From Surf Wiki (app.surf) — the open knowledge base
Stericated 6-orthoplexes
| Orthogonal projections in B6 Coxeter plane |
|---|
In six-dimensional geometry, a stericated 6-orthoplex is a convex uniform 6-polytope, constructed as a sterication (4th order truncation) of the regular 6-orthoplex.
There are 16 unique sterications for the 6-orthoplex with permutations of truncations, cantellations, and runcinations. Eight are better represented from the stericated 6-cubes.
Stericated 6-orthoplex
| Stericated 6-orthoplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter-Dynkin diagrams |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter groups |
| Properties |
Alternate names
- Small cellated hexacontatetrapeton (Acronym: scag) (Jonathan Bowers)
Images
Steritruncated 6-orthoplex
| Steritruncated 6-orthoplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter-Dynkin diagrams |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter groups |
| Properties |
Alternate names
- Cellitruncated hexacontatetrapeton (Acronym: catog) (Jonathan Bowers)
Images
Stericantellated 6-orthoplex
| Stericantellated 6-orthoplex |
|---|
| Type |
| Schläfli symbols |
| Coxeter-Dynkin diagrams |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter groups |
| Properties |
Alternate names
- Cellirhombated hexacontatetrapeton (Acronym: crag) (Jonathan Bowers)
Images
Stericantitruncated 6-orthoplex
| Stericantitruncated 6-orthoplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter-Dynkin diagrams |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter groups |
| Properties |
Alternate names
- Celligreatorhombated hexacontatetrapeton (Acronym: cagorg) (Jonathan Bowers)
Images
Steriruncinated 6-orthoplex
| Steriruncinated 6-orthoplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter-Dynkin diagrams |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter groups |
| Properties |
Alternate names
- Celliprismated hexacontatetrapeton (Acronym: copog) (Jonathan Bowers)
Images
Steriruncitruncated 6-orthoplex
| Steriruncitruncated 6-orthoplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter-Dynkin diagrams |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter groups |
| Properties |
Alternate names
- Celliprismatotruncated hexacontatetrapeton (Acronym: captog) (Jonathan Bowers)
Images
Steriruncicantellated 6-orthoplex
| Steriruncicantellated 6-orthoplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter-Dynkin diagrams |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter groups |
| Properties |
Alternate names
- Celliprismatorhombated hexacontatetrapeton (Acronym: coprag) (Jonathan Bowers)
Images
Steriruncicantitruncated 6-orthoplex
| Steriuncicantitruncated 6-orthoplex |
|---|
| Type |
| Schläfli symbols |
| Coxeter-Dynkin diagrams |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter groups |
| Properties |
Alternate names
- Great cellated hexacontatetrapeton (Acronym: gocog) (Jonathan Bowers)
Images
Snub 6-demicube
The snub 6-demicube defined as an alternation of the omnitruncated 6-demicube is not uniform, but it can be given Coxeter diagram or and symmetry [32,1,1,1]+ or [4,(3,3,3,3)+], and constructed from 12 snub 5-demicubes, 64 snub 5-simplexes, 60 snub 24-cell antiprisms, 160 3-s{3,4} duoantiprisms, 240 2-sr{3,3} duoantiprisms, and 11520 irregular 5-simplexes filling the gaps at the deleted vertices.
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.
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.
Ask Mako anything about Stericated 6-orthoplexes — get instant answers, deeper analysis, and related topics.
Research with MakoFree with your Surf account
Create a free account to save articles, ask Mako questions, and organize your research.
Sign up freeThis 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