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Stericated 6 simplexes

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Stericated 6-simplexes

In six-dimensional geometry, a stericated 6-simplex is a convex uniform 6-polytope with 4th order truncations (sterication) of the regular 6-simplex.

Contents

There are 8 unique sterications for the 6-simplex with permutations of truncations, cantellations, and runcinations.

Alternate names

  • Small cellated heptapeton (Acronym: scal) (Jonathan Bowers)

    • Coordinates

    The vertices of the stericated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,1,1,1,1,2). This construction is based on facets of the stericated 7-orthoplex.

    Alternate names

  • Cellirhombated heptapeton (Acronym: catal) (Jonathan Bowers)

    • Coordinates

    The vertices of the steritruncated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,1,1,1,2,3). This construction is based on facets of the steritruncated 7-orthoplex.

    Alternate names

  • Cellirhombated heptapeton (Acronym: cral) (Jonathan Bowers)

    • Coordinates

    The vertices of the stericantellated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,1,1,2,2,3). This construction is based on facets of the stericantellated 7-orthoplex.

    Alternate names

  • Celligreatorhombated heptapeton (Acronym: cagral) (Jonathan Bowers)

    • Coordinates

    The vertices of the stericanttruncated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,0,1,2,3,4). This construction is based on facets of the stericantitruncated 7-orthoplex.

    Alternate names

  • Celliprismated heptapeton (Acronym: copal) (Jonathan Bowers)

    • Coordinates

    The vertices of the steriruncinated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,1,2,2,3,3). This construction is based on facets of the steriruncinated 7-orthoplex.

    Alternate names

  • Celliprismatotruncated heptapeton (Acronym: captal) (Jonathan Bowers)

    • Coordinates

    The vertices of the steriruncittruncated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,0,1,2,3,4). This construction is based on facets of the steriruncitruncated 7-orthoplex.

    Alternate names

  • Bistericantitruncated 6-simplex as t1,2,3,5{3,3,3,3,3}
  • Celliprismatorhombated heptapeton (Acronym: copril) (Jonathan Bowers)

    • Coordinates

    The vertices of the steriruncitcantellated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,0,1,2,3,4). This construction is based on facets of the steriruncicantellated 7-orthoplex.

    Alternate names

  • Great cellated heptapeton (Acronym: gacal) (Jonathan Bowers)

    • Coordinates

    The vertices of the steriruncicantittruncated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,1,2,3,4,5). This construction is based on facets of the steriruncicantitruncated 7-orthoplex.

    The truncated 6-simplex is one of 35 uniform 6-polytopes based on the [3,3,3,3,3] Coxeter group, all shown here in A6 Coxeter plane orthographic projections.

    References

    Stericated 6-simplexes Wikipedia
    (Text) CC BY-SA