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
Stericated 6-orthoplex | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | 2r2r{3,3,3,3,4} |
Coxeter-Dynkin diagrams | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 5760 |
Vertices | 960 |
Vertex figure | |
Coxeter groups | B6, [4,3,3,3,3] |
Properties | convex |
Alternate names
- Small cellated hexacontatetrapeton (Acronym: scag) (Jonathan Bowers)[1]
Images
Coxeter plane | B6 | B5 | B4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [12] | [10] | [8] |
Coxeter plane | B3 | B2 | |
Graph | |||
Dihedral symmetry | [6] | [4] | |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
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
Coxeter plane | B6 | B5 | B4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [12] | [10] | [8] |
Coxeter plane | B3 | B2 | |
Graph | |||
Dihedral symmetry | [6] | [4] | |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
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
Coxeter plane | B6 | B5 | B4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [12] | [10] | [8] |
Coxeter plane | B3 | B2 | |
Graph | |||
Dihedral symmetry | [6] | [4] | |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
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
Coxeter plane | B6 | B5 | B4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [12] | [10] | [8] |
Coxeter plane | B3 | B2 | |
Graph | |||
Dihedral symmetry | [6] | [4] | |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
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
Coxeter plane | B6 | B5 | B4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [12] | [10] | [8] |
Coxeter plane | B3 | B2 | |
Graph | |||
Dihedral symmetry | [6] | [4] | |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
Steriruncitruncated 6-orthoplex
Steriruncitruncated 6-orthoplex | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | 2t2r{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
- Celliprismatotruncated hexacontatetrapeton (Acronym: captog) (Jonathan Bowers)[6]
Images
Coxeter plane | B6 | B5 | B4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [12] | [10] | [8] |
Coxeter plane | B3 | B2 | |
Graph | |||
Dihedral symmetry | [6] | [4] | |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
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
Coxeter plane | B6 | B5 | B4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [12] | [10] | [8] |
Coxeter plane | B3 | B2 | |
Graph | |||
Dihedral symmetry | [6] | [4] | |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
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 | 536: 12 t0,1,2,3{3,3,3,4} 60 {}×t0,1,2{3,3,4} × 160 {6}×t0,1,2{3,3} × 240 {4}×t0,1,2{3,3} × 64 t0,1,2,3,4{34} |
4-faces | 8216 |
Cells | 38400 |
Faces | 76800 |
Edges | 69120 |
Vertices | 23040 |
Vertex figure | irregular 5-simplex |
Coxeter groups | B6, [4,3,3,3,3] |
Properties | convex |
Alternate names
- Great cellated hexacontatetrapeton (Acronym: gocog) (Jonathan Bowers)[8]
Images
Coxeter plane | B6 | B5 | B4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [12] | [10] | [8] |
Coxeter plane | B3 | B2 | |
Graph | |||
Dihedral symmetry | [6] | [4] | |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
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.
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.
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, 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)".