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Rectified 9-cubes

Orthogonal projections in BC9 Coxeter plane

In nine-dimensional geometry, a rectified 9-cube is a convex uniform 9-polytope, being a rectification of the regular 9-cube.

There are 9 rectifications of the 9-cube. The zeroth is the 9-cube itself, and the 8th is the dual 9-orthoplex. Vertices of the rectified 9-cube are located at the edge-centers of the 9-orthoplex. Vertices of the birectified 9-cube are located in the square face centers of the 9-cube. Vertices of the trirectified 9-orthoplex are located in the cube cell centers of the 9-cube. Vertices of the quadrirectified 9-cube are located in the tesseract centers of the 9-cube.

These polytopes are part of a family 511 uniform 9-polytopes with BC9 symmetry.

Rectified 9-cube

Alternate names

  • Rectified enneract (Acronym ren) (Jonathan Bowers)

Images

Birectified 9-cube

Alternate names

  • Birectified enneract (Acronym barn) (Jonathan Bowers)

Images

Trirectified 9-cube

Alternate names

  • Trirectified enneract (Acronym tarn) (Jonathan Bowers)

Images

Quadrirectified 9-cube

Alternate names

  • Quadrirectified enneract (Acronym nav) (Jonathan Bowers)

Images

Notes

References

  • H.S.M. Coxeter:
    • H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
    • Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html
      • (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
      • (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
      • (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
  • Norman Johnson Uniform Polytopes, Manuscript (1991)
    • N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. (1966)
  • x3o3o3o3o3o3o3o4o - vee, o3x3o3o3o3o3o3o4o - riv, o3o3x3o3o3o3o3o4o - brav, o3o3o3x3o3o3o3o4o - tarv, o3o3o3o3x3o3o3o4o - nav, o3o3o3o3o3x3o3o4o - tarn, o3o3o3o3o3o3x3o4o - barn, o3o3o3o3o3o3o3x4o - ren, o3o3o3o3o3o3o3o4x - enne

References

  1. Klitzing (o3o3o3o3o3o3o3x4o - ren)
  2. Klitzing (o3o3o3o3o3o3x3o4o - barn)
  3. Klitzing (o3o3o3o3o3x3o3o4o - tarn)
  4. Klitzing (o3o3o3o3x3o3o3o4o - nav)
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