Misplaced Pages

Rectified 9-cubes

Article snapshot taken from Wikipedia with creative commons attribution-sharealike license. Give it a read and then ask your questions in the chat. We can research this topic together.
(Redirected from Birectified 9-cube)

9-orthoplex
Rectified 9-orthoplex
Birectified 9-orthoplex

Trirectified 9-orthoplex
Quadrirectified 9-cube
Trirectified 9-cube

Birectified 9-cube
Rectified 9-cube
9-cube
Orthogonal projections in BC9 Coxeter plane

In nine-dimensional geometry, a rectified 9-cube is a convex uniform 9-polytope, being a rectification of the regular 9-cube.

There are 9 rectifications of the 9-cube. The zeroth is the 9-cube itself, and the 8th is the dual 9-orthoplex. Vertices of the rectified 9-cube are located at the edge-centers of the 9-orthoplex. Vertices of the birectified 9-cube are located in the square face centers of the 9-cube. Vertices of the trirectified 9-orthoplex are located in the cube cell centers of the 9-cube. Vertices of the quadrirectified 9-cube are located in the tesseract centers of the 9-cube.

These polytopes are part of a family 511 uniform 9-polytopes with BC9 symmetry.

Rectified 9-cube

Alternate names

  • Rectified enneract (Acronym ren) (Jonathan Bowers)

Images

orthographic projections
B9 B8 B7
B6 B5
B4 B3 B2
A7 A5 A3
— — —

Birectified 9-cube

Alternate names

  • Birectified enneract (Acronym barn) (Jonathan Bowers)

Images

orthographic projections
B9 B8 B7
B6 B5
B4 B3 B2
A7 A5 A3
— — —

Trirectified 9-cube

Alternate names

  • Trirectified enneract (Acronym tarn) (Jonathan Bowers)

Images

orthographic projections
B9 B8 B7
B6 B5
B4 B3 B2
A7 A5 A3
— — —

Quadrirectified 9-cube

Alternate names

  • Quadrirectified enneract (Acronym nav) (Jonathan Bowers)

Images

orthographic projections
B9 B8 B7
B6 B5
B4 B3 B2
A7 A5 A3
— — —

Notes

  1. Klitzing (o3o3o3o3o3o3o3x4o - ren)
  2. Klitzing (o3o3o3o3o3o3x3o4o - barn)
  3. Klitzing (o3o3o3o3o3x3o3o4o - tarn)
  4. Klitzing (o3o3o3o3x3o3o3o4o - nav)

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, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6
      • (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I,
      • (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II,
      • (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III,
  • Norman Johnson Uniform Polytopes, Manuscript (1991)
    • N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. (1966)
  • Klitzing, Richard. "9D uniform polytopes (polyyotta)". x3o3o3o3o3o3o3o4o - vee, o3x3o3o3o3o3o3o4o - riv, o3o3x3o3o3o3o3o4o - brav, o3o3o3x3o3o3o3o4o - tarv, o3o3o3o3x3o3o3o4o - nav, o3o3o3o3o3x3o3o4o - tarn, o3o3o3o3o3o3x3o4o - barn, o3o3o3o3o3o3o3x4o - ren, o3o3o3o3o3o3o3o4x - enne

External links

Fundamental convex regular and uniform polytopes in dimensions 2–10
Family An Bn I2(p) / Dn E6 / E7 / E8 / F4 / G2 Hn
Regular polygon Triangle Square p-gon Hexagon Pentagon
Uniform polyhedron Tetrahedron Octahedron • Cube Demicube Dodecahedron • Icosahedron
Uniform polychoron Pentachoron 16-cell • Tesseract Demitesseract 24-cell 120-cell • 600-cell
Uniform 5-polytope 5-simplex 5-orthoplex • 5-cube 5-demicube
Uniform 6-polytope 6-simplex 6-orthoplex • 6-cube 6-demicube 122 • 221
Uniform 7-polytope 7-simplex 7-orthoplex • 7-cube 7-demicube 132 • 231 • 321
Uniform 8-polytope 8-simplex 8-orthoplex • 8-cube 8-demicube 142 • 241 • 421
Uniform 9-polytope 9-simplex 9-orthoplex • 9-cube 9-demicube
Uniform 10-polytope 10-simplex 10-orthoplex • 10-cube 10-demicube
Uniform n-polytope n-simplex n-orthoplex • n-cube n-demicube 1k2 • 2k1 • k21 n-pentagonal polytope
Topics: Polytope families • Regular polytope • List of regular polytopes and compounds
Category: