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Stericated 8-simplexes

Class of eight-dimensional polytopes

Class of eight-dimensional polytopes

Orthogonal projections in A8 Coxeter plane

In eight-dimensional geometry, a stericated 8-simplex is a convex uniform 8-polytope with 4th order truncations (sterication) of the regular 8-simplex. There are 16 unique sterications for the 8-simplex including permutations of truncation, cantellation, and runcination.

Stericated 8-simplex

Stericated 8-simplex
Type
Schläfli symbol
Coxeter-Dynkin diagrams
7-faces
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter group
Properties

Acronym: secane (Jonathan Bowers)

Coordinates

The Cartesian coordinates of the vertices of the stericated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,1,1,1,1,2). This construction is based on facets of the stericated 9-orthoplex.

Images

Bistericated 8-simplex

Bistericated 8-simplex
Type
Schläfli symbol
Coxeter-Dynkin diagrams
7-faces
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter group
Properties

Acronym: sobcane (Jonathan Bowers)

Coordinates

The Cartesian coordinates of the vertices of the bistericated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,1,1,1,1,2,2). This construction is based on facets of the bistericated 9-orthoplex.

Images

Steritruncated 8-simplex

Steritruncated 8-simplex
Type
Schläfli symbol
Coxeter-Dynkin diagrams
7-faces
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter group
Properties

Acronym: catene (Jonathan Bowers)

Images

Bisteritruncated 8-simplex

Bisteritruncated 8-simplex
Type
Schläfli symbol
Coxeter-Dynkin diagrams
7-faces
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter group
Properties

Acronym: bictane (Jonathan Bowers)

Images

Stericantellated 8-simplex

Acronym: crane (Jonathan Bowers)

Images

Bistericantellated 8-simplex

Acronym: bocrane (Jonathan Bowers)

Images

Stericantitruncated 8-simplex

Acronym: cograne (Jonathan Bowers)

Images

Bistericantitruncated 8-simplex

Acronym: bocagrane (Jonathan Bowers)

Images

Steriruncinated 8-simplex

Acronym: capene (Jonathan Bowers)

Images

Bisteriruncinated 8-simplex

Acronym: bacpane (Jonathan Bowers)

Images

Steriruncitruncated 8-simplex

Acronym: coptane (Jonathan Bowers)

Images

Bisteriruncitruncated 8-simplex

Acronym: bicpotane (Jonathan Bowers)

Images

Steriruncicantellated 8-simplex

Acronym: coprene (Jonathan Bowers)

Images

Bisteriruncicantellated 8-simplex

Acronym: bicprene (Jonathan Bowers)

Images

Steriruncicantitruncated 8-simplex

Acronym: gacene (Jonathan Bowers)

Images

Bisteriruncicantitruncated 8-simplex

Acronym: gobcane (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.
  • x3o3o3o3x3o3o3o - secane, o3x3o3o3o3x3o3o - sobcane, x3x3o3o3x3o3o3o - catene, o3x3x3o3o3x3o3o - bictane, x3o3x3o3x3o3o3o - crane, o3x3o3x3o3x3o3o - bocrane, x3x3x3o3x3o3o3o - cograne, o3x3x3x3ox3o3o3 - bocagrane, x3o3o3x3x3o3o3o - capene, o3x3o3o3x3x3o3o - bacpane, x3x3o3x3x3o3o3o - coptane, o3x3x3o3x3x3o3o - bicpotane, x3o3x3x3x3o3o3o - coprene, o3x3o3x3x3x3o3o - bicprene, x3x3x3x3x3o3o3o - gacene, o3x3x3x3x3x3o3o - gobcane

References

  1. Klitzing, (x3o3o3o3x3o3o3o - secane)
  2. Klitzing, (o3x3o3o3o3x3o3o - sobcane)
  3. Klitzing, (x3x3o3o3x3o3o3o - catene)
  4. Klitzing, (o3x3x3o3o3x3o3o - bictane)
  5. Klitzing, (x3o3x3o3x3o3o3o - crane)
  6. Klitzing, (o3x3o3x3o3x3o3o - bocrane)
  7. Klitzing, (x3x3x3o3x3o3o3o - cograne)
  8. Klitzing, (o3x3x3x3ox3o3o3 - bocagrane)
  9. Klitzing, (x3o3o3x3x3o3o3o - capene)
  10. Klitzing, (o3x3o3o3x3x3o3o - bacpane)
  11. Klitzing, (x3x3o3x3x3o3o3o - coptane)
  12. Klitzing, (o3x3x3o3x3x3o3o - bicpotane)
  13. Klitzing, (x3o3x3x3x3o3o3o - coprene)
  14. Klitzing, (o3x3o3x3x3x3o3o - bicprene)
  15. Klitzing, (x3x3x3x3x3o3o3o - gacene)
  16. Klitzing, (o3x3x3x3x3x3o3o - gobcane)
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