Stericated 6-cubes

From Wikipedia, the free encyclopedia
  (Redirected from Steriruncicantellated 6-cube)
Jump to: navigation, search
6-cube t0.svg
6-cube
CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
6-cube t04.svg
Stericated 6-cube
CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
6-cube t014.svg
Steritruncated 6-cube
CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
6-cube t024.svg
Stericantellated 6-cube
CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
6-cube t0124.svg
Stericantitruncated 6-cube
CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
6-cube t034.svg
Steriruncinated 6-cube
CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
6-cube t0134.svg
Steriruncitruncated 6-cube
CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
6-cube t0234.svg
Steriruncicantellated 6-cube
CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
6-cube t01234.svg
Steriruncicantitruncated 6-cube
CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
Orthogonal projections in B6 Coxeter plane

In six-dimensional geometry, a stericated 6-cube is a convex uniform 6-polytope, constructed as a sterication (4th order truncation) of the regular 6-cube.

There are 8 unique sterications for the 6-cube with permutations of truncations, cantellations, and runcinations.

Stericated 6-cube[edit]

Stericated 6-cube
Type uniform 6-polytope
Schläfli symbol 2r2r{4,3,3,3,3}
Coxeter-Dynkin diagrams CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
CDel node.pngCDel split1.pngCDel nodes.pngCDel 3a4b.pngCDel nodes 11.pngCDel 3a.pngCDel nodea.png
5-faces
4-faces
Cells
Faces
Edges 5760
Vertices 960
Vertex figure
Coxeter groups B6, [4,3,3,3,3]
Properties convex

Alternate names[edit]

  • Small cellated hexeract (Acronym: scox) (Jonathan Bowers)[1]

Images[edit]

orthographic projections
Coxeter plane B6 B5 B4
Graph 6-cube t04.svg 6-cube t04 B5.svg 6-cube t04 B4.svg
Dihedral symmetry [12] [10] [8]
Coxeter plane B3 B2
Graph 6-cube t04 B3.svg 6-cube t04 B2.svg
Dihedral symmetry [6] [4]
Coxeter plane A5 A3
Graph 6-cube t04 A5.svg 6-cube t04 A3.svg
Dihedral symmetry [6] [4]

Steritruncated 6-cube[edit]

Steritruncated 6-cube
Type uniform 6-polytope
Schläfli symbol t0,1,4{4,3,3,3,3}
Coxeter-Dynkin diagrams CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
5-faces
4-faces
Cells
Faces
Edges 19200
Vertices 3840
Vertex figure
Coxeter groups B6, [4,3,3,3,3]
Properties convex

Alternate names[edit]

  • Cellirhombated hexeract (Acronym: catax) (Jonathan Bowers)[2]

Images[edit]

orthographic projections
Coxeter plane B6 B5 B4
Graph 6-cube t014.svg 6-cube t014 B5.svg 6-cube t014 B4.svg
Dihedral symmetry [12] [10] [8]
Coxeter plane B3 B2
Graph 6-cube t014 B3.svg 6-cube t014 B2.svg
Dihedral symmetry [6] [4]
Coxeter plane A5 A3
Graph 6-cube t014 A5.svg 6-cube t014 A3.svg
Dihedral symmetry [6] [4]

Stericantellated 6-cube[edit]

Stericantellated 6-cube
Type uniform 6-polytope
Schläfli symbol 2r2r{4,3,3,3,3}
Coxeter-Dynkin diagrams CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
CDel node 1.pngCDel split1.pngCDel nodes.pngCDel 3a4b.pngCDel nodes 11.pngCDel 3a.pngCDel nodea.png
5-faces
4-faces
Cells
Faces
Edges 28800
Vertices 5760
Vertex figure
Coxeter groups B6, [4,3,3,3,3]
Properties convex

Alternate names[edit]

  • Cellirhombated hexeract (Acronym: crax) (Jonathan Bowers)[3]

Images[edit]

orthographic projections
Coxeter plane B6 B5 B4
Graph 6-cube t024.svg 6-cube t024 B5.svg 6-cube t024 B4.svg
Dihedral symmetry [12] [10] [8]
Coxeter plane B3 B2
Graph 6-cube t024 B3.svg 6-cube t024 B2.svg
Dihedral symmetry [6] [4]
Coxeter plane A5 A3
Graph 6-cube t024 A5.svg 6-cube t024 A3.svg
Dihedral symmetry [6] [4]

Stericantitruncated 6-cube[edit]

stericantitruncated 6-cube
Type uniform 6-polytope
Schläfli symbol t0,1,2,4{4,3,3,3,3}
Coxeter-Dynkin diagrams CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
5-faces
4-faces
Cells
Faces
Edges 46080
Vertices 11520
Vertex figure
Coxeter groups B6, [4,3,3,3,3]
Properties convex

Alternate names[edit]

  • Celligreatorhombated hexeract (Acronym: cagorx) (Jonathan Bowers)[4]

Images[edit]

orthographic projections
Coxeter plane B6 B5 B4
Graph 6-cube t0124.svg 6-cube t0124 B5.svg 6-cube t0124 B4.svg
Dihedral symmetry [12] [10] [8]
Coxeter plane B3 B2
Graph 6-cube t0124 B3.svg 6-cube t0124 B2.svg
Dihedral symmetry [6] [4]
Coxeter plane A5 A3
Graph 6-cube t0124 A5.svg 6-cube t0124 A3.svg
Dihedral symmetry [6] [4]

Steriruncinated 6-cube[edit]

steriruncinated 6-cube
Type uniform 6-polytope
Schläfli symbol t0,3,4{4,3,3,3,3}
Coxeter-Dynkin diagrams CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
5-faces
4-faces
Cells
Faces
Edges 15360
Vertices 3840
Vertex figure
Coxeter groups B6, [4,3,3,3,3]
Properties convex

Alternate names[edit]

  • Celliprismated hexeract (Acronym: copox) (Jonathan Bowers)[5]

Images[edit]

orthographic projections
Coxeter plane B6 B5 B4
Graph 6-cube t034.svg 6-cube t034 B5.svg 6-cube t034 B4.svg
Dihedral symmetry [12] [10] [8]
Coxeter plane B3 B2
Graph 6-cube t034 B3.svg 6-cube t034 B2.svg
Dihedral symmetry [6] [4]
Coxeter plane A5 A3
Graph 6-cube t034 A5.svg 6-cube t034 A3.svg
Dihedral symmetry [6] [4]

Steriruncitruncated 6-cube[edit]

steriruncitruncated 6-cube
Type uniform 6-polytope
Schläfli symbol 2t2r{4,3,3,3,3}
Coxeter-Dynkin diagrams CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
CDel node.pngCDel split1.pngCDel nodes 11.pngCDel 3a4b.pngCDel nodes 11.pngCDel 3a.pngCDel nodea.png
5-faces
4-faces
Cells
Faces
Edges 40320
Vertices 11520
Vertex figure
Coxeter groups B6, [4,3,3,3,3]
Properties convex

Alternate names[edit]

  • Celliprismatotruncated hexeract (Acronym: captix) (Jonathan Bowers)[6]

Images[edit]

orthographic projections
Coxeter plane B6 B5 B4
Graph 6-cube t0134.svg 6-cube t0134 B5.svg 6-cube t0134 B4.svg
Dihedral symmetry [12] [10] [8]
Coxeter plane B3 B2
Graph 6-cube t0134 B3.svg 6-cube t0134 B2.svg
Dihedral symmetry [6] [4]
Coxeter plane A5 A3
Graph 6-cube t0134 A5.svg 6-cube t0134 A3.svg
Dihedral symmetry [6] [4]

Steriruncicantellated 6-cube[edit]

steriruncicantellated 6-cube
Type uniform 6-polytope
Schläfli symbol t0,2,3,4{4,3,3,3,3}
Coxeter-Dynkin diagrams CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
5-faces
4-faces
Cells
Faces
Edges 40320
Vertices 11520
Vertex figure
Coxeter groups B6, [4,3,3,3,3]
Properties convex

Alternate names[edit]

  • Celliprismatorhombated hexeract (Acronym: coprix) (Jonathan Bowers)[7]

Images[edit]

orthographic projections
Coxeter plane B6 B5 B4
Graph 6-cube t0234.svg 6-cube t0234 B5.svg 6-cube t0234 B4.svg
Dihedral symmetry [12] [10] [8]
Coxeter plane B3 B2
Graph 6-cube t0234 B3.svg 6-cube t0234 B2.svg
Dihedral symmetry [6] [4]
Coxeter plane A5 A3
Graph 6-cube t0234 A5.svg 6-cube t0234 A3.svg
Dihedral symmetry [6] [4]

Steriruncicantitruncated 6-cube[edit]

Steriuncicantitruncated 6-cube
Type uniform 6-polytope
Schläfli symbol tr2r{4,3,3,3,3}
Coxeter-Dynkin diagrams CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
CDel node 1.pngCDel split1.pngCDel nodes 11.pngCDel 3a4b.pngCDel nodes 11.pngCDel 3a.pngCDel nodea.png
5-faces
4-faces
Cells
Faces
Edges 69120
Vertices 23040
Vertex figure
Coxeter groups B6, [4,3,3,3,3]
Properties convex

Alternate names[edit]

  • Great cellated hexeract (Acronym: gocax) (Jonathan Bowers)[8]

Images[edit]

orthographic projections
Coxeter plane B6 B5 B4
Graph 6-cube t01234.svg 6-cube t01234 B5.svg 6-cube t01234 B4.svg
Dihedral symmetry [12] [10] [8]
Coxeter plane B3 B2
Graph 6-cube t01234 B3.svg 6-cube t01234 B2.svg
Dihedral symmetry [6] [4]
Coxeter plane A5 A3
Graph 6-cube t01234 A5.svg 6-cube t01234 A3.svg
Dihedral symmetry [6] [4]

Related polytopes[edit]

These polytopes are from a set of 63 uniform 6-polytopes generated from the B6 Coxeter plane, including the regular 6-cube or 6-orthoplex.


Notes[edit]

  1. ^ Klitzing, (x4o3o3o3x3o - scox)
  2. ^ Klitzing, (x4x3o3o3x3o - catax)
  3. ^ Klitzing, (x4o3x3o3x3o - crax)
  4. ^ Klitzing, (x4x3x3o3x3o - cagorx)
  5. ^ Klitzing, (x4o3o3x3x3o - copox))
  6. ^ Klitzing, (x4x3o3x3x3o - captix)
  7. ^ Klitzing, (x4o3x3x3x3o - coprix)
  8. ^ Klitzing, (x4x3x3x3x3o - gocax)

References[edit]

  • 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 links[edit]

Fundamental convex regular and uniform polytopes in dimensions 2–10
Family An Bn I2(p) / Dn E6 / E7 / E8 / E9 / E10 / F4 / G2 Hn
Regular polygon Triangle Square p-gon Hexagon Pentagon
Uniform polyhedron Tetrahedron OctahedronCube Demicube DodecahedronIcosahedron
Uniform 4-polytope 5-cell 16-cellTesseract Demitesseract 24-cell 120-cell600-cell
Uniform 5-polytope 5-simplex 5-orthoplex5-cube 5-demicube
Uniform 6-polytope 6-simplex 6-orthoplex6-cube 6-demicube 122221
Uniform 7-polytope 7-simplex 7-orthoplex7-cube 7-demicube 132231321
Uniform 8-polytope 8-simplex 8-orthoplex8-cube 8-demicube 142241421
Uniform 9-polytope 9-simplex 9-orthoplex9-cube 9-demicube
Uniform 10-polytope 10-simplex 10-orthoplex10-cube 10-demicube
Uniform n-polytope n-simplex n-orthoplexn-cube n-demicube 1k22k1k21 n-pentagonal polytope
Topics: Polytope familiesRegular polytopeList of regular polytopes and compounds