Stericated 6-orthoplexes
6-orthoplex
    |
Stericated 6-orthoplex
|
Steritruncated 6-orthoplex
|
Stericantellated 6-orthoplex
|
Stericantitruncated 6-orthoplex
|
Steriruncinated 6-orthoplex
|
Steriruncitruncated 6-orthoplex
|
Steriruncicantellated 6-orthoplex
|
Steriruncicantitruncated 6-orthoplex
|
| 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-cube.
Stericated 6-orthoplex
Alternate names
- Small cellated hexacontatetrapeton (Acronym: scag) (Jonathan Bowers)[1]
Images
Steritruncated 6-orthoplex
| Steritruncated 6-orthoplex |
|---|
| Type | uniform 6-polytope |
| Schläfli symbol | t0,1,4{3,3,3,3,4} |
| Coxeter-Dynkin diagrams | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 19200 |
| Vertices | 3840 |
| Vertex figure | |
| Coxeter groups | B6, [4,3,3,3,3] |
| Properties | convex |
Alternate names
- Cellitruncated hexacontatetrapeton (Acronym: catog) (Jonathan Bowers)[2]
Images
Stericantellated 6-orthoplex
| Stericantellated 6-orthoplex |
|---|
| Type | uniform 6-polytope |
| Schläfli symbols | t0,2,4{34,4}
rr2r{3,3,3,3,4} |
| Coxeter-Dynkin diagrams |       |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 28800 |
| Vertices | 5760 |
| Vertex figure | |
| Coxeter groups | B6, [4,3,3,3,3] |
| Properties | convex |
Alternate names
- Cellirhombated hexacontatetrapeton (Acronym: crag) (Jonathan Bowers)[3]
Images
Stericantitruncated 6-orthoplex
| stericantitruncated 6-orthoplex |
|---|
| Type | uniform 6-polytope |
| Schläfli symbol | t0,1,2,4{3,3,3,3,4} |
| Coxeter-Dynkin diagrams | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 46080 |
| Vertices | 11520 |
| Vertex figure | |
| Coxeter groups | B6, [4,3,3,3,3] |
| Properties | convex |
Alternate names
- Celligreatorhombated hexacontatetrapeton (Acronym: cagorg) (Jonathan Bowers)[4]
Images
Steriruncinated 6-orthoplex
| steriruncinated 6-orthoplex |
|---|
| Type | uniform 6-polytope |
| Schläfli symbol | t0,3,4{3,3,3,3,4} |
| Coxeter-Dynkin diagrams | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 15360 |
| Vertices | 3840 |
| Vertex figure | |
| Coxeter groups | B6, [4,3,3,3,3] |
| Properties | convex |
Alternate names
- Celliprismated hexacontatetrapeton (Acronym: copog) (Jonathan Bowers)[5]
Images
Steriruncitruncated 6-orthoplex
Alternate names
- Celliprismatotruncated hexacontatetrapeton (Acronym: captog) (Jonathan Bowers)[6]
Images
Steriruncicantellated 6-orthoplex
| steriruncicantellated 6-orthoplex |
|---|
| Type | uniform 6-polytope |
| Schläfli symbol | t0,2,3,4{3,3,3,3,4} |
| Coxeter-Dynkin diagrams | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 40320 |
| Vertices | 11520 |
| Vertex figure | |
| Coxeter groups | B6, [4,3,3,3,3] |
| Properties | convex |
Alternate names
- Celliprismatorhombated hexacontatetrapeton (Acronym: coprag) (Jonathan Bowers)[7]
Images
Steriruncicantitruncated 6-orthoplex
| Steriuncicantitruncated 6-orthoplex |
|---|
| Type | uniform 6-polytope |
| Schläfli symbols | t0,1,2,3,4{34,4}
tr2r{3,3,3,3,4} |
| Coxeter-Dynkin diagrams | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 69120 |
| Vertices | 23040 |
| Vertex figure | |
| Coxeter groups | B6, [4,3,3,3,3] |
| Properties | convex |
Alternate names
- Great cellated hexacontatetrapeton (Acronym: gocog) (Jonathan Bowers)[8]
Images
Related polytopes
These polytopes are from a set of 63 uniform 6-polytopes generated from the B6 Coxeter plane, including the regular 6-orthoplex or 6-orthoplex.
| B6 polytopes |
|---|
β6 |
t1β6 |
t2β6 |
t2γ6 |
t1γ6 |
γ6 |
t0,1β6 |
t0,2β6 |
t1,2β6 |
t0,3β6 |
t1,3β6 |
t2,3γ6 |
t0,4β6 |
t1,4γ6 |
t1,3γ6 |
t1,2γ6 |
t0,5γ6 |
t0,4γ6 |
t0,3γ6 |
t0,2γ6 |
t0,1γ6 |
t0,1,2β6 |
t0,1,3β6 |
t0,2,3β6 |
t1,2,3β6 |
t0,1,4β6 |
t0,2,4β6 |
t1,2,4β6 |
t0,3,4β6 |
t1,2,4γ6 |
t1,2,3γ6 |
t0,1,5β6 |
t0,2,5β6 |
t0,3,4γ6 |
t0,2,5γ6 |
t0,2,4γ6 |
t0,2,3γ6 |
t0,1,5γ6 |
t0,1,4γ6 |
t0,1,3γ6 |
t0,1,2γ6 |
t0,1,2,3β6 |
t0,1,2,4β6 |
t0,1,3,4β6 |
t0,2,3,4β6 |
t1,2,3,4γ6 |
t0,1,2,5β6 |
t0,1,3,5β6 |
t0,2,3,5γ6 |
t0,2,3,4γ6 |
t0,1,4,5γ6 |
t0,1,3,5γ6 |
t0,1,3,4γ6 |
t0,1,2,5γ6 |
t0,1,2,4γ6 |
t0,1,2,3γ6 |
t0,1,2,3,4β6 |
t0,1,2,3,5β6 |
t0,1,2,4,5β6 |
t0,1,2,4,5γ6 |
t0,1,2,3,5γ6 |
t0,1,2,3,4γ6 |
t0,1,2,3,4,5γ6 |
Notes
- ↑ Klitzing, (x3o3o3o3x4o - scag)
- ↑ Klitzing, (x3x3o3o3x4o - catog)
- ↑ Klitzing, (x3o3x3o3x4o - crag)
- ↑ Klitzing, (x3x3x3o3x4o - cagorg)
- ↑ Klitzing, (x3o3o3x3x4o - copog)
- ↑ Klitzing, (x3x3o3x3x4o - captog)
- ↑ Klitzing, (x3o3x3x3x4o - coprag)
- ↑ Klitzing, (x3x3x3x3x4o - gocog)
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
- (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.
- Klitzing, Richard. "6D uniform polytopes (polypeta)".
External links
