Steriruncinated_6-orthoplex
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.
More information Orthogonal projections in B6 Coxeter plane ...
 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 | ||
|---|---|---|
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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 | |
|---|---|
| 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
More information Coxeter plane, B6 ...
| 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] |
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More information 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 |
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Alternate names
- Cellitruncated hexacontatetrapeton (Acronym: catog) (Jonathan Bowers)[2]
Images
More information Coxeter plane, B6 ...
| 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] |
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More information 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 |
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Alternate names
- Cellirhombated hexacontatetrapeton (Acronym: crag) (Jonathan Bowers)[3]
Images
More information Coxeter plane, B6 ...
| 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] |
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More information 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 |
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Alternate names
- Celligreatorhombated hexacontatetrapeton (Acronym: cagorg) (Jonathan Bowers)[4]
Images
More information Coxeter plane, B6 ...
| 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] |
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More information 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 |
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Alternate names
- Celliprismated hexacontatetrapeton (Acronym: copog) (Jonathan Bowers)[5]
Images
More information Coxeter plane, B6 ...
| 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] |
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More information 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 |
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Alternate names
- Celliprismatotruncated hexacontatetrapeton (Acronym: captog) (Jonathan Bowers)[6]
Images
More information Coxeter plane, B6 ...
| 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] |
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More information 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 |
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Alternate names
- Celliprismatorhombated hexacontatetrapeton (Acronym: coprag) (Jonathan Bowers)[7]
Images
More information Coxeter plane, B6 ...
| 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] |
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More information Steriuncicantitruncated 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 |
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Alternate names
- Great cellated hexacontatetrapeton (Acronym: gocog) (Jonathan Bowers)[8]
Images
More information Coxeter plane, B6 ...
| 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] |
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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.
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.
More information B6 polytopes ...
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- 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)".
More information Family, Regular polygon ...
Fundamental convex regular and uniform polytopes in dimensions 2–10
| ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Family | An | Bn | I2(p) / Dn | E6 / E7 / E8 / F4 / G2 | Hn | |||||||
| Regular polygon | Triangle | Square | p-gon | Hexagon | Pentagon | |||||||
| Uniform polyhedron | Tetrahedron | Octahedron • Cube | Demicube | Dodecahedron • Icosahedron | ||||||||
| Uniform polychoron | Pentachoron | 16-cell • Tesseract | Demitesseract | 24-cell | 120-cell • 600-cell | |||||||
| Uniform 5-polytope | 5-simplex | 5-orthoplex • 5-cube | 5-demicube | |||||||||
| Uniform 6-polytope | 6-simplex | 6-orthoplex • 6-cube | 6-demicube | 122 • 221 | ||||||||
| Uniform 7-polytope | 7-simplex | 7-orthoplex • 7-cube | 7-demicube | 132 • 231 • 321 | ||||||||
| Uniform 8-polytope | 8-simplex | 8-orthoplex • 8-cube | 8-demicube | 142 • 241 • 421 | ||||||||
| Uniform 9-polytope | 9-simplex | 9-orthoplex • 9-cube | 9-demicube | |||||||||
| Uniform 10-polytope | 10-simplex | 10-orthoplex • 10-cube | 10-demicube | |||||||||
| Uniform n-polytope | n-simplex | n-orthoplex • n-cube | n-demicube | 1k2 • 2k1 • k21 | n-pentagonal polytope | |||||||
| Topics: Polytope families • Regular polytope • List of regular polytopes and compounds | ||||||||||||
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