Surf Wiki
Save to docs
general/7-polytopes

From Surf Wiki (app.surf) — the open knowledge base

Stericated 7-orthoplexes

Orthogonal projections in B6 Coxeter plane
[[File:7-cube t0 B6.svg160px]]7-orthoplex
[[File:7-cube t125 B6.svg160px]]Bisteritruncated 7-orthoplex
[[File:7-cube t1235 B6.svg160px]]Bistericantitruncated 7-orthoplex
[[File:7-cube t0234 B6.svg160px]]Steriruncicantellated 7-orthoplex

In seven-dimensional geometry, a stericated 7-orthoplex is a convex uniform 7-polytope with 4th order truncations (sterication) of the regular 7-orthoplex.

There are 24 unique sterication for the 7-orthoplex with permutations of truncations, cantellations, and runcinations. 14 are more simply constructed from the 7-cube.

This polytope is one of 127 uniform 7-polytopes with B7 symmetry.

Stericated 7-orthoplex

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

Alternate names

  • Small cellated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)

Images

Steritruncated 7-orthoplex

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

Alternate names

  • Cellitruncated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)

Images

Bisteritruncated 7-orthoplex

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

Alternate names

  • Bicellitruncated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)

Images

Stericantellated 7-orthoplex

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

Alternate names

  • Cellirhombated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)

Images

Stericantitruncated 7-orthoplex

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

Alternate names

  • Celligreatorhombated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)

Images

Bistericantitruncated 7-orthoplex

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

Alternate names

  • Bicelligreatorhombated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)

Images

Steriruncinated 7-orthoplex

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

Alternate names

  • Celliprismated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)

Images

Steriruncitruncated 7-orthoplex

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

Alternate names

  • Celliprismatotruncated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)

Images

Steriruncicantellated 7-orthoplex

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

Alternate names

  • Celliprismatorhombated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)

Images

Steriruncicantitruncated 7-orthoplex

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

Alternate names

  • Great cellated hecatonicosoctaexon (acronym: ) (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. Klitizing, (x3o3o3o3x3o4o - )
  2. Klitizing, (x3x3o3o3x3o4o - )
  3. Klitizing, (o3x3x3o3o3x4o - )
  4. Klitizing, (x3o3x3o3x3o4o - )
  5. Klitizing, (x3x3x3o3x3o4o - )
  6. Klitizing, (o3x3x3x3o3x4o - )
  7. Klitizing, (x3o3o3x3x3o4o - )
  8. Klitizing, (x3x3x3o3x3o4o - )
  9. Klitizing, (x3o3x3x3x3o4o - )
  10. Klitizing, (x3x3x3x3x3o4o - )
Info: Wikipedia Source

This article was imported from Wikipedia and is available under the Creative Commons Attribution-ShareAlike 4.0 License. Content has been adapted to SurfDoc format. Original contributors can be found on the article history page.

7-polytopes
Want to explore this topic further?

Ask Mako anything about Stericated 7-orthoplexes — get instant answers, deeper analysis, and related topics.

Research with Mako

Free with your Surf account

Content sourced from Wikipedia, available under CC BY-SA 4.0.

This content may have been generated or modified by AI. CloudSurf Software LLC is not responsible for the accuracy, completeness, or reliability of AI-generated content. Always verify important information from primary sources.

Report