Pentellated_6-orthoplexes

Pentellated 6-orthoplexes

Pentellated 6-orthoplexes

Add article description


In six-dimensional geometry, a pentellated 6-orthoplex is a convex uniform 6-polytope with 5th order truncations of the regular 6-orthoplex.

More information Orthogonal projections in B6 Coxeter plane ...

There are unique 16 degrees of pentellations of the 6-orthoplex with permutations of truncations, cantellations, runcinations, and sterications. Ten are shown, with the other 6 more easily constructed as a pentellated 6-cube. The simple pentellated 6-orthoplex (Same as pentellated 5-cube) is also called an expanded 6-orthoplex, constructed by an expansion operation applied to the regular 6-orthoplex. The highest form, the pentisteriruncicantitruncated 6-orthoplex, is called an omnitruncated 6-orthoplex with all of the nodes ringed.

Pentitruncated 6-orthoplex

More information Pentitruncated 6-orthoplex ...

Alternate names

  • Teritruncated hexacontatetrapeton (Acronym: tacox) (Jonathan Bowers)[1]

Images

More information Coxeter plane, B6 ...

Penticantellated 6-orthoplex

More information Penticantellated 6-orthoplex ...

Alternate names

  • Terirhombated hexacontitetrapeton (Acronym: tapox) (Jonathan Bowers)[2]

Images

More information Coxeter plane, B6 ...

Penticantitruncated 6-orthoplex

More information Penticantitruncated 6-orthoplex ...

Alternate names

  • Terigreatorhombated hexacontitetrapeton (Acronym: togrig) (Jonathan Bowers)[3]

Images

More information Coxeter plane, B6 ...

Pentiruncitruncated 6-orthoplex

More information Pentiruncitruncated 6-orthoplex ...

Alternate names

  • Teriprismatotruncated hexacontitetrapeton (Acronym: tocrax) (Jonathan Bowers)[4]

Images

More information Coxeter plane, B6 ...

Pentiruncicantitruncated 6-orthoplex

More information Pentiruncicantitruncated 6-orthoplex ...

Alternate names

  • Terigreatoprismated hexacontitetrapeton (Acronym: tagpog) (Jonathan Bowers)[5]

Images

More information Coxeter plane, B6 ...

Pentistericantitruncated 6-orthoplex

More information Pentistericantitruncated 6-orthoplex ...

Alternate names

  • Tericelligreatorhombated hexacontitetrapeton (Acronym: tecagorg) (Jonathan Bowers)[6]

Images

More information Coxeter plane, B6 ...


These polytopes are from a set of 63 uniform 6-polytopes generated from the B6 Coxeter plane, including the regular 6-cube or 6-orthoplex.


Notes

  1. Klitzing, (x4o3o3o3x3x - tacox)
  2. Klitzing, (x4o3o3x3o3x - tapox)
  3. Klitzing, (x4o3o3x3x3x - togrig)
  4. Klitzing, (x4o3x3o3x3x - tocrax)
  5. Klitzing, (x4x3o3x3x3x - tagpog)
  6. Klitzing, (x4x3o3x3x3x - tecagorg)

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, ISBN 978-0-471-01003-6
      • (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.
  • Klitzing, Richard. "6D uniform polytopes (polypeta)". x4o3o3o3x3x - tacox, x4o3o3x3o3x - tapox, x4o3o3x3x3x - togrig, x4o3x3o3x3x - tocrax, x4x3o3x3x3x - tagpog, x4x3o3x3x3x - tecagorg
More information Family, Regular polygon ...

Share this article:

This article uses material from the Wikipedia article Pentellated_6-orthoplexes, and is written by contributors. Text is available under a CC BY-SA 4.0 International License; additional terms may apply. Images, videos and audio are available under their respective licenses.