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Hexicated 7 cubes

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Hexicated 7-cubes

In seven-dimensional geometry, a hexicated 7-cube is a convex uniform 7-polytope, including 6th-order truncations (hexication) from the regular 7-cube.

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There are 32 hexications for the 7-cube, including all permutations of truncations, cantellations, runcinations, sterications, and pentellations. 20 are represented here, while 12 are more easily constructed from the 7-orthoplex.

The simple hexicated 7-cube is also called an expanded 7-cube, with only the first and last nodes ringed, is constructed by an expansion operation applied to the regular 7-cube. The highest form, the hexipentisteriruncicantitruncated 7-cube is more simply called a omnitruncated 7-cube with all of the nodes ringed.

These polytope are among a family of 127 uniform 7-polytopes with B7 symmetry.

Hexicated 7-cube

In seven-dimensional geometry, a hexicated 7-cube is a convex uniform 7-polytope, a hexication (6th order truncation) of the regular 7-cube, or alternately can be seen as an expansion operation.

Alternate names

  • Small petated hepteract (acronym: ) (Jonathan Bowers)

    • Alternate names

  • Petitruncated hepteract (acronym: ) (Jonathan Bowers)

    • Alternate names

  • Petirhombated hepteract (acronym: ) (Jonathan Bowers)

    • Alternate names

  • Petiprismated hepteract (acronym: ) (Jonathan Bowers)

    • Alternate names

  • Petigreatorhombated hepteract (acronym: ) (Jonathan Bowers)

    • Alternate names

  • Petiprismatotruncated hepteract (acronym: ) (Jonathan Bowers)

    • Hexiruncicantellated 7-cube

    In seven-dimensional geometry, a hexiruncicantellated 7-cube is a uniform 7-polytope.

    Alternate names

  • Petiprismatorhombated hepteract (acronym: ) (Jonathan Bowers)

    • Alternate names

  • Peticellitruncated hepteract (acronym: ) (Jonathan Bowers)

    • Alternate names

  • Peticellirhombihepteract (acronym: ) (Jonathan Bowers)

    • Alternate names

  • Petiteritruncated hepteract (acronym: ) (Jonathan Bowers)

    • Alternate names

  • Petigreatoprismated hepteract (acronym: ) (Jonathan Bowers)

    • Alternate names

  • Peticelligreatorhombated hepteract (acronym: ) (Jonathan Bowers)

    • Alternate names

  • Peticelliprismatotruncated hepteract (acronym: ) (Jonathan Bowers)

    • Alternate names

  • Peticelliprismatorhombihepteract (acronym: ) (Jonathan Bowers)

    • Alternate names

  • Petiterigreatorhombated hepteract (acronym: ) (Jonathan Bowers)

    • Alternate names

  • Great petacellated hepteract (acronym: ) (Jonathan Bowers)

    • Alternate names

  • Great petacellated hepteract (acronym: ) (Jonathan Bowers)

    • Alternate names

  • Petiterigreatoprismated hepteract (acronym: ) (Jonathan Bowers)

    • Alternate names

  • Petitericelligreatorhombihepteract (acronym: putcagroh) (Jonathan Bowers)

    • Omnitruncated 7-cube

    The omnitruncated 7-cube is the largest uniform 7-polytope in the B7 symmetry of the regular 7-cube. It can also be called the hexipentisteriruncicantitruncated 7-cube which is the long name for the omnitruncation for 7 dimensions, with all reflective mirrors active.

    Alternate names

  • Great petated hepteract (Acronym: ) (Jonathan Bowers)

    • References

    Hexicated 7-cubes Wikipedia
    (Text) CC BY-SA


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