In seven-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 cantellated 7-cube is a convex
uniform 7-polytope, being a
cantellation
In geometry, a cantellation is a 2nd-order truncation in any dimension that bevels a regular polytope at its edges and at its vertices, creating a new facet in place of each edge and of each vertex. Cantellation also applies to regular tiling ...
of the regular
7-cube.
There are 10 degrees of cantellation for the 7-cube, including truncations. 4 are most simply constructible from the dual
7-orthoplex.
Cantellated 7-cube
Alternate names
* Small rhombated hepteract (acronym: sersa) (Jonathan Bowers)
Images
Bicantellated 7-cube
Alternate names
* Small birhombated hepteract (acronym: sibrosa) (Jonathan Bowers)
Images
Tricantellated 7-cube
Alternate names
* Small trirhombihepteractihecatonicosoctaexon (acronym: strasaz) (Jonathan Bowers)
Images
Cantitruncated 7-cube
Alternate names
* Great rhombated hepteract (acronym: gersa) (Jonathan Bowers)
Images
It is fifth in a series of cantitruncated hypercubes:
Bicantitruncated 7-cube
Alternate names
* Great birhombated hepteract (acronym: gibrosa) (Jonathan Bowers)
Images
Tricantitruncated 7-cube
Alternate names
* Great trirhombihepteractihecatonicosoctaexon (acronym: gotrasaz) (Jonathan Bowers)
[Klitizing, (o3o3x3x3x3o4o - gotrasaz)]
Images
Related polytopes
These polytopes are from a family of 127
uniform 7-polytopes with B
7 symmetry.
See also
*
List of B7 polytopes
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.
* x3o3x3o3o3o4o- sersa, o3x3o3x3o3o4o - sibrosa, o3o3x3o3x3o4o - strasaz, x3x3x3o3o3o4o - gersa, o3x3x3x3o3o4o - gibrosa, o3o3x3x3x3o4o - gotrasaz
External links
Polytopes of Various Dimensions{{Polytopes
7-polytopes