Rectified 9-cubes explained

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)^[1]

Images

Birectified 9-cube

Alternate names

• Birectified enneract (Acronym barn) (Jonathan Bowers)^[2]

Images

Trirectified 9-cube

Alternate names

• Trirectified enneract (Acronym tarn) (Jonathan Bowers)^[3]

Images

Quadrirectified 9-cube

Alternate names

• Quadrirectified enneract (Acronym nav) (Jonathan Bowers)^[4]

Images

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

External links

• Polytopes of Various Dimensions
• Multi-dimensional Glossary

Notes and References

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