Stericated 7-simplexes


7-simplex

Stericated 7-simplex

Bistericated 7-simplex

Steritruncated 7-simplex

Bisteritruncated 7-simplex

Stericantellated 7-simplex

Bistericantellated 7-simplex

Stericantitruncated 7-simplex

Bistericantitruncated 7-simplex

Steriruncinated 7-simplex

Steriruncitruncated 7-simplex

Steriruncicantellated 7-simplex

Bisteriruncitruncated 7-simplex

Steriruncicantitruncated 7-simplex

Bisteriruncicantitruncated 7-simplex

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

There are 14 unique sterication for the 7-simplex with permutations of truncations, cantellations, and runcinations.

Stericated 7-simplex

Stericated 7-simplex
Typeuniform 7-polytope
Schläfli symbol t0,4{3,3,3,3,3,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges2240
Vertices280
Vertex figure
Coxeter groupA7, [36], order 40320
Propertiesconvex

Alternate names

Coordinates

The vertices of the stericated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,1,1,1,1,2). This construction is based on facets of the stericated 8-orthoplex.

Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [5] [4] [3]

Bistericated 7-simplex

bistericated 7-simplex
Typeuniform 7-polytope
Schläfli symbol t1,5{3,3,3,3,3,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges3360
Vertices420
Vertex figure
Coxeter groupA7×2, [[3<sup>6</sup>]], order 80320
Propertiesconvex

Alternate names

Coordinates

The vertices of the bistericated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,1,1,1,2,2). This construction is based on facets of the bistericated 8-orthoplex.

Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [[7]] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [[5]] [4] [[3]]

Steritruncated 7-simplex

steritruncated 7-simplex
Typeuniform 7-polytope
Schläfli symbol t0,1,4{3,3,3,3,3,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges7280
Vertices1120
Vertex figure
Coxeter groupA7, [36], order 40320
Propertiesconvex

Alternate names

Coordinates

The vertices of the steritruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,1,1,1,2,3). This construction is based on facets of the steritruncated 8-orthoplex.

Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [5] [4] [3]

Bisteritruncated 7-simplex

bisteritruncated 7-simplex
Typeuniform 7-polytope
Schläfli symbol t1,2,5{3,3,3,3,3,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges9240
Vertices1680
Vertex figure
Coxeter groupA7, [36], order 40320
Propertiesconvex

Alternate names

Coordinates

The vertices of the bisteritruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,1,1,2,3,3). This construction is based on facets of the bisteritruncated 8-orthoplex.

Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [5] [4] [3]

Stericantellated 7-simplex

Stericantellated 7-simplex
Typeuniform 7-polytope
Schläfli symbol t0,2,4{3,3,3,3,3,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges10080
Vertices1680
Vertex figure
Coxeter groupA7, [36], order 40320
Propertiesconvex

Alternate names

Coordinates

The vertices of the stericantellated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,1,1,2,2,3). This construction is based on facets of the stericantellated 8-orthoplex.

Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [5] [4] [3]

Bistericantellated 7-simplex

Bistericantellated 7-simplex
Typeuniform 7-polytope
Schläfli symbol t1,3,5{3,3,3,3,3,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges15120
Vertices2520
Vertex figure
Coxeter groupA7×2, [[3<sup>6</sup>]], order 80320
Propertiesconvex

Alternate names

Coordinates

The vertices of the bistericantellated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,1,2,2,3,3). This construction is based on facets of the stericantellated 8-orthoplex.

Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [5] [4] [3]

Stericantitruncated 7-simplex

stericantitruncated 7-simplex
Typeuniform 7-polytope
Schläfli symbol t0,1,2,4{3,3,3,3,3,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges16800
Vertices3360
Vertex figure
Coxeter groupA7, [36], order 40320
Propertiesconvex

Alternate names

Coordinates

The vertices of the stericantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,1,1,2,3,4). This construction is based on facets of the stericantitruncated 8-orthoplex.

Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [5] [4] [3]

Bistericantitruncated 7-simplex

bistericantitruncated 7-simplex
Typeuniform 7-polytope
Schläfli symbol t1,2,3,5{3,3,3,3,3,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges22680
Vertices5040
Vertex figure
Coxeter groupA7, [36], order 40320
Propertiesconvex

Alternate names

Coordinates

The vertices of the bistericantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,1,2,3,4,4). This construction is based on facets of the bistericantitruncated 8-orthoplex.

Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [5] [4] [3]

Steriruncinated 7-simplex

Steriruncinated 7-simplex
Typeuniform 7-polytope
Schläfli symbol t0,3,4{3,3,3,3,3,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges5040
Vertices1120
Vertex figure
Coxeter groupA7, [36], order 40320
Propertiesconvex

Alternate names

Coordinates

The vertices of the steriruncinated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,1,2,2,2,3). This construction is based on facets of the steriruncinated 8-orthoplex.

Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [5] [4] [3]

Steriruncitruncated 7-simplex

steriruncitruncated 7-simplex
Typeuniform 7-polytope
Schläfli symbol t0,1,3,4{3,3,3,3,3,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges13440
Vertices3360
Vertex figure
Coxeter groupA7, [36], order 40320
Propertiesconvex

Alternate names

Coordinates

The vertices of the steriruncitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,1,2,2,3,4). This construction is based on facets of the steriruncitruncated 8-orthoplex.

Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [5] [4] [3]

Steriruncicantellated 7-simplex

steriruncicantellated 7-simplex
Typeuniform 7-polytope
Schläfli symbol t0,2,3,4{3,3,3,3,3,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges13440
Vertices3360
Vertex figure
Coxeter groupA7, [36], order 40320
Propertiesconvex

Alternate names

Coordinates

The vertices of the steriruncicantellated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,1,2,3,3,4). This construction is based on facets of the steriruncicantellated 8-orthoplex.

Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [5] [4] [3]

Bisteriruncitruncated 7-simplex

bisteriruncitruncated 7-simplex
Typeuniform 7-polytope
Schläfli symbol t1,2,4,5{3,3,3,3,3,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges20160
Vertices5040
Vertex figure
Coxeter groupA7×2, [[3<sup>6</sup>]], order 80320
Propertiesconvex

Alternate names

Coordinates

The vertices of the bisteriruncitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,2,2,3,4,4). This construction is based on facets of the bisteriruncitruncated 8-orthoplex.

Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [[7]] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [[5]] [4] [[3]]

Steriruncicantitruncated 7-simplex

steriruncicantitruncated 7-simplex
Typeuniform 7-polytope
Schläfli symbol t0,1,2,3,4{3,3,3,3,3,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges23520
Vertices6720
Vertex figure
Coxeter groupA7, [36], order 40320
Propertiesconvex

Alternate names

Coordinates

The vertices of the steriruncicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,1,2,3,4,5). This construction is based on facets of the steriruncicantitruncated 8-orthoplex.

Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [5] [4] [3]

Bisteriruncicantitruncated 7-simplex

bisteriruncicantitruncated 7-simplex
Typeuniform 7-polytope
Schläfli symbol t1,2,3,4,5{3,3,3,3,3,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges35280
Vertices10080
Vertex figure
Coxeter groupA7×2, [[3<sup>6</sup>]], order 80320
Propertiesconvex

Alternate names

Coordinates

The vertices of the bisteriruncicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,2,3,4,5,5). This construction is based on facets of the bisteriruncicantitruncated 8-orthoplex.

Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [[7]] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [[5]] [4] [[3]]

Related polytopes

This polytope is one of 71 uniform 7-polytopes with A7 symmetry.

Notes

  1. Klitizing, (x3o3o3o3x3o3o - sco)
  2. Klitizing, (x3o3x3o3x3o3o - sabach)
  3. Klitizing, (x3x3o3o3x3o3o - cato)
  4. Klitizing, (o3x3x3o3o3x3o - bacto)
  5. Klitizing, (x3o3x3o3x3o3o - caro)
  6. Klitizing, (o3x3o3x3o3x3o - bacroh)
  7. Klitizing, (x3x3x3o3x3o3o - cagro)
  8. Klitizing, (o3x3x3x3o3x3o - bacogro)
  9. Klitizing, (x3o3o3x3x3o3o - cepo)
  10. Klitizing, (x3x3x3o3x3o3o - capto)
  11. Klitizing, (x3o3x3x3x3o3o - capro)
  12. Klitizing, (o3x3x3o3x3x3o - bicpath)
  13. Klitizing, (x3x3x3x3x3o3o - gecco)
  14. Klitizing, (o3x3x3x3x3x3o - gabach)

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
This article is issued from Wikipedia - version of the 9/21/2015. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.