Cantitruncated 6-orthoplex

Cantellated 6-orthoplex

In six-dimensional geometry, a cantellated 6-orthoplex is a convex uniform 6-polytope, being a cantellation of the regular 6-orthoplex.

There are 8 cantellation for the 6-orthoplex including truncations. Half of them are more easily constructed from the dual 5-cube

Cantellated 6-orthoplex

Alternate names

Construction

There are two Coxeter groups associated with the cantellated 6-orthoplex, one with the C₆ or [4,3,3,3,3] Coxeter group, and a lower symmetry with the D₆ or [3] Coxeter group.

Coordinates

Cartesian coordinates for the vertices of a truncated 6-orthoplex, centered at the origin, are all 120 vertices are all sign and coordinate permutations of

(2,1,1,0,0,0)

Images

Bicantellated 6-orthoplex

Alternate names

Images

Cantitruncated 6-orthoplex

Alternate names

Images

Bicantitruncated 6-orthoplex

Alternate names

Images

Related polytopes

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

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, editied by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [1]
    • (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.
• Richard Klitzing, 6D, uniform polytopes (polypeta) x3o3x3o3o4o - srog, o3x3o3x3o4o - siborg, x3x3x3o3o4o - grog, o3x3x3x3o4o - gaborg

External links

• Olshevsky, George, Cross polytope at Glossary for Hyperspace.
• Polytopes of Various Dimensions
• Multi-dimensional Glossary

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