In five-dimensional geometry, a cantellated 5-orthoplex is a convex uniform 5-polytope, being a cantellation of the regular 5-orthoplex.
There are 6 cantellation for the 5-orthoplex, including truncations. Some of them are more easily constructed from the dual 5-cube.
Cantellated 5-orthoplex
Alternate names
Cantellated 5-orthoplex
Bicantellated 5-demicube
Small rhombated triacontiditeron (Acronym: sart) (Jonathan Bowers)
Coordinates
The vertices of the can be made in 5-space, as permutations and sign combinations of: (0,0,1,1,2)
Images
The cantellated 5-orthoplex is constructed by a cantellation operation applied to the 5-orthoplex.
Cantitruncated 5-orthoplex
Alternate names
Cantitruncated pentacross
Cantitruncated triacontiditeron (Acronym: gart) (Jonathan Bowers)
Coordinates
Cartesian coordinates for the vertices of a cantitruncated 5-orthoplex, centered at the origin, are all sign and coordinate permutations of (±3,±2,±1,0,0)
Images
Related polytopes
These polytopes are from a set of 31 uniform 5-polytopes generated from the regular 5-cube or 5-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 Ivic Weiss, Wiley-Interscience Publication, 1995, (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. x3o3x3o4o - sart, x3x3x3o4o - gart