- Source: Pentellated 6-orthoplexes
In six-dimensional geometry, a pentellated 6-orthoplex is a convex uniform 6-polytope with 5th order truncations of the regular 6-orthoplex.
There are unique 16 degrees of pentellations of the 6-orthoplex with permutations of truncations, cantellations, runcinations, and sterications. Ten are shown, with the other 6 more easily constructed as a pentellated 6-cube. The simple pentellated 6-orthoplex (Same as pentellated 5-cube) is also called an expanded 6-orthoplex, constructed by an expansion operation applied to the regular 6-orthoplex. The highest form, the pentisteriruncicantitruncated 6-orthoplex, is called an omnitruncated 6-orthoplex with all of the nodes ringed.
Pentitruncated 6-orthoplex
= Alternate names
=Teritruncated hexacontatetrapeton (Acronym: tacox) (Jonathan Bowers)
= Images
=Penticantellated 6-orthoplex
= Alternate names
=Terirhombated hexacontitetrapeton (Acronym: tapox) (Jonathan Bowers)
= Images
=Penticantitruncated 6-orthoplex
= Alternate names
=Terigreatorhombated hexacontitetrapeton (Acronym: togrig) (Jonathan Bowers)
= Images
=Pentiruncitruncated 6-orthoplex
= Alternate names
=Teriprismatotruncated hexacontitetrapeton (Acronym: tocrax) (Jonathan Bowers)
= Images
=Pentiruncicantitruncated 6-orthoplex
= Alternate names
=Terigreatoprismated hexacontitetrapeton (Acronym: tagpog) (Jonathan Bowers)
= Images
=Pentistericantitruncated 6-orthoplex
= Alternate names
=Tericelligreatorhombated hexacontitetrapeton (Acronym: tecagorg) (Jonathan Bowers)
= Images
=Related polytopes
These polytopes are from a set of 63 uniform 6-polytopes generated from the B6 Coxeter plane, including the regular 6-cube or 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 Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [1]
(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.
Klitzing, Richard. "6D uniform polytopes (polypeta)". x4o3o3o3x3x - tacox, x4o3o3x3o3x - tapox, x4o3o3x3x3x - togrig, x4o3x3o3x3x - tocrax, x4x3o3x3x3x - tagpog, x4x3o3x3x3x - tecagorg
External links
Glossary for hyperspace, George Olshevsky.
Polytopes of Various Dimensions
Multi-dimensional Glossary
