Stericated 6-orthoplexes


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

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-orthoplex

Stericated 6-orthoplex
Typeuniform 6-polytope
Schläfli symbol 2r2r{3,3,3,3,4}
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges5760
Vertices960
Vertex figure
Coxeter groupsB6, [4,3,3,3,3]
Propertiesconvex

Alternate names

Images

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-orthoplex

Steritruncated 6-orthoplex
Typeuniform 6-polytope
Schläfli symbol t0,1,4{3,3,3,3,4}
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges19200
Vertices3840
Vertex figure
Coxeter groupsB6, [4,3,3,3,3]
Propertiesconvex

Alternate names

Images

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-orthoplex

Stericantellated 6-orthoplex
Typeuniform 6-polytope
Schläfli symbolst0,2,4{34,4}
rr2r{3,3,3,3,4}
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges28800
Vertices5760
Vertex figure
Coxeter groupsB6, [4,3,3,3,3]
Propertiesconvex

Alternate names


Images

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-orthoplex

stericantitruncated 6-orthoplex
Typeuniform 6-polytope
Schläfli symbol t0,1,2,4{3,3,3,3,4}
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges46080
Vertices11520
Vertex figure
Coxeter groupsB6, [4,3,3,3,3]
Propertiesconvex

Alternate names

Images

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-orthoplex

steriruncinated 6-orthoplex
Typeuniform 6-polytope
Schläfli symbol t0,3,4{3,3,3,3,4}
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges15360
Vertices3840
Vertex figure
Coxeter groupsB6, [4,3,3,3,3]
Propertiesconvex

Alternate names

Images

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-orthoplex

steriruncitruncated 6-orthoplex
Typeuniform 6-polytope
Schläfli symbol 2t2r{3,3,3,3,4}
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges40320
Vertices11520
Vertex figure
Coxeter groupsB6, [4,3,3,3,3]
Propertiesconvex

Alternate names

Images

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-orthoplex

steriruncicantellated 6-orthoplex
Typeuniform 6-polytope
Schläfli symbol t0,2,3,4{3,3,3,3,4}
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges40320
Vertices11520
Vertex figure
Coxeter groupsB6, [4,3,3,3,3]
Propertiesconvex

Alternate names

Images

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-orthoplex

Steriuncicantitruncated 6-orthoplex
Typeuniform 6-polytope
Schläfli symbolst0,1,2,3,4{34,4}
tr2r{3,3,3,3,4}
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges69120
Vertices23040
Vertex figure
Coxeter groupsB6, [4,3,3,3,3]
Propertiesconvex

Alternate names

Images

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]

Related polytopes

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.


Notes

  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)

References

External links

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
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