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Runcinated 6-orthoplexes#Runcinated 6-orthoplex

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6-cube
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Runcinated 6-cube
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Biruncinated 6-cube
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Runcinated 6-orthoplex
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6-orthoplex
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Runcitruncated 6-cube
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Biruncitruncated 6-cube
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Runcicantellated 6-orthoplex
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Runcicantellated 6-cube
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Biruncitruncated 6-orthoplex
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Runcitruncated 6-orthoplex
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Runcicantitruncated 6-cube
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Biruncicantitruncated 6-cube
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Runcicantitruncated 6-orthoplex
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colspan=5|Orthogonal projections in BC6 Coxeter plane

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

There are 12 unique runcinations of the 6-orthoplex with permutations of truncations, and cantellations. 7 are expressed relative to the dual 6-cube.

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Runcinated 6-orthoplex

= Alternate names =

  • Small prismatohexacontatetrapeton (spog) (Jonathan Bowers){{sfn|Klitzing|at=[https://bendwavy.org/klitzing/incmats/spog.htm (x3o3o3x3o4o - spog)]}}

= Images =

{{6-cube Coxeter plane graphs|t25|150}}

Runcicantellated 6-orthoplex

= Alternate names =

  • Prismatorhombated hexacontatetrapeton (prog) (Jonathan Bowers){{sfn|Klitzing|at=[https://bendwavy.org/klitzing/incmats/prog.htm (x3o3x3x3o4o - prog)]}}

= Images =

{{6-cube Coxeter plane graphs|t235|150}}

Biruncitruncated 6-orthoplex

= Alternate names =

  • Biprismatotruncated hexacontatetrapeton (boprax) (Jonathan Bowers){{sfn|Klitzing|at=[https://bendwavy.org/klitzing/incmats/boprax.htm (o3x3x3o3x4o - boprax)]}}

= Images =

{{6-cube Coxeter plane graphs|t134|150}}

Runcitruncated 6-orthoplex

= Alternate names =

  • Prismatotruncated hexacontatetrapeton (potag) (Jonathan Bowers){{sfn|Klitzing|at=[https://bendwavy.org/klitzing/incmats/potag.htm (x3x3o3x3o4o - potag)]}}

= Images =

{{6-cube Coxeter plane graphs|t245|150}}

Runcicantitruncated 6-orthoplex

= Alternate names =

  • Great prismated hexacontatetrapeton (gopog) (Jonathan Bowers){{sfn|Klitzing|at=[https://bendwavy.org/klitzing/incmats/gopog.htm (x3x3x3x3o4o - gopog)]}}

= Images =

{{6-cube Coxeter plane graphs|t2345|150}}

Related polytopes

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.

{{Hexeract family}}

Notes

{{reflist}}

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, [https://www.wiley.com/en-us/Kaleidoscopes-p-9780471010036 wiley.com], {{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.
  • {{KlitzingPolytopes|polypeta.htm|6D uniform polytopes (polypeta) with acronyms}} x3o3o3x3o4o - spog, x3o3x3x3o4o - prog, x3x3o3x3o4o - potag, o3x3x3o3x4o - boprax, x3x3x3x3o4o - gopog {{sfn whitelist|CITEREFKlitzing}}

External links

  • {{MathWorld|title=Hypercube|urlname=Hypercube}}
  • [https://web.archive.org/web/20070310205351/http://members.cox.net/hedrondude/topes.htm Polytopes of Various Dimensions]
  • [http://tetraspace.alkaline.org/glossary.htm Multi-dimensional Glossary]

{{Polytopes}}

Category:6-polytopes