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Runcinated 7-cubes

Orthogonal projections in B7 Coxeter plane

In seven-dimensional geometry, a runcinated 7-cube is a convex uniform 7-polytope with 3rd order truncations (runcination) of the regular 7-cube.

There are 16 unique runcinations of the 7-cube with permutations of truncations, and cantellations. 8 are more simply constructed from the 7-orthoplex.

These polytopes are among 127 uniform 7-polytopes with B7 symmetry.

Runcinated 7-cube

Runcinated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Small prismated hepteract (acronym: spesa) (Jonathan Bowers)

Images

Biruncinated 7-cube

Biruncinated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Small biprismated hepteract (Acronym sibposa) (Jonathan Bowers)

Images

Runcitruncated 7-cube

Runcitruncated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Prismatotruncated hepteract (acronym: petsa) (Jonathan Bowers)

Images

Biruncitruncated 7-cube

Biruncitruncated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Biprismatotruncated hepteract (acronym: biptesa) (Jonathan Bowers)

Images

Runcicantellated 7-cube

Runcicantellated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Prismatorhombated hepteract (acronym: parsa) (Jonathan Bowers)

Images

Biruncicantellated 7-cube

biruncicantellated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Biprismatorhombated hepteract (acronym: bopresa) (Jonathan Bowers)

Images

Runcicantitruncated 7-cube

Runcicantitruncated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Great prismated hepteract (acronym: gapsa) (Jonathan Bowers)

Images

Biruncicantitruncated 7-cube

biruncicantitruncated 7-cube
Type
Schläfli symbol
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups
Properties

Alternate names

  • Great biprismated hepteract (acronym: gibposa) (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. (1966)
  • x3o3o3x3o3o4o - spo, o3x3o3o3x3o4o - sibpo, x3x3o3x3o3o4o - patto, o3x3x3o3x3o4o - bipto, x3o3x3x3o3o4o - paro, x3x3x3x3o3o4o - gapo, o3x3x3x3x3o3o- gibpo

References

  1. Klitzing, (x3o3o3x3o3o4o - spesa)
  2. Klitzing, (o3x3o3o3x3o4o - sibposa)
  3. Klitzing, (x3x3o3x3o3o4o - petsa)
  4. Klitzing, (o3x3x3o3x3o4o - biptesa)
  5. Klitzing, (x3o3x3x3o3o4o - parsa)
  6. Klitzing, (o3o3x3x3o3x4o - bopresa)
  7. Klitzing, (x3x3x3x3o3o4o - gapsa)
  8. Klitzing, (o3x3x3x3x3o3o - gibposa)
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