In nine-dimensional
geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...
, 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
A cube or regular hexahedron is a three-dimensional space, three-dimensional solid object in geometry, which is bounded by six congruent square (geometry), square faces, a type of polyhedron. It has twelve congruent edges and eight vertices. It i ...
cell centers of the 9-cube. Vertices of the quadrirectified 9-cube are located in the
tesseract
In geometry, a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional square and a three-dimensional cube. Just as the perimeter of the square consists of four edges and the surface of the cube consists of six ...
centers of the 9-cube.
These polytopes are part of a family 511
uniform 9-polytopes with BC
9 symmetry.
Rectified 9-cube
Alternate names
* Rectified enneract (Acronym ren) (Jonathan Bowers)
Images
Birectified 9-cube
Alternate names
* Birectified enneract (Acronym barn) (Jonathan Bowers)
Images
Trirectified 9-cube
Alternate names
* Trirectified enneract (Acronym tarn) (Jonathan Bowers)
Images
Quadrirectified 9-cube
Alternate names
* Quadrirectified enneract (Acronym nav) (Jonathan Bowers)
[Klitzing (o3o3o3o3x3o3o3o4o - nav)]
Images
Notes
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,
*** (Paper 22) H.S.M. Coxeter, ''Regular and Semi Regular Polytopes I'',
ath. Zeit. 46 (1940) 380-407, MR 2,10*** (Paper 23) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes II'',
ath. Zeit. 188 (1985) 559-591*** (Paper 24) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes III'',
ath. Zeit. 200 (1988) 3-45*
Norman Johnson ''Uniform Polytopes'', Manuscript (1991)
** N.W. Johnson: ''The Theory of Uniform Polytopes and Honeycombs'', Ph.D. (1966)
* x3o3o3o3o3o3o3o4o - vee, o3x3o3o3o3o3o3o4o - riv, o3o3x3o3o3o3o3o4o - brav, o3o3o3x3o3o3o3o4o - tarv, o3o3o3o3x3o3o3o4o - nav, o3o3o3o3o3x3o3o4o - tarn, o3o3o3o3o3o3x3o4o - barn, o3o3o3o3o3o3o3x4o - ren, o3o3o3o3o3o3o3o4x - enne
External links
Polytopes of Various Dimensions
{{Polytopes
9-polytopes