6-cubeCantellated 6-cubeBicantellated 6-cube6-orthoplexCantellated 6-orthoplexBicantellated 6-orthoplexCantitruncated 6-cubeBicantitruncated 6-cubeBicantitruncated 6-orthoplexCantitruncated 6-orthoplexOrthogonal projections in B6 Coxeter plane In six-dimensional geometry, a cantellated 6-cube is a convex uniform 6-polytope, being a cantellation of the regular 6-cube.
There are 8 cantellations for the 6-cube, including truncations. Half of them are more easily constructed from the dual 6-orthoplex.
Cantellated 6-cube Cantellated 6-cubeTypeuniform 6-polytopeSchläfli symbol rr{4,3,3,3,3}or Coxeter-Dynkin diagrams5-faces4-facesCellsFacesEdges4800Vertices960Vertex figureCoxeter groupsB6, [3,3,3,3,4]Propertiesconvex
Alternate names Cantellated hexeract Small rhombated hexeract (acronym: srox) (Jonathan Bowers)
Images
Bicantellated 6-cube Bicantellated 6-cubeTypeuniform 6-polytopeSchläfli symbol 2rr{4,3,3,3,3}or Coxeter-Dynkin diagrams5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB6, [3,3,3,3,4]Propertiesconvex
Alternate names Bicantellated hexeract Small birhombated hexeract (acronym: saborx) (Jonathan Bowers)
Images
Cantitruncated 6-cube Cantitruncated 6-cubeTypeuniform 6-polytopeSchläfli symbol tr{4,3,3,3,3}or Coxeter-Dynkin diagrams5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB6, [3,3,3,3,4]Propertiesconvex
Alternate names Cantitruncated hexeract Great rhombihexeract (acronym: grox) (Jonathan Bowers)
Images
It is fourth in a series of cantitruncated hypercubes:
Bicantitruncated 6-cube Bicantitruncated 6-cubeTypeuniform 6-polytopeSchläfli symbol 2tr{4,3,3,3,3}or Coxeter-Dynkin diagrams5-faces4-facesCellsFacesEdgesVerticesVertex figureCoxeter groupsB6, [3,3,3,3,4]Propertiesconvex
Alternate names Bicantitruncated hexeract Great birhombihexeract (acronym: gaborx) (Jonathan Bowers)
Images
Related polytopes These polytopes are part of a set of 63 uniform 6-polytopes generated from the B6 Coxeter plane, including the regular 6-cube and 6-orthoplex.
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 Ivić Weiss, Wiley-Interscience Publication, 1995, wiley.com, (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. o3o3o3x3o4x - srox, o3o3x3o3x4o - saborx, o3o3o3x3x4x - grox, o3o3x3x3x4o - gaborx
External links Polytopes of Various Dimensions Multi-dimensional Glossary