In six-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 stericated 6-cube is a convex
uniform 6-polytope, constructed as a
sterication
In geometry, a uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform Facet (mathematics), facets. Here, "vertex-transitive" means that it has symmetries taking every vertex to every other vertex; the sam ...
(4th order truncation) of the regular
6-cube
In geometry, a 6-cube is a six-dimensional hypercube with 64 vertices, 192 edges, 240 square faces, 160 cubic cells, 60 tesseract 4-faces, and 12 5-cube 5-faces.
It has Schläfli symbol , being composed of 3 5-cubes around each 4-face. It ...
.
There are 8 unique sterications for the 6-cube with permutations of truncations, cantellations, and runcinations.
Stericated 6-cube
Alternate names
* Small cellated hexeract (Acronym: scox) (Jonathan Bowers)
Images
Steritruncated 6-cube
Alternate names
* Cellirhombated hexeract (Acronym: catax) (Jonathan Bowers)
Images
Stericantellated 6-cube
Alternate names
* Cellirhombated hexeract (Acronym: crax) (Jonathan Bowers)
Images
Stericantitruncated 6-cube
Alternate names
* Celligreatorhombated hexeract (Acronym: cagorx) (Jonathan Bowers)
Images
Steriruncinated 6-cube
Alternate names
* Celliprismated hexeract (Acronym: copox) (Jonathan Bowers)
Images
Steriruncitruncated 6-cube
Alternate names
* Celliprismatotruncated hexeract (Acronym: captix) (Jonathan Bowers)
Images
Steriruncicantellated 6-cube
Alternate names
* Celliprismatorhombated hexeract (Acronym: coprix) (Jonathan Bowers)
Images
Steriruncicantitruncated 6-cube
Alternate names
* Great cellated hexeract (Acronym: gocax) (Jonathan Bowers)
[Klitzing, (x4x3x3x3x3o - gocax)]
Images
Related polytopes
These polytopes are from a set of 63
uniform 6-polytopes generated from the B
6 Coxeter plane
In mathematics, a Coxeter element is an element of an irreducible Coxeter group which is a product of all simple reflections. The product depends on the order in which they are taken, but different orderings produce conjugate elements, which hav ...
, including the regular
6-cube
In geometry, a 6-cube is a six-dimensional hypercube with 64 vertices, 192 edges, 240 square faces, 160 cubic cells, 60 tesseract 4-faces, and 12 5-cube 5-faces.
It has Schläfli symbol , being composed of 3 5-cubes around each 4-face. It ...
or
6-orthoplex
In geometry, a 6-orthoplex, or 6-cross polytope, is a regular 6-polytope with 12 Vertex (geometry), vertices, 60 Edge (geometry), edges, 160 triangle Face (geometry), faces, 240 tetrahedron Cell (mathematics), cells, 192 5-cell ''4-faces'', and 64 ...
.
Notes
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
wiley.com
*** (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.
*
External links
Polytopes of Various Dimensions
{{Polytopes
6-polytopes