Stericated 6-orthoplexes

  (Redirected from Steritruncated 6-orthoplex)
6-cube t5.svg
6-orthoplex
CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
6-cube t15.svg
Stericated 6-orthoplex
CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.png
6-cube t145.svg
Steritruncated 6-orthoplex
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.png
6-cube t135.svg
Stericantellated 6-orthoplex
CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.png
6-cube t1345.svg
Stericantitruncated 6-orthoplex
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.png
6-cube t125.svg
Steriruncinated 6-orthoplex
CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.png
6-cube t1245.svg
Steriruncitruncated 6-orthoplex
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.png
6-cube t1235.svg
Steriruncicantellated 6-orthoplex
CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.png
6-cube t12345.svg
Steriruncicantitruncated 6-orthoplex
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.png
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-orthoplexEdit

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 namesEdit

  • Small cellated hexacontatetrapeton (Acronym: scag) (Jonathan Bowers)[1]

ImagesEdit

orthographic projections
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-orthoplexEdit

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 namesEdit

  • Cellitruncated hexacontatetrapeton (Acronym: catog) (Jonathan Bowers)[2]

ImagesEdit

orthographic projections
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-orthoplexEdit

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 namesEdit

  • Cellirhombated hexacontatetrapeton (Acronym: crag) (Jonathan Bowers)[3]


ImagesEdit

orthographic projections
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-orthoplexEdit

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 namesEdit

  • Celligreatorhombated hexacontatetrapeton (Acronym: cagorg) (Jonathan Bowers)[4]

ImagesEdit

orthographic projections
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-orthoplexEdit

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 namesEdit

  • Celliprismated hexacontatetrapeton (Acronym: copog) (Jonathan Bowers)[5]

ImagesEdit

orthographic projections
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-orthoplexEdit

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 namesEdit

  • Celliprismatotruncated hexacontatetrapeton (Acronym: captog) (Jonathan Bowers)[6]

ImagesEdit

orthographic projections
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-orthoplexEdit

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 namesEdit

  • Celliprismatorhombated hexacontatetrapeton (Acronym: coprag) (Jonathan Bowers)[7]

ImagesEdit

orthographic projections
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-orthoplexEdit

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 namesEdit

  • Great cellated hexacontatetrapeton (Acronym: gocog) (Jonathan Bowers)[8]

ImagesEdit

orthographic projections
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-demicubeEdit

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 polytopesEdit

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.


NotesEdit

  1. ^ Klitzing, (x3o3o3o3x4o - scag)
  2. ^ Klitzing, (x3x3o3o3x4o - catog)
  3. ^ Klitzing, (x3o3x3o3x4o - crag)
  4. ^ Klitzing, (x3x3x3o3x4o - cagorg)
  5. ^ Klitzing, (x3o3o3x3x4o - copog)
  6. ^ Klitzing, (x3x3o3x3x4o - captog)
  7. ^ Klitzing, (x3o3x3x3x4o - coprag)
  8. ^ Klitzing, (x3x3x3x3x4o - gocog)

ReferencesEdit

  • 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 [1]
      • (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 linksEdit

Fundamental convex regular and uniform polytopes in dimensions 2–10
An Bn I2(p) / Dn E6 / E7 / E8 / F4 / G2 Hn
Triangle Square p-gon Hexagon Pentagon
Tetrahedron OctahedronCube Demicube DodecahedronIcosahedron
5-cell 16-cellTesseract Demitesseract 24-cell 120-cell600-cell
5-simplex 5-orthoplex5-cube 5-demicube
6-simplex 6-orthoplex6-cube 6-demicube 122221
7-simplex 7-orthoplex7-cube 7-demicube 132231321
8-simplex 8-orthoplex8-cube 8-demicube 142241421
9-simplex 9-orthoplex9-cube 9-demicube
10-simplex 10-orthoplex10-cube 10-demicube
n-simplex n-orthoplexn-cube n-demicube 1k22k1k21 n-pentagonal polytope
Topics: Polytope familiesRegular polytopeList of regular polytopes and compounds