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Rectified 7 cubes

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Rectified 7-cubes

In seven-dimensional geometry, a rectified 7-cube is a convex uniform 7-polytope, being a rectification of the regular 7-cube.

Contents

There are unique 7 degrees of rectifications, the zeroth being the 7-cube, and the 6th and last being the 7-cube. Vertices of the rectified 7-cube are located at the edge-centers of the 7-ocube. Vertices of the birectified 7-cube are located in the square face centers of the 7-cube. Vertices of the trirectified 7-cube are located in the cube cell centers of the 7-cube.

Alternate names

  • rectified hepteract (Acronym resa) (Jonathan Bowers)

    • Cartesian coordinates

    Cartesian coordinates for the vertices of a rectified 7-cube, centered at the origin, edge length 2   are all permutations of:

    (±1,±1,±1,±1,±1,±1,0)

    Alternate names

  • Birectified hepteract (Acronym bersa) (Jonathan Bowers)

    • Cartesian coordinates

    Cartesian coordinates for the vertices of a birectified 7-cube, centered at the origin, edge length 2   are all permutations of:

    (±1,±1,±1,±1,±1,0,0)

    Alternate names

  • Trirectified hepteract
  • Trirectified 7-orthoplex
  • Trirectified heptacross (Acronym sez) (Jonathan Bowers)

    • Cartesian coordinates

    Cartesian coordinates for the vertices of a trirectified 7-cube, centered at the origin, edge length 2   are all permutations of:

    (±1,±1,±1,±1,0,0,0)

    References

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