Stericated 7-orthoplexes

Orthogonal projections in B6 Coxeter plane

7-orthoplex
Stericated 7-orthoplex
Steritruncated 7-orthoplex

Bisteritruncated 7-orthoplex
Stericantellated 7-orthoplex
Stericantitruncated 7-orthoplex

Bistericantitruncated 7-orthoplex
Steriruncinated 7-orthoplex
Steriruncitruncated 7-orthoplex

Steriruncicantellated 7-orthoplex
Bisteriruncitruncated 7-orthoplex
Steriruncicantitruncated 7-orthoplex

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

Stericated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,4{35,4}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

Alternate names

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

Images

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

Steritruncated 7-orthoplex

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

Alternate names

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

Images

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

Bisteritruncated 7-orthoplex

bisteritruncated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t1,2,5{35,4}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

Alternate names

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

Images

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

Stericantellated 7-orthoplex

Stericantellated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,2,4{35,4}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

Alternate names

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

Images

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

Stericantitruncated 7-orthoplex

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

Alternate names

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

Images

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

Bistericantitruncated 7-orthoplex

bistericantitruncated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t1,2,3,5{35,4}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

Alternate names

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

Images

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

Steriruncinated 7-orthoplex

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

Alternate names

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

Images

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

Steriruncitruncated 7-orthoplex

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

Alternate names

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

Images

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

Steriruncicantellated 7-orthoplex

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

Alternate names

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

Images

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

Steriruncicantitruncated 7-orthoplex

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

Alternate names

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

Images

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

Notes

  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

  • 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)".
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