Stericated 5-cubes


5-cube

Stericated 5-cube

Steritruncated 5-cube

Stericantellated 5-cube

Steritruncated 5-orthoplex

Stericantitruncated 5-cube

Steriruncitruncated 5-cube

Stericantitruncated 5-orthoplex

Omnitruncated 5-cube
Orthogonal projections in B5 Coxeter plane

In five-dimensional geometry, a stericated 5-cube is a convex uniform 5-polytope with fourth-order truncations (sterication) of the regular 5-cube.

There are eight degrees of sterication for the 5-cube, including permutations of runcination, cantellation, and truncation. The simple stericated 5-cube is also called an expanded 5-cube, with the first and last nodes ringed, for being constructible by an expansion operation applied to the regular 5-cube. The highest form, the steriruncicantitruncated 5-cube, is more simply called an omnitruncated 5-cube with all of the nodes ringed.

Stericated 5-cube

Stericated 5-cube
Type Uniform 5-polytope
Schläfli symbol 2r2r{4,3,3,3}
Coxeter-Dynkin diagram
4-faces 242
Cells 800
Faces 1040
Edges 640
Vertices 160
Vertex figure
Coxeter group B5 [4,3,3,3]
Properties convex

Alternate names

Coordinates

The Cartesian coordinates of the vertices of a stericated 5-cube having edge length 2 are all permutations of:

Images

The stericated 5-cube is constructed by a sterication operation applied to the 5-cube.

orthographic projections
Coxeter plane B5 B4 / D5 B3 / D4 / A2
Graph
Dihedral symmetry [10] [8] [6]
Coxeter plane B2 A3
Graph
Dihedral symmetry [4] [4]

Steritruncated 5-cube

Steritruncated 5-cube
Typeuniform 5-polytope
Schläfli symbol t0,1,4{4,3,3,3}
Coxeter-Dynkin diagrams
4-faces242
Cells1600
Faces2960
Edges2240
Vertices640
Vertex figure
Coxeter groupsB5, [3,3,3,4]
Propertiesconvex

Alternate names

Construction and coordinates

The Cartesian coordinates of the vertices of a steritruncated 5-cube having edge length 2 are all permutations of:

Images

orthographic projections
Coxeter plane B5 B4 / D5 B3 / D4 / A2
Graph
Dihedral symmetry [10] [8] [6]
Coxeter plane B2 A3
Graph
Dihedral symmetry [4] [4]

Stericantellated 5-cube

Stericantellated 5-cube
Type Uniform 5-polytope
Schläfli symbol t0,2,4{4,3,3,3}
Coxeter-Dynkin diagram
4-faces242
Cells2080
Faces4720
Edges3840
Vertices960
Vertex figure
Coxeter group B5 [4,3,3,3]
Properties convex

Alternate names

Coordinates

The Cartesian coordinates of the vertices of a stericantellated 5-cube having edge length 2 are all permutations of:

Images

orthographic projections
Coxeter plane B5 B4 / D5 B3 / D4 / A2
Graph
Dihedral symmetry [10] [8] [6]
Coxeter plane B2 A3
Graph
Dihedral symmetry [4] [4]

Stericantitruncated 5-cube

Stericantitruncated 5-cube
Type Uniform 5-polytope
Schläfli symbol t0,1,2,4{4,3,3,3}
Coxeter-Dynkin
diagram
4-faces242
Cells2400
Faces6000
Edges5760
Vertices1920
Vertex figure
Coxeter group B5 [4,3,3,3]
Properties convex, isogonal

Alternate names

Coordinates

The Cartesian coordinates of the vertices of an stericantitruncated 5-cube having an edge length of 2 are given by all permutations of coordinates and sign of:

Images

orthographic projections
Coxeter plane B5 B4 / D5 B3 / D4 / A2
Graph
Dihedral symmetry [10] [8] [6]
Coxeter plane B2 A3
Graph
Dihedral symmetry [4] [4]

Steriruncitruncated 5-cube

Steriruncitruncated 5-cube
Type Uniform 5-polytope
Schläfli symbol 2t2r{4,3,3,3}
Coxeter-Dynkin
diagram

4-faces242
Cells2160
Faces5760
Edges5760
Vertices1920
Vertex figure
Coxeter group B5 [4,3,3,3]
Properties convex, isogonal

Alternate names

Coordinates

The Cartesian coordinates of the vertices of an steriruncitruncated penteract having an edge length of 2 are given by all permutations of coordinates and sign of:

Images

orthographic projections
Coxeter plane B5 B4 / D5 B3 / D4 / A2
Graph
Dihedral symmetry [10] [8] [6]
Coxeter plane B2 A3
Graph
Dihedral symmetry [4] [4]

Steritruncated 5-orthoplex

Steritruncated 5-orthoplex
Typeuniform 5-polytope
Schläfli symbol t0,1,4{3,3,3,4}
Coxeter-Dynkin diagrams
4-faces242
Cells1520
Faces2880
Edges2240
Vertices640
Vertex figure
Coxeter groupB5, [3,3,3,4]
Propertiesconvex

Alternate names

Coordinates

Cartesian coordinates for the vertices of a steritruncated 5-orthoplex, centered at the origin, are all permutations of

Images

orthographic projections
Coxeter plane B5 B4 / D5 B3 / D4 / A2
Graph
Dihedral symmetry [10] [8] [6]
Coxeter plane B2 A3
Graph
Dihedral symmetry [4] [4]

Stericantitruncated 5-orthoplex

Stericantitruncated 5-orthoplex
Type Uniform 5-polytope
Schläfli symbol t0,2,3,4{4,3,3,3}
Coxeter-Dynkin
diagram
4-faces242
Cells2320
Faces5920
Edges5760
Vertices1920
Vertex figure
Coxeter group B5 [4,3,3,3]
Properties convex, isogonal

Alternate names

Coordinates

The Cartesian coordinates of the vertices of an stericantitruncated 5-orthoplex having an edge length of 2 are given by all permutations of coordinates and sign of:

Images

orthographic projections
Coxeter plane B5 B4 / D5 B3 / D4 / A2
Graph
Dihedral symmetry [10] [8] [6]
Coxeter plane B2 A3
Graph
Dihedral symmetry [4] [4]

Omnitruncated 5-cube

Omnitruncated 5-cube
Type Uniform 5-polytope
Schläfli symbol tr2r{4,3,3,3}
Coxeter-Dynkin
diagram

4-faces242
Cells2640
Faces8160
Edges9600
Vertices3840
Vertex figure
irr. {3,3,3}
Coxeter group B5 [4,3,3,3]
Properties convex, isogonal

Alternate names

Coordinates

The Cartesian coordinates of the vertices of an omnitruncated tesseract having an edge length of 2 are given by all permutations of coordinates and sign of:

Images

orthographic projections
Coxeter plane B5 B4 / D5 B3 / D4 / A2
Graph
Dihedral symmetry [10] [8] [6]
Coxeter plane B2 A3
Graph
Dihedral symmetry [4] [4]

This polytope is one of 31 uniform 5-polytopes generated from the regular 5-cube or 5-orthoplex.

Notes

  1. Klitzing, (x3o3o3o4x - scan)
  2. Klitzing, (x3o3o3x4x - capt)
  3. Klitzing, (x3o3x3o4x - carnit)
  4. Klitzing, (x3o3x3x4x - cogrin)
  5. Klitzing, (x3x3o3x4x - captint)
  6. Klitzing, (x3x3o3o4x - cappin)
  7. Klitzing, (x3x3x3o4x - cogart)
  8. Klitzing, (x3x3x3x4x - gacnet)

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
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.