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Orthogonal projections in B6
Coxeter plane
7-orthoplex
Runcinated 7-orthoplex
Biruncinated 7-orthoplex
Runcitruncated 7-orthoplex
Biruncitruncated 7-orthoplex
Runcicantellated 7-orthoplex
Biruncicantellated 7-orthoplex
Runcicantitruncated 7-orthoplex
Biruncicantitruncated 7-orthoplex
In seven-dimensional
geometry , 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 B7 symmetry.
Small prismated hecatonicosoctaexon (acronym: spaz) (Jonathan Bowers)
[1]
Small biprismated hecatonicosoctaexon (Acronym sibpaz) (Jonathan Bowers)
[2]
Runcitruncated 7-orthoplex
Prismatotruncated hecatonicosoctaexon (acronym: potaz) (Jonathan Bowers)
[3]
Biruncitruncated 7-orthoplex
Biprismatotruncated hecatonicosoctaexon (acronym: baptize) (Jonathan Bowers)
[4]
Runcicantellated 7-orthoplex
Prismatorhombated hecatonicosoctaexon (acronym: parz) (Jonathan Bowers)
[5]
Biruncicantellated 7-orthoplex
Biprismatorhombated hecatonicosoctaexon (acronym: boparz) (Jonathan Bowers)
[6]
Runcicantitruncated 7-orthoplex
Great prismated hecatonicosoctaexon (acronym: gopaz) (Jonathan Bowers)
[7]
Biruncicantitruncated 7-orthoplex
Great biprismated hecatonicosoctaexon (acronym: gibpaz) (Jonathan Bowers)
[8]
^ Klitzing, (o3o3o3x3o3o4x - spaz)
^ Klitzing, (o3x3o3o3x3o4o - sibpaz)
^ Klitzing, (o3o3o3x3x3o4x - potaz)
^ Klitzing, (o3o3x3o3x3x4o - baptize)
^ Klitzing, (o3o3o3x3x3o4x - parz)
^ Klitzing, (o3x3o3x3x3o4o - boparz)
^ Klitzing, (o3o3o3x3x3x4x - gopaz)
^ Klitzing, (o3o3x3x3x3x3o - gibpaz)
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,
ISBN
978-0-471-01003-6
Wiley: Kaleidoscopes: Selected Writings of H.S.M. Coxeter
(Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I , [Math. Zeit. 46 (1940) 380-407, MR 2,10]
(Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II , [Math. Zeit. 188 (1985) 559-591]
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III , [Math. Zeit. 200 (1988) 3-45]
Norman Johnson Uniform Polytopes , Manuscript (1991)
N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs , Ph.D. (1966)
Klitzing, Richard.
"7D uniform polytopes (polyexa)" . o3o3o3x3o3o4x - spaz, o3x3o3o3x3o4o - sibpaz, o3o3o3x3x3o4x - potaz, o3o3x3o3x3x4o - baptize, o3o3o3x3x3o4x - parz, o3x3o3x3x3o4o - boparz, o3o3o3x3x3x4x - gopaz, o3o3x3x3x3x3o - gibpaz