Cantellated_6-demicube

Runcic 6-cubes

In six-dimensional geometry, a runcic 6-cube is a convex uniform 6-polytope. There are 2 unique runcic for the 6-cube.

More information Orthogonal projections in D6 Coxeter plane ...

Runcic 6-cube

Runcic 6-cube
Typeuniform 6-polytope
Schläfli symbolt0,2{3,33,1}
h3{4,34}
Coxeter-Dynkin diagram =
5-faces
4-faces
Cells
Faces
Edges3840
Vertices640
Vertex figure
Coxeter groupsD6, [33,1,1]
Propertiesconvex

Alternate names

  • Cantellated 6-demicube/demihexeract
  • Small rhombated hemihexeract (Acronym sirhax) (Jonathan Bowers)[1]

Cartesian coordinates

The Cartesian coordinates for the vertices of a runcic 6-cube centered at the origin are coordinate permutations:

(±1,±1,±1,±3,±3,±3)

with an odd number of plus signs.

Images

More information Coxeter plane, B6 ...
More information n-cubes, n ...

Runcicantic 6-cube

More information Runcicantic 6-cube ...

Alternate names

  • Cantitruncated 6-demicube/demihexeract
  • Great rhombated hemihexeract (Acronym girhax) (Jonathan Bowers)[2]

Cartesian coordinates

The Cartesian coordinates for the vertices of a runcicantic 6-cube centered at the origin are coordinate permutations:

(±1,±1,±3,±5,±5,±5)

with an odd number of plus signs.

Images

More information Coxeter plane, B6 ...

This polytope is based on the 6-demicube, a part of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family.

There are 47 uniform polytopes with D6 symmetry, 31 are shared by the B6 symmetry, and 16 are unique:


Notes

  1. Klitzing, (x3o3o *b3x3o3o - sirhax)
  2. Klitzing, (x3x3o *b3x3o3o - girhax)

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, 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.
  • Klitzing, Richard. "6D uniform polytopes (polypeta)". x3o3o *b3x3o3o, x3x3o *b3x3o3o
More information Family, Regular polygon ...

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