • Coordinates

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

    Alternate names

  • Bicellirhombihexadecaexon (acronym: bacroh) (Jonathan Bowers)

    • Coordinates

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

    Alternate names

  • Celligreatorhombated octaexon (acronym: cagro) (Jonathan Bowers)

    • Coordinates

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

    Alternate names

  • Bicelligreatorhombated octaexon (acronym: bacogro) (Jonathan Bowers)

    • Coordinates

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

    Alternate names

  • Celliprismated octaexon (acronym: cepo) (Jonathan Bowers)

    • Coordinates

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

    Alternate names

  • Celliprismatotruncated octaexon (acronym: capto) (Jonathan Bowers)

    • Coordinates

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

    Alternate names

  • Celliprismatorhombated octaexon (acronym: capro) (Jonathan Bowers)

    • Coordinates

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

    Alternate names

  • Bicelliprismatotruncated hexadecaexon (acronym: bicpath) (Jonathan Bowers)

    • Coordinates

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

    Alternate names

  • Great cellated octaexon (acronym: gecco) (Jonathan Bowers)

    • Coordinates

    The vertices of the steriruncicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,1,2,3,4,5). This construction is based on facets of the steriruncicantitruncated 8-orthoplex.

    Alternate names

  • Great bicellated hexadecaexon (gabach) (Jonathan Bowers)

    • Coordinates

    The vertices of the bisteriruncicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,2,3,4,5,5). This construction is based on facets of the bisteriruncicantitruncated 8-orthoplex.

    This polytope is one of 71 uniform 7-polytopes with A7 symmetry.

    References

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


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