Cantellated 7-orthoplexes

7-orthoplex	Cantellated 7-orthoplex	Bicantellated 7-orthoplex	Birectified 7-orthoplex
Cantitruncated 7-orthoplex	Bicantitruncated 7-orthoplex	Cantellated 7-cube	Bicantellated 7-cube
Tricantellated 7-cube	Cantitruncated 7-cube	Bicantitruncated 7-cube	Tricantitruncated 7-cube
Orthogonal projections in B6 Coxeter plane

In seven-dimensional geometry, a cantellated 7-orthoplex is a convex uniform 7-polytope, being a cantellation of the regular 7-orthoplex.

There are ten degrees of cantellation for the 7-orthoplex, including truncations. Six are most simply constructible from the dual 7-cube.

Cantellated 7-orthoplex

Cantellated 7-orthoplex
Type	uniform 7-polytope
Schläfli symbol	rr{3,3,3,3,3,4}
Coxeter-Dynkin diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges	7560
Vertices	840
Vertex figure
Coxeter groups	B7, [4,3,3,3,3,3]
Properties	convex

Alternate names

• Small rhombated hecatonicosoctaexon (acronym: sarz) (Jonathan Bowers)

Bicantellated 7-orthoplex

Bicantellated 7-orthoplex
Type	uniform 7-polytope
Schläfli symbol	2rr{3,3,3,3,3,4}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B7, [4,3,3,3,3,3]
Properties	convex

Alternate names

• Small birhombated hecatonicosoctaexon (acronym: sebraz) (Jonathan Bowers)

Cantitruncated 7-orthoplex

Cantitruncated 7-orthoplex
Type	uniform 7-polytope
Schläfli symbol	tr{3,3,3,3,3,4}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges	8400
Vertices	1680
Vertex figure
Coxeter groups	B7, [4,3,3,3,3,3]
Properties	convex

Alternate names

• Great rhombated hecatonicosoctaexon (acronym: garz) (Jonathan Bowers)

Bicantitruncated 7-orthoplex

Bicantitruncated 7-orthoplex
Type	uniform 7-polytope
Schläfli symbol	2tr{3,3,3,3,3,4}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges	30240
Vertices	6720
Vertex figure
Coxeter groups	B7, [4,3,3,3,3,3]
Properties	convex

Alternate names

• Great birhombated hecatonicosoctaexon (acronym: gebraz) (Jonathan Bowers)

Related polytopes

These polytopes are from a family of 127 uniform 7-polytopes with B₇ symmetry.

See also

• List of B7 polytopes

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 [1]
    • (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
• Klitzing, Richard. "7D uniform polytopes (polyexa)". https://bendwavy.org/klitzing/dimensions/polyexa.htm.  - o3o3o3o3x3o4x - sarz, o3o3o3x3o3x4o - sebraz, o3o3o3o3x3x4x - garz, o3o3o3x3x3x4o - gebraz

External links

• Polytopes of Various Dimensions
• Multi-dimensional Glossary