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 B₇ symmetry. {{-}}

Pentellated 7-orthoplex

Alternate names

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

Coordinates

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

Pentitruncated 7-orthoplex

Alternate names

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

Coordinates

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

Penticantellated 7-orthoplex

Alternate names

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

Coordinates

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

Penticantitruncated 7-orthoplex

Alternate names

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

Coordinates

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

Pentiruncinated 7-orthoplex

Alternate names

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

Coordinates

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

Pentiruncitruncated 7-orthoplex

Alternate names

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

Coordinates

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

Pentiruncicantellated 7-orthoplex

Alternate names

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

Coordinates

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

Pentiruncicantitruncated 7-orthoplex

Alternate names

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

Coordinates

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

Pentistericated 7-orthoplex

Alternate names

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

Coordinates

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

Pentisteritruncated 7-orthoplex

Alternate names

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

Coordinates

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

Pentistericantellated 7-orthoplex

Alternate names

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

Coordinates

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

Pentistericantitruncated 7-orthoplex

Alternate names

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

Coordinates

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

Pentisteriruncinated 7-orthoplex

Alternate names

• Bipenticantitruncated 7-orthoplex as t_1,2,3,6{3⁵,4}
• Tericelliprismated hecatonicosaoctaexon (acronym: Tecpaz) (Jonathan Bowers)

Coordinates

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

Pentisteriruncitruncated 7-orthoplex

Alternate names

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

Coordinates

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

Pentisteriruncicantellated 7-orthoplex

Alternate names

• Bipentiruncicantitruncated 7-orthoplex as t_1,2,3,4,6{3⁵,4}
• Tericelliprismatorhombated hecatonicosaoctaexon (acronym: Tacparez) (Jonathan Bowers)

Coordinates

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

Pentisteriruncicantitruncated 7-orthoplex

Alternate names

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

Coordinates

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

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 Ivić 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.

• x3o3o3o3o3x4o - staz, x3x3o3o3o3x4o - tetaz, x3o3x3o3o3x4o - teroz, x3x3x3oxo3x4o - tograz, x3o3o3x3o3x4o - topaz, x3x3o3x3o3x4o - toptaz, x3o3x3x3o3x4o - toparz, x3x3x3x3o3x4o - tegopaz, x3o3o3o3x3x4o - tocaz, x3x3o3o3x3x4o - tacotaz, x3o3x3o3x3x4o - tocarz, x3x3x3o3x3x4o - tecagraz, x3o3o3x3x3x4o - tecpaz, x3x3o3x3x3x4o - tecpotaz, x3o3x3x3x3x4o - tacparez, x3x3x3x3x3x4o - gotaz

External links

• Polytopes of Various Dimensions
• Multi-dimensional Glossary