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Cantic 6-cube

{{Short description|Shape in six-dimensional geometry}}

class="wikitable" align="right" style="margin-left:10px" width="250"

!bgcolor=#e7dcc3 colspan=2|Cantic 6-cube
Truncated 6-demicube

bgcolor=#ffffff align=center colspan=2|280px
D6 Coxeter plane projection
bgcolor=#e7dcc3|Typeuniform polypeton
bgcolor=#e7dcc3|Schläfli symbolt0,1{3,33,1}
h2{4,34}
bgcolor=#e7dcc3|Coxeter-Dynkin diagram{{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node}} = {{CDD|node_h1|4|node|3|node_1|3|node|3|node|3|node}}
bgcolor=#e7dcc3|5-faces76
bgcolor=#e7dcc3|4-faces636
bgcolor=#e7dcc3|Cells2080
bgcolor=#e7dcc3|Faces3200
bgcolor=#e7dcc3|Edges2160
bgcolor=#e7dcc3|Vertices480
bgcolor=#e7dcc3|Vertex figure( )v[{ }x{3,3}]
bgcolor=#e7dcc3|Coxeter groupsD6, [33,1,1]
bgcolor=#e7dcc3|Propertiesconvex

In six-dimensional geometry, a cantic 6-cube (or a truncated 6-demicube) is a uniform 6-polytope.

Alternate names

  • Truncated 6-demicube/demihexeract (Acronym thax) (Jonathan Bowers)Klitizing, (x3x3o *b3o3o3o – thax)

Cartesian coordinates

The Cartesian coordinates for the 480 vertices of a cantic 6-cube centered at the origin and edge length 6{{radic|2}} are coordinate permutations:

: (±1,±1,±3,±3,±3,±3)

with an odd number of plus signs.

Images

{{6-demicube Coxeter plane graphs|t01|200}}

Related polytopes

{{Cantic cube table}}

There are 47 uniform polytopes with D6 symmetry, 31 are shared by the B6 symmetry, and 16 are unique:

{{Demihexeract_family}}

Notes

{{reflist}}

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}} [http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html]
  • (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.
  • {{KlitzingPolytopes|polypeta.htm|6D|uniform polytopes (polypeta)}} x3x3o *b3o3o3o – thax

External links

  • [https://web.archive.org/web/20070310205351/http://members.cox.net/hedrondude/topes.htm Polytopes of Various Dimensions]
  • [http://tetraspace.alkaline.org/glossary.htm Multi-dimensional Glossary]

Category:6-polytopes

{{Polytopes}}