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Stericated 5 cubes

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Stericated 5-cubes

In five-dimensional geometry, a stericated 5-cube is a convex uniform 5-polytope with fourth-order truncations (sterication) of the regular 5-cube.

Contents

There are eight degrees of sterication for the 5-cube, including permutations of runcination, cantellation, and truncation. The simple stericated 5-cube is also called an expanded 5-cube, with the first and last nodes ringed, for being constructible by an expansion operation applied to the regular 5-cube. The highest form, the steriruncicantitruncated 5-cube, is more simply called an omnitruncated 5-cube with all of the nodes ringed.

Alternate names

  • Stericated penteract / Stericated 5-orthoplex / Stericated pentacross
  • Expanded penteract / Expanded 5-orthoplex / Expanded pentacross
  • Small cellated penteract (Acronym: scan) (Jonathan Bowers)

    • Coordinates

    The Cartesian coordinates of the vertices of a stericated 5-cube having edge length 2 are all permutations of:

    ( ± 1 ,   ± 1 ,   ± 1 ,   ± 1 ,   ± ( 1 + 2 ) )

    Images

    The stericated 5-cube is constructed by a sterication operation applied to the 5-cube.

    Alternate names

  • Steritruncated penteract
  • Prismatotruncated penteract (Acronym: capt) (Jonathan Bowers)

    • Construction and coordinates

    The Cartesian coordinates of the vertices of a steritruncated 5-cube having edge length 2 are all permutations of:

    ( ± 1 ,   ± ( 1 + 2 ) ,   ± ( 1 + 2 ) ,   ± ( 1 + 2 ) ,   ± ( 1 + 2 2 ) )

    Alternate names

  • Stericantellated penteract
  • Stericantellated 5-orthoplex, stericantellated pentacross
  • Cellirhombated penteractitriacontiditeron (Acronym: carnit) (Jonathan Bowers)

    • Coordinates

    The Cartesian coordinates of the vertices of a stericantellated 5-cube having edge length 2 are all permutations of:

    ( ± 1 ,   ± 1 ,   ± 1 ,   ± ( 1 + 2 ) ,   ± ( 1 + 2 2 ) )

    Alternate names

  • Stericantitruncated penteract
  • Steriruncicantellated 16-cell / Biruncicantitruncated pentacross
  • Celligreatorhombated penteract (cogrin) (Jonathan Bowers)

    • Coordinates

    The Cartesian coordinates of the vertices of an stericantitruncated 5-cube having an edge length of 2 are given by all permutations of coordinates and sign of:

    ( 1 ,   1 + 2 ,   1 + 2 2 ,   1 + 2 2 ,   1 + 3 2 )

    Alternate names

  • Steriruncitruncated penteract / Steriruncitruncated 5-orthoplex / Steriruncitruncated pentacross
  • Celliprismatotruncated penteractitriacontiditeron (captint) (Jonathan Bowers)

    • Coordinates

    The Cartesian coordinates of the vertices of an steriruncitruncated penteract having an edge length of 2 are given by all permutations of coordinates and sign of:

    ( 1 ,   1 + 2 ,   1 + 1 2 ,   1 + 2 2 ,   1 + 3 2 )

    Alternate names

  • Steritruncated pentacross
  • Celliprismated penteract (Acronym: cappin) (Jonathan Bowers)

    • Coordinates

    Cartesian coordinates for the vertices of a steritruncated 5-orthoplex, centered at the origin, are all permutations of

    ( ± 1 ,   ± 1 ,   ± 1 ,   ± 1 ,   ± ( 1 + 2 ) )

    Alternate names

  • Stericantitruncated pentacross
  • Celligreatorhombated pentacross (cogart) (Jonathan Bowers)

    • Coordinates

    The Cartesian coordinates of the vertices of an stericantitruncated 5-orthoplex having an edge length of 2 are given by all permutations of coordinates and sign of:

    ( 1 ,   1 ,   1 + 2 ,   1 + 2 2 ,   1 + 3 2 )

    Alternate names

  • Steriruncicantitruncated 5-cube (Full expansion of omnitruncation for 5-polytopes by Johnson)
  • Omnitruncated penteract
  • Omnitruncated 16-cell / omnitruncated pentacross
  • Great cellated penteractitriacontiditeron (Jonathan Bowers)

    • Coordinates

    The Cartesian coordinates of the vertices of an omnitruncated tesseract having an edge length of 2 are given by all permutations of coordinates and sign of:

    ( 1 ,   1 + 2 ,   1 + 2 2 ,   1 + 3 2 ,   1 + 4 2 )

    This polytope is one of 31 uniform 5-polytopes generated from the regular 5-cube or 5-orthoplex.

    References

    Stericated 5-cubes Wikipedia
    (Text) CC BY-SA