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 runcinated 7-orthoplex is a convex
uniform 7-polytope with 3rd order
truncations (
runcination) of the regular
7-orthoplex.
There are 16 unique runcinations of the 7-orthoplex with permutations of truncations, and cantellations. 8 are more simply constructed from the
7-cube.
These polytopes are among 127
uniform 7-polytopes with B
7 symmetry.
Runcinated 7-orthoplex
Alternate names
* Small prismated hecatonicosoctaexon (acronym: spaz) (Jonathan Bowers)
Images
Biruncinated 7-orthoplex
Alternate names
* Small biprismated hecatonicosoctaexon (Acronym sibpaz) (Jonathan Bowers)
Images
Runcitruncated 7-orthoplex
Alternate names
* Prismatotruncated hecatonicosoctaexon (acronym: potaz) (Jonathan Bowers)
Images
Biruncitruncated 7-orthoplex
Alternate names
* Biprismatotruncated hecatonicosoctaexon (acronym: baptize) (Jonathan Bowers)
Images
Runcicantellated 7-orthoplex
Alternate names
* Prismatorhombated hecatonicosoctaexon (acronym: parz) (Jonathan Bowers)
Images
Biruncicantellated 7-orthoplex
Alternate names
* Biprismatorhombated hecatonicosoctaexon (acronym: boparz) (Jonathan Bowers)
Images
Runcicantitruncated 7-orthoplex
Alternate names
* Great prismated hecatonicosoctaexon (acronym: gopaz) (Jonathan Bowers)
Images
Biruncicantitruncated 7-orthoplex
Alternate names
* Great biprismated hecatonicosoctaexon (acronym: gibpaz) (Jonathan Bowers)
[Klitzing, (o3o3x3x3x3x3o - gibpaz)]
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,
Wiley: Kaleidoscopes: Selected Writings of H.S.M. Coxeter*** (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)
* o3o3o3x3o3o4x - spaz, o3x3o3o3x3o4o - sibpaz, o3o3o3x3x3o4x - potaz, o3o3x3o3x3x4o - baptize, o3o3o3x3x3o4x - parz, o3x3o3x3x3o4o - boparz, o3o3o3x3x3x4x - gopaz, o3o3x3x3x3x3o - gibpaz
External links
Polytopes of Various Dimensions{{Polytopes
7-polytopes