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Stericated 6-cubes

Orthogonal projections in B6 Coxeter plane

In six-dimensional geometry, a stericated 6-cube is a convex uniform 6-polytope, constructed as a sterication (4th order truncation) of the regular 6-cube.

There are 8 unique sterications for the 6-cube with permutations of truncations, cantellations, and runcinations.

Stericated 6-cube

Stericated 6-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Small cellated hexeract (Acronym: scox) (Jonathan Bowers)

Images

Steritruncated 6-cube

Steritruncated 6-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Cellirhombated hexeract (Acronym: catax) (Jonathan Bowers)

Images

Stericantellated 6-cube

Stericantellated 6-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Cellirhombated hexeract (Acronym: crax) (Jonathan Bowers)

Images

Stericantitruncated 6-cube

stericantitruncated 6-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Celligreatorhombated hexeract (Acronym: cagorx) (Jonathan Bowers)

Images

Steriruncinated 6-cube

steriruncinated 6-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Celliprismated hexeract (Acronym: copox) (Jonathan Bowers)

Images

Steriruncitruncated 6-cube

steriruncitruncated 6-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Celliprismatotruncated hexeract (Acronym: captix) (Jonathan Bowers)

Images

Steriruncicantellated 6-cube

steriruncicantellated 6-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Celliprismatorhombated hexeract (Acronym: coprix) (Jonathan Bowers)

Images

Steriruncicantitruncated 6-cube

Steriuncicantitruncated 6-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Great cellated hexeract (Acronym: gocax) (Jonathan Bowers)

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, wiley.com,
      • (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.

References

  1. Klitzing, (x4x3x3o3x3o - cagorx)
  2. Klitzing, (x4x3o3x3x3o - captix)
  3. Klitzing, (x4x3x3x3x3o - gocax)
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