Data matrix (multivariate statistics)

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10-orthoplex
Template:CDD

Rectified 10-orthoplex
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Birectified 10-orthoplex
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Trirectified 10-orthoplex
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Quadirectified 10-orthoplex
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Quadrirectified 10-cube
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Trirectified 10-cube
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Birectified 10-cube
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Rectified 10-cube
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10-cube
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Orthogonal projections in BC10 Coxeter plane

In ten-dimensional geometry, a rectified 10-cube is a convex uniform 10-polytope, being a rectification of the regular 10-cube.

There are 10 rectifications of the 10-cube, with the zeroth being the 10-cube itself. Vertices of the rectified 10-cube are located at the edge-centers of the 10-cube. Vertices of the birectified 10-cube are located in the square face centers of the 10-cube. Vertices of the trirectified 10-cube are located in the cubic cell centers of the 10-cube. The others are more simply constructed relative to the 10-cube dual polytpoe, the 10-orthoplex.

These polytopes are part of a family 1023 uniform 10-polytopes with BC10 symmetry.

Rectified 10-cube

Rectified 10-orthoplex
Type uniform 10-polytope
Schläfli symbol t1{38,4}
Coxeter-Dynkin diagrams Template:CDD
Template:CDD
7-faces
6-faces
5-faces
4-faces
Cells
Faces
Edges 46080
Vertices 5120
Vertex figure 8-simplex prism
Coxeter groups C10, [4,38]
D10, [37,1,1]
Properties convex

Alternate names

  • Rectified dekeract (Acronym rade) (Jonathan Bowers)[1]

Cartesian coordinates

Cartesian coordinates for the vertices of a rectified 10-cube, centered at the origin, edge length are all permutations of:

(±1,±1,±1,±1,±1,±1,±1,±1,±1,0)

Images

Template:B10 Coxeter plane graphs

Birectified 10-cube

Birectified 10-orthoplex
Type uniform 10-polytope
Schläfli symbol t2{38,4}
Coxeter-Dynkin diagrams Template:CDD
Template:CDD
7-faces
6-faces
5-faces
4-faces
Cells
Faces
Edges 184320
Vertices 11520
Vertex figure {4}x{36}
Coxeter groups C10, [4,38]
D10, [37,1,1]
Properties convex

Alternate names

  • Birectified dekeract (Acronym brade) (Jonathan Bowers)[2]

Cartesian coordinates

Cartesian coordinates for the vertices of a birectified 10-cube, centered at the origin, edge length are all permutations of:

(±1,±1,±1,±1,±1,±1,±1,±1,0,0)

Images

Template:B10 Coxeter plane graphs

Trirectified 10-cube

Trirectified 10-orthoplex
Type uniform 10-polytope
Schläfli symbol t3{38,4}
Coxeter-Dynkin diagrams Template:CDD
Template:CDD
7-faces
6-faces
5-faces
4-faces
Cells
Faces
Edges 322560
Vertices 15360
Vertex figure {4,3}x{35}
Coxeter groups C10, [4,38]
D10, [37,1,1]
Properties convex

Alternate names

  • Tririrectified dekeract (Acronym trade) (Jonathan Bowers)[3]

Cartesian coordinates

Cartesian coordinates for the vertices of a triirectified 10-cube, centered at the origin, edge length are all permutations of:

(±1,±1,±1,±1,±1,±1,±1,0,0,0)

Images

Template:B10 Coxeter plane graphs

Quadrirectified 10-cube

Quadrirectified 10-orthoplex
Type uniform 10-polytope
Schläfli symbol t4{38,4}
Coxeter-Dynkin diagrams Template:CDD
Template:CDD
7-faces
6-faces
5-faces
4-faces
Cells
Faces
Edges 322560
Vertices 13440
Vertex figure {4,3,3}x{34}
Coxeter groups C10, [4,38]
D10, [37,1,1]
Properties convex

Alternate names

  • Quadrirectified dekeract
  • Quadrirectified decacross (Acronym trade) (Jonathan Bowers)[4]

Cartesian coordinates

Cartesian coordinates for the vertices of a quadrirectified 10-cube, centered at the origin, edge length are all permutations of:

(±1,±1,±1,±1,±1,±1,0,0,0,0)

Images

Template:B10 Coxeter plane graphs

Notes

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

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, editied 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. (1966)
  • Template:KlitzingPolytopes x3o3o3o3o3o3o3o3o4o - ka, o3x3o3o3o3o3o3o3o4o - rake, o3o3x3o3o3o3o3o3o4o - brake, o3o3o3x3o3o3o3o3o4o - trake, o3o3o3o3x3o3o3o3o4o - terake, o3o3o3o3o3x3o3o3o4o - terade, o3o3o3o3o3o3x3o3o4o - trade, o3o3o3o3o3o3o3x3o4o - brade, o3o3o3o3o3o3o3o3x4o - rade, o3o3o3o3o3o3o3o3o4x - deker

External links

Template:Polytopes

  1. Klitzing, (o3o3o3o3o3o3o3o3x4o - rade)
  2. Klitzing, (o3o3o3o3o3o3o3x3o4o - brade)
  3. Klitzing, (o3o3o3o3o3o3x3o3o4o - trade)
  4. Klitzing, (o3o3o3o3o3x3o3o3o4o - terade)