Stericated 7-orthoplexes

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Orthogonal projections in B6 Coxeter plane
7-cube t0 B6.svg
7-orthoplex
CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
7-cube t04 B6.svg
Stericated 7-orthoplex
CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
7-cube t014 B6.svg
Steritruncated 7-orthoplex
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
7-cube t125 B6.svg
Bisteritruncated 7-orthoplex
CDel node.pngCDel 3.pngCDel 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
7-cube t024 B6.svg
Stericantellated 7-orthoplex
CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
7-cube t0124 B6.svg
Stericantitruncated 7-orthoplex
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
7-cube t1235 B6.svg
Bistericantitruncated 7-orthoplex
CDel node.pngCDel 3.pngCDel 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
7-cube t034 B6.svg
Steriruncinated 7-orthoplex
CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
7-cube t0134 B6.svg
Steriruncitruncated 7-orthoplex
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
7-cube t0234 B6.svg
Steriruncicantellated 7-orthoplex
CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
7-cube t1245 B6.svg
Bisteriruncitruncated 7-orthoplex
CDel node.pngCDel 3.pngCDel 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
7-cube t01234 B6.svg
Steriruncicantitruncated 7-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 3.pngCDel node.pngCDel 4.pngCDel node.png

In seven-dimensional geometry, a stericated 7-orthoplex is a convex uniform 7-polytope with 4th order truncations (sterication) of the regular 7-orthoplex.

There are 24 unique sterication for the 7-orthoplex with permutations of truncations, cantellations, and runcinations. 14 are more simply constructed from the 7-cube.

This polytope is one of 127 uniform 7-polytopes with B7 symmetry.

Stericated 7-orthoplex[edit]

Stericated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,4{35,4}
Coxeter-Dynkin diagrams CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel split1.pngCDel nodes.png
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

Alternate names[edit]

  • Small cellated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[1]

Images[edit]

orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph 7-cube t26.svg 7-cube t26 B6.svg 7-cube t26 B5.svg
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph 7-cube t26 B4.svg 7-cube t26 B3.svg 7-cube t26 B2.svg
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph 7-cube t26 A5.svg 7-cube t26 A3.svg
Dihedral symmetry [6] [4]

Steritruncated 7-orthoplex[edit]

steritruncated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,1,4{35,4}
Coxeter-Dynkin diagrams CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel split1.pngCDel nodes.png
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

Alternate names[edit]

  • Cellitruncated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[2]

Images[edit]

orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph 7-cube t256.svg 7-cube t256 B6.svg 7-cube t256 B5.svg
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph 7-cube t256 B4.svg 7-cube t256 B3.svg 7-cube t256 B2.svg
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph 7-cube t256 A5.svg 7-cube t256 A3.svg
Dihedral symmetry [6] [4]

Bisteritruncated 7-orthoplex[edit]

bisteritruncated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t1,2,5{35,4}
Coxeter-Dynkin diagrams CDel node.pngCDel 3.pngCDel 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
CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel split1.pngCDel nodes 11.png
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

Alternate names[edit]

  • Bicellitruncated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[3]

Images[edit]

orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph 7-cube t145.svg 7-cube t145 B6.svg 7-cube t145 B5.svg
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph 7-cube t145 B4.svg 7-cube t145 B3.svg 7-cube t145 B2.svg
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph 7-cube t145 A5.svg 7-cube t145 A3.svg
Dihedral symmetry [6] [4]

Stericantellated 7-orthoplex[edit]

Stericantellated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,2,4{35,4}
Coxeter-Dynkin diagrams CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel split1.pngCDel nodes.png
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

Alternate names[edit]

  • Cellirhombated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[4]

Images[edit]

orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph 7-cube t246.svg 7-cube t246 B6.svg 7-cube t246 B5.svg
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph 7-cube t246 B4.svg 7-cube t246 B3.svg 7-cube t246 B2.svg
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph 7-cube t246 A5.svg 7-cube t246 A3.svg
Dihedral symmetry [6] [4]

Stericantitruncated 7-orthoplex[edit]

stericantitruncated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,1,2,4{35,4}
Coxeter-Dynkin diagrams CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel split1.pngCDel nodes.png
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

Alternate names[edit]

  • Celligreatorhombated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[5]

Images[edit]

orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph 7-cube t2456.svg 7-cube t2456 B6.svg 7-cube t2456 B5.svg
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph 7-cube t2456 B4.svg 7-cube t2456 B3.svg 7-cube t2456 B2.svg
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph 7-cube t2456 A5.svg 7-cube t2456 A3.svg
Dihedral symmetry [6] [4]

Bistericantitruncated 7-orthoplex[edit]

bistericantitruncated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t1,2,3,5{35,4}
Coxeter-Dynkin diagrams CDel node.pngCDel 3.pngCDel 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
CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel split1.pngCDel nodes 11.png
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

Alternate names[edit]

  • Bicelligreatorhombated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[6]

Images[edit]

orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph 7-cube t1345.svg 7-cube t1345 B6.svg 7-cube t1345 B5.svg
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph 7-cube t1345 B4.svg 7-cube t1345 B3.svg 7-cube t1345 B2.svg
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph 7-cube t1345 A5.svg 7-cube t1345 A3.svg
Dihedral symmetry [6] [4]

Steriruncinated 7-orthoplex[edit]

Steriruncinated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,3,4{35,4}
Coxeter-Dynkin diagrams CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel split1.pngCDel nodes.png
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

Alternate names[edit]

  • Celliprismated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[7]

Images[edit]

orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph too complex 7-cube t236 B6.svg 7-cube t236 B5.svg
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph 7-cube t236 B4.svg 7-cube t236 B3.svg 7-cube t236 B2.svg
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph 7-cube t236 A5.svg 7-cube t236 A3.svg
Dihedral symmetry [6] [4]

Steriruncitruncated 7-orthoplex[edit]

steriruncitruncated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,1,3,4{35,4}
Coxeter-Dynkin diagrams CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel split1.pngCDel nodes.png
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

Alternate names[edit]

  • Celliprismatotruncated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[8]

Images[edit]

orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph 7-cube t2356.svg 7-cube t2356 B6.svg 7-cube t2356 B5.svg
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph 7-cube t2356 B4.svg 7-cube t2356 B3.svg 7-cube t2356 B2.svg
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph 7-cube t2356 A5.svg 7-cube t2356 A3.svg
Dihedral symmetry [6] [4]

Steriruncicantellated 7-orthoplex[edit]

steriruncicantellated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,2,3,4{35,4}
Coxeter-Dynkin diagrams CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel split1.pngCDel nodes.png
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

Alternate names[edit]

  • Celliprismatorhombated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[9]

Images[edit]

orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph 7-cube t2346.svg 7-cube t2346 B6.svg 7-cube t2346 B5.svg
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph 7-cube t2346 B4.svg 7-cube t2346 B3.svg 7-cube t2346 B2.svg
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph 7-cube t2346 A5.svg 7-cube t2346 A3.svg
Dihedral symmetry [6] [4]

Steriruncicantitruncated 7-orthoplex[edit]

steriruncicantitruncated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,1,2,3,4{35,4}
Coxeter-Dynkin diagrams CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel split1.pngCDel nodes.png
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

Alternate names[edit]

  • Great cellated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[10]

Images[edit]

orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph 7-cube t23456.svg 7-cube t23456 B6.svg 7-cube t23456 B5.svg
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph 7-cube t23456 B4.svg 7-cube t23456 B3.svg 7-cube t23456 B2.svg
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph 7-cube t23456 A5.svg 7-cube t23456 A3.svg
Dihedral symmetry [6] [4]

Notes[edit]

  1. ^ Klitizing, (x3o3o3o3x3o4o - )
  2. ^ Klitizing, (x3x3o3o3x3o4o - )
  3. ^ Klitizing, (o3x3x3o3o3x4o - )
  4. ^ Klitizing, (x3o3x3o3x3o4o - )
  5. ^ Klitizing, (x3x3x3o3x3o4o - )
  6. ^ Klitizing, (o3x3x3x3o3x4o - )
  7. ^ Klitizing, (x3o3o3x3x3o4o - )
  8. ^ Klitizing, (x3x3x3o3x3o4o - )
  9. ^ Klitizing, (x3o3x3x3x3o4o - )
  10. ^ Klitizing, (x3x3x3x3x3o4o - )

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. "7D uniform polytopes (polyexa)". 

External links[edit]

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 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