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
Typeuniform 7-polytope
Schläfli symbol t0,4{35,4}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex

Alternate names

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
Typeuniform 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 groupsB7, [4,35]
Propertiesconvex

Alternate names

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
Typeuniform 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 groupsB7, [4,35]
Propertiesconvex

Alternate names

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
Typeuniform 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 groupsB7, [4,35]
Propertiesconvex

Alternate names

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
Typeuniform 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 groupsB7, [4,35]
Propertiesconvex

Alternate names

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
Typeuniform 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 groupsB7, [4,35]
Propertiesconvex

Alternate names

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
Typeuniform 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 groupsB7, [4,35]
Propertiesconvex

Alternate names

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
Typeuniform 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 groupsB7, [4,35]
Propertiesconvex

Alternate names

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
Typeuniform 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 groupsB7, [4,35]
Propertiesconvex

Alternate names

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
Typeuniform 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 groupsB7, [4,35]
Propertiesconvex

Alternate names

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

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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