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Cantellated 5-orthoplexes

Orthogonal projections in B5 Coxeter plane

In five-dimensional geometry, a cantellated 5-orthoplex is a convex uniform 5-polytope, being a cantellation of the regular 5-orthoplex.

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

Cantellated 5-orthoplex

Propertiesconvex

Alternate names

  • Cantellated 5-orthoplex
  • Bicantellated 5-demicube
  • Small rhombated triacontiditeron (Acronym: sart) (Jonathan Bowers)

Coordinates

The vertices of the can be made in 5-space, as permutations and sign combinations of: : (0,0,1,1,2)

Images

The cantellated 5-orthoplex is constructed by a cantellation operation applied to the 5-orthoplex.

Cantitruncated 5-orthoplex

Cantitruncated 5-orthoplex
Type
Schläfli symbol
Coxeter-Dynkin diagrams
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Cantitruncated pentacross
  • Cantitruncated triacontiditeron (Acronym: gart) (Jonathan Bowers)

Coordinates

Cartesian coordinates for the vertices of a cantitruncated 5-orthoplex, centered at the origin, are all sign and coordinate permutations of : (±3,±2,±1,0,0)

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, http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html
      • (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.
  • x3o3x3o4o - sart, x3x3x3o4o - gart

References

  1. Klitizing, (x3o3x3o4o - sart)
  2. Klitizing, (x3x3x3o4o - gart)
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