In eight-dimensional
geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
, a rectified 8-cube is a convex
uniform 8-polytope
In Eight-dimensional space, eight-dimensional geometry, an eight-dimensional polytope or 8-polytope is a polytope contained by 7-polytope facets. Each 6-polytope Ridge (geometry), ridge being shared by exactly two 7-polytope Facet (mathematics), fa ...
, being a
rectification
Rectification has the following technical meanings:
Mathematics
* Rectification (geometry), truncating a polytope by marking the midpoints of all its edges, and cutting off its vertices at those points
* Rectifiable curve, in mathematics
* Recti ...
of the regular
8-cube.
There are unique 8 degrees of rectifications, the zeroth being the
8-cube, and the 7th and last being the
8-orthoplex. Vertices of the rectified 8-cube are located at the edge-centers of the 8-cube. Vertices of the ''birectified 8-cube'' are located in the square face centers of the 8-cube. Vertices of the ''trirectified 8-cube'' are located in the
7-cube cell centers of the 8-cube.
Rectified 8-cube
Alternate names
* rectified octeract
Images
Birectified 8-cube
Alternate names
* Birectified octeract
* Rectified 8-demicube
Images
Trirectified 8-cube
Alternate names
* trirectified octeract
Images
Notes
References
*
H.S.M. Coxeter
Harold Scott MacDonald "Donald" Coxeter, (9 February 1907 – 31 March 2003) was a British and later also Canadian geometer. He is regarded as one of the greatest geometers of the 20th century.
Biography
Coxeter was born in Kensington t ...
:
** 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.
* o3o3o3o3o3o3x4o, o3o3o3o3o3x3o4o, o3o3o3o3x3o3o4o
External links
Polytopes of Various Dimensions
{{Polytopes
8-polytopes