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Runcinated 6-cubes

Orthogonal projections in B6 Coxeter plane

In six-dimensional geometry, a runcinated 6-cube is a convex uniform 6-polytope with 3rd order truncations (runcination) of the regular 6-cube.

There are 12 unique runcinations of the 6-cube with permutations of truncations, and cantellations. 5 are expressed relative to the dual 6-orthoplex.

Runcinated 6-cube

Propertiesconvex

Alternate names

  • Small prismated hexeract (spox) (Jonathan Bowers)

Images

Biruncinated 6-cube

Propertiesconvex

Alternate names

  • Small biprismated hexeractihexacontatetrapeton (sobpoxog) (Jonathan Bowers)

Images

Runcitruncated 6-cube

Propertiesconvex

Alternate names

  • Prismatotruncated hexeract (potax) (Jonathan Bowers)

Images

Biruncitruncated 6-cube

Propertiesconvex

Alternate names

  • Biprismatotruncated hexeract (boprag) (Jonathan Bowers)

Images

Runcicantellated 6-cube

Propertiesconvex

Alternate names

  • Prismatorhombated hexeract (prox) (Jonathan Bowers)

Images

Runcicantitruncated 6-cube

Propertiesconvex

Alternate names

  • Great prismated hexeract (gippox) (Jonathan Bowers)

Images

Biruncicantitruncated 6-cube

Propertiesconvex

Alternate names

  • Great biprismated hexeractihexacontitetrapeton (gobpoxog) (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, wiley.com,
      • (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.
  • o3o3x3o3o4x - spox, o3x3o3o3x4o - sobpoxog, o3o3x3o3x4x - potax, o3x3o3x3x4o - boprag, o3o3x3x3o4x - prox, o3o3x3x3x4x - gippox, o3x3x3x3x4o - gobpoxog

References

  1. Klitzing, (o3o3x3x3x4x - gippox)
  2. Klitzing, (o3x3x3x3x4o - gobpoxog)
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