In seven-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 cantellated 7-orthoplex is a convex
uniform 7-polytope
In seven-dimensional space, seven-dimensional geometry, a 7-polytope is a polytope contained by 6-polytope facets. Each 5-polytope Ridge (geometry), ridge being shared by exactly two 6-polytope Facet (mathematics), facets.
A uniform 7-polytope is ...
, 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-orthoplex
In geometry, a 7-orthoplex, or 7- cross polytope, is a regular 7-polytope with 14 vertices, 84 edges, 280 triangle faces, 560 tetrahedron cells, 672 5-cell ''4-faces'', 448 ''5-faces'', and 128 ''6-faces''.
It has two constructed forms, th ...
.
There are ten degrees of cantellation for the 7-orthoplex, including
truncation
In mathematics and computer science, truncation is limiting the number of digits right of the decimal point.
Truncation and floor function
Truncation of positive real numbers can be done using the floor function. Given a number x \in \mathbb ...
s. Six are most simply constructible from the dual
7-cube
In geometry, a 7-cube is a seven-dimensional hypercube with 128 vertices, 448 edges, 672 square faces, 560 cubic cells, 280 tesseract 4-faces, 84 penteract 5-faces, and 14 hexeract 6-faces.
It can be named by its Schläfli symbol , being com ...
.
Cantellated 7-orthoplex
Alternate names
* Small rhombated hecatonicosoctaexon (acronym: sarz) (Jonathan Bowers)
Images
Bicantellated 7-orthoplex
Alternate names
* Small birhombated hecatonicosoctaexon (acronym: sebraz) (Jonathan Bowers)
Images
Cantitruncated 7-orthoplex
Alternate names
* Great rhombated hecatonicosoctaexon (acronym: garz) (Jonathan Bowers)
Images
Bicantitruncated 7-orthoplex
Alternate names
* Great birhombated hecatonicosoctaexon (acronym: gebraz) (Jonathan Bowers)
[Klitizing, (o3o3o3x3x3x4o - gebraz)]
Images
Related polytopes
These polytopes are from a family of 127
uniform 7-polytope
In seven-dimensional space, seven-dimensional geometry, a 7-polytope is a polytope contained by 6-polytope facets. Each 5-polytope Ridge (geometry), ridge being shared by exactly two 6-polytope Facet (mathematics), facets.
A uniform 7-polytope is ...
s 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-Canadian geometer and mathematician. He is regarded as one of the greatest geometers of the 20th century.
Coxeter was born in England and educated ...
:
** 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
* - o3o3o3o3x3o4x - sarz, o3o3o3x3o3x4o - sebraz, o3o3o3o3x3x4x - garz, o3o3o3x3x3x4o - gebraz
External links
Polytopes of Various Dimensions
{{Polytopes
7-polytopes