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Runcic 7-cubes

Orthogonal projections in D7 Coxeter plane

In seven-dimensional geometry, a runcic 7-cube is a convex uniform 7-polytope, related to the uniform 7-demicube. There are 2 unique forms.

Runcic 7-cube

Runcic 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagram
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

A runcic 7-cube, h3{4,35}, has half the vertices of a runcinated 7-cube, t0,3{4,35}.

Alternate names

  • Small rhombated hemihepteract (Acronym sirhesa) (Jonathan Bowers)

Cartesian coordinates

The Cartesian coordinates for the vertices of a cantellated demihepteract centered at the origin are coordinate permutations: : (±1,±1,±1,±3,±3,±3,±3) with an odd number of plus signs.

Images

Runcicantic 7-cube

Runcicantic 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagram
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

A runcicantic 7-cube, h2,3{4,35}, has half the vertices of a runcicantellated 7-cube, t0,1,3{4,35}.

Alternate names

  • Great rhombated hemihepteract (Acronym girhesa) (Jonathan Bowers)

Cartesian coordinates

The Cartesian coordinates for the vertices of a runcicantic 7-cube centered at the origin are coordinate permutations: : (±1,±1,±1,±1,±3,±5,±5) with an odd number of plus signs.

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.
  • x3o3o *b3x3o3o3o - sirhesa, x3x3o *b3x3o3o3o - girhesa

References

  1. Klitzing, (x3o3o *b3x3o3o3o - sirhesa)
  2. Klitzing, (x3x3o *b3x3o3o3o - girhesa)
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