In seven-dimensional geometry , a cantellated 7-orthoplex is a convex uniform 7-polytope , being a cantellation of the regular 7-orthoplex .
There are ten degrees of cantellation for the 7-orthoplex, including truncations . Six are most simply constructible from the dual 7-cube .
Cantellated 7-orthoplex
Cantellated 7-orthoplex
Type
uniform 7-polytope
Schläfli symbol rr{3,3,3,3,3,4}
Coxeter-Dynkin diagram File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 3.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node.png
6-faces
5-faces
4-faces
Cells
Faces
Edges
7560
Vertices
840
Vertex figure
Coxeter groups B7 , [4,3,3,3,3,3]
Properties
convex
Alternate names Small rhombated hecatonicosoctaexon (acronym: sarz) (Jonathan Bowers)[ 1] Images Bicantellated 7-orthoplex
Bicantellated 7-orthoplex
Type
uniform 7-polytope
Schläfli symbol 2rr{3,3,3,3,3,4}
Coxeter-Dynkin diagrams File:CDel node.png File:CDel 3.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 3.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node.png
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups B7 , [4,3,3,3,3,3]
Properties
convex
Alternate names Small birhombated hecatonicosoctaexon (acronym: sebraz) (Jonathan Bowers)[ 2] Images Cantitruncated 7-orthoplex
Cantitruncated 7-orthoplex
Type
uniform 7-polytope
Schläfli symbol tr{3,3,3,3,3,4}
Coxeter-Dynkin diagrams File:CDel node 1.png File:CDel 3.png File:CDel node 1.png File:CDel 3.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node.png
6-faces
5-faces
4-faces
Cells
Faces
Edges
8400
Vertices
1680
Vertex figure
Coxeter groups B7 , [4,3,3,3,3,3]
Properties
convex
Alternate names Great rhombated hecatonicosoctaexon (acronym: garz) (Jonathan Bowers)[ 3] Images Bicantitruncated 7-orthoplex
Bicantitruncated 7-orthoplex
Type
uniform 7-polytope
Schläfli symbol 2tr{3,3,3,3,3,4}
Coxeter-Dynkin diagrams File:CDel node.png File:CDel 3.png File:CDel node 1.png File:CDel 3.png File:CDel node 1.png File:CDel 3.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node.png
6-faces
5-faces
4-faces
Cells
Faces
Edges
30240
Vertices
6720
Vertex figure
Coxeter groups B7 , [4,3,3,3,3,3]
Properties
convex
Alternate names Great birhombated hecatonicosoctaexon (acronym: gebraz) (Jonathan Bowers)[ 4] Images Related polytopes These polytopes are from a family of 127 uniform 7-polytopes with B7 symmetry.
See also Notes
↑ Klitizing, (o3o3o3o3x3o4x - sarz)
↑ Klitizing, (o3o3o3x3o3x4o - sebraz)
↑ Klitizing, (o3o3o3o3x3x4x - garz)
↑ Klitizing, (o3o3o3x3x3x4o - gebraz)
References 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 [1]
(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)" . External links
