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-cube is a convex
uniform 7-polytope with 3rd order
truncations (
runcination
In geometry, runcination is an operation that cuts a regular polytope (or honeycomb) simultaneously along the faces, edges, and vertices, creating new facets in place of the original face, edge, and vertex centers.
It is a higher order truncatio ...
) of the regular
7-cube.
There are 16 unique runcinations of the 7-cube with permutations of truncations, and cantellations. 8 are more simply constructed from the
7-orthoplex.
These polytopes are among 127
uniform 7-polytopes with B
7 symmetry.
Runcinated 7-cube
Alternate names
* Small prismated hepteract (acronym: spesa) (Jonathan Bowers)
Images
Biruncinated 7-cube
Alternate names
* Small biprismated hepteract (Acronym sibposa) (Jonathan Bowers)
Images
Runcitruncated 7-cube
Alternate names
* Prismatotruncated hepteract (acronym: petsa) (Jonathan Bowers)
Images
Biruncitruncated 7-cube
Alternate names
* Biprismatotruncated hepteract (acronym: biptesa) (Jonathan Bowers)
Images
Runcicantellated 7-cube
Alternate names
* Prismatorhombated hepteract (acronym: parsa) (Jonathan Bowers)
Images
Biruncicantellated 7-cube
Alternate names
* Biprismatorhombated hepteract (acronym: bopresa) (Jonathan Bowers)
Images
Runcicantitruncated 7-cube
Alternate names
* Great prismated hepteract (acronym: gapsa) (Jonathan Bowers)
Images
Biruncicantitruncated 7-cube
Alternate names
* Great biprismated hepteract (acronym: gibposa) (Jonathan Bowers)
[Klitzing, (o3x3x3x3x3o3o - gibposa)]
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,
*** (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)
* x3o3o3x3o3o4o - spo, o3x3o3o3x3o4o - sibpo, x3x3o3x3o3o4o - patto, o3x3x3o3x3o4o - bipto, x3o3x3x3o3o4o - paro, x3x3x3x3o3o4o - gapo, o3x3x3x3x3o3o- gibpo
External links
Polytopes of Various Dimensions{{Polytopes
7-polytopes