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Pentellated 7-orthoplexes

In seven-dimensional geometry, a pentellated 7-orthoplex is a convex uniform 7-polytope with 5th order truncations (pentellation) of the regular 7-orthoplex.

There are 32 unique of the 7-orthoplex with permutations of truncations, cantellations, runcinations, and . 16 are more simply constructed relative to the 7-cube.

These polytopes are a part of a set of 127 uniform 7-polytopes with B<sub>7</sub> symmetry.

Pentellated 7-orthoplex

Alternate names

  • Small hecatonicosoctaexon (acronym: Staz) (Jonathan Bowers)

Coordinates

Coordinates are permutations of (0,1,1,1,1,1,2)

Images

Pentitruncated 7-orthoplex

Alternate names

  • Teritruncated hecatonicosoctaexon (acronym: Tetaz) (Jonathan Bowers)

Images

Coordinates

Coordinates are permutations of (0,1,1,1,1,2,3).

Penticantellated 7-orthoplex

Alternate names

  • Terirhombated hecatonicosoctaexon (acronym: Teroz) (Jonathan Bowers)

Coordinates

Coordinates are permutations of (0,1,1,1,2,2,3).

Images

Penticantitruncated 7-orthoplex

Alternate names

  • Terigreatorhombated hecatonicosoctaexon (acronym: Tograz) (Jonathan Bowers)

Coordinates

Coordinates are permutations of (0,1,1,1,2,3,4).

Images

Pentiruncinated 7-orthoplex

Alternate names

  • Teriprismated hecatonicosoctaexon (acronym: Topaz) (Jonathan Bowers)

Coordinates

The coordinates are permutations of (0,1,1,2,2,2,3).

Images

Pentiruncitruncated 7-orthoplex

Alternate names

  • Teriprismatotruncated hecatonicosoctaexon (acronym: Toptaz) (Jonathan Bowers)

Coordinates

Coordinates are permutations of (0,1,1,2,2,3,4).

Images

Pentiruncicantellated 7-orthoplex

Alternate names

  • Teriprismatorhombated hecatonicosoctaexon (acronym: Toparz) (Jonathan Bowers)

Coordinates

Coordinates are permutations of (0,1,1,2,3,3,4).

Images

Pentiruncicantitruncated 7-orthoplex

Alternate names

  • Terigreatoprismated hecatonicosoctaexon (acronym: Tegopaz) (Jonathan Bowers)

Coordinates

Coordinates are permutations of (0,1,1,2,3,4,5).

Images

Pentistericated 7-orthoplex

Alternate names

  • Tericellated hecatonicosoctaexon (acronym: Tocaz) (Jonathan Bowers)

Images

Coordinates

Coordinates are permutations of (0,1,2,2,2,2,3).

Pentisteritruncated 7-orthoplex

Alternate names

  • Tericellitruncated hecatonicosoctaexon (acronym: Tacotaz) (Jonathan Bowers)

Coordinates

Coordinates are permutations of (0,1,2,2,2,3,4).

Images

Pentistericantellated 7-orthoplex

Alternate names

  • Tericellirhombated hecatonicosoctaexon (acronym: Tocarz) (Jonathan Bowers)

Coordinates

Coordinates are permutations of (0,1,2,2,3,3,4).

Images

Pentistericantitruncated 7-orthoplex

Alternate names

  • Tericelligreatorhombated hecatonicosoctaexon (acronym: Tecagraz) (Jonathan Bowers)

Coordinates

Coordinates are permutations of (0,1,2,2,3,4,5).

Images

Pentisteriruncinated 7-orthoplex

Alternate names

  • Bipenticantitruncated 7-orthoplex as t<sub>1,2,3,6</sub>{3<sup>5</sup>,4}
  • Tericelliprismated hecatonicosoctaexon (acronym: Tecpaz) (Jonathan Bowers)

Coordinates

Coordinates are permutations of (0,1,2,3,3,3,4).

Images

Pentisteriruncitruncated 7-orthoplex

Alternate names

  • Tericelliprismatotruncated hecatonicosoctaexon (acronym: Tecpotaz) (Jonathan Bowers)

Coordinates

Coordinates are permutations of (0,1,2,3,3,4,5).

Images

Pentisteriruncicantellated 7-orthoplex

Alternate names

  • Bipentiruncicantitruncated 7-orthoplex as t<sub>1,2,3,4,6</sub>{3<sup>5</sup>,4}
  • Tericelliprismatorhombated hecatonicosoctaexon (acronym: Tacparez) (Jonathan Bowers)

Coordinates

Coordinates are permutations of (0,1,2,3,4,4,5).

Images

Pentisteriruncicantitruncated 7-orthoplex

Alternate names

  • Great hecatonicosoctaexon (acronym: Gotaz) (Jonathan Bowers)

Coordinates

Coordinates are permutations of (0,1,2,3,4,5,6).

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.

External links