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Rectified 10 cubes

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Rectified 10-cubes

In ten-dimensional geometry, a rectified 10-cube is a convex uniform 10-polytope, being a rectification of the regular 10-cube.

Contents

There are 10 rectifications of the 10-cube, with the zeroth being the 10-cube itself. Vertices of the rectified 10-cube are located at the edge-centers of the 10-cube. Vertices of the birectified 10-cube are located in the square face centers of the 10-cube. Vertices of the trirectified 10-cube are located in the cubic cell centers of the 10-cube. The others are more simply constructed relative to the 10-cube dual polytpoe, the 10-orthoplex.

These polytopes are part of a family 1023 uniform 10-polytopes with BC10 symmetry.

Alternate names

  • Rectified dekeract (Acronym rade) (Jonathan Bowers)

    • Cartesian coordinates

    Cartesian coordinates for the vertices of a rectified 10-cube, centered at the origin, edge length 2 are all permutations of:

    (±1,±1,±1,±1,±1,±1,±1,±1,±1,0)

    Alternate names

  • Birectified dekeract (Acronym brade) (Jonathan Bowers)

    • Cartesian coordinates

    Cartesian coordinates for the vertices of a birectified 10-cube, centered at the origin, edge length 2 are all permutations of:

    (±1,±1,±1,±1,±1,±1,±1,±1,0,0)

    Alternate names

  • Tririrectified dekeract (Acronym trade) (Jonathan Bowers)

    • Cartesian coordinates

    Cartesian coordinates for the vertices of a triirectified 10-cube, centered at the origin, edge length 2 are all permutations of:

    (±1,±1,±1,±1,±1,±1,±1,0,0,0)

    Alternate names

  • Quadrirectified dekeract
  • Quadrirectified decacross (Acronym terade) (Jonathan Bowers)

    • Cartesian coordinates

    Cartesian coordinates for the vertices of a quadrirectified 10-cube, centered at the origin, edge length 2 are all permutations of:

    (±1,±1,±1,±1,±1,±1,0,0,0,0)

    References

    Rectified 10-cubes Wikipedia
    (Text) CC BY-SA


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