- Source: Pentellated 6-cubes
In six-dimensional geometry, a pentellated 6-cube is a convex uniform 6-polytope with 5th order truncations of the regular 6-cube.
There are unique 16 degrees of pentellations of the 6-cube with permutations of truncations, cantellations, runcinations, and sterications. The simple pentellated 6-cube is also called an expanded 6-cube, constructed by an expansion operation applied to the regular 6-cube. The highest form, the pentisteriruncicantitruncated 6-cube, is called an omnitruncated 6-cube with all of the nodes ringed. Six of them are better constructed from the 6-orthoplex given at pentellated 6-orthoplex.
Pentellated 6-cube
= Alternate names
=Pentellated 6-orthoplex
Expanded 6-cube, expanded 6-orthoplex
Small teri-hexeractihexacontitetrapeton (Acronym: stoxog) (Jonathan Bowers)
= Images
=Pentitruncated 6-cube
= Alternate names
=Teritruncated hexeract (Acronym: tacog) (Jonathan Bowers)
= Images
=Penticantellated 6-cube
= Alternate names
=Terirhombated hexeract (Acronym: topag) (Jonathan Bowers)
= Images
=Penticantitruncated 6-cube
= Alternate names
=Terigreatorhombated hexeract (Acronym: togrix) (Jonathan Bowers)
= Images
=Pentiruncitruncated 6-cube
= Alternate names
=Tericellirhombated hexacontitetrapeton (Acronym: tocrag) (Jonathan Bowers)
= Images
=Pentiruncicantellated 6-cube
= Alternate names
=Teriprismatorhombi-hexeractihexacontitetrapeton (Acronym: tiprixog) (Jonathan Bowers)
= Images
=Pentiruncicantitruncated 6-cube
= Alternate names
=Terigreatoprismated hexeract (Acronym: tagpox) (Jonathan Bowers)
= Images
=Pentisteritruncated 6-cube
= Alternate names
=Tericellitrunki-hexeractihexacontitetrapeton (Acronym: tactaxog) (Jonathan Bowers)
= Images
=Pentistericantitruncated 6-cube
= Alternate names
=Tericelligreatorhombated hexeract (Acronym: tocagrax) (Jonathan Bowers)
= Images
=Omnitruncated 6-cube
The omnitruncated 6-cube has 5040 vertices, 15120 edges, 16800 faces (4200 hexagons and 1260 squares), 8400 cells, 1806 4-faces, and 126 5-faces. With 5040 vertices, it is the largest of 35 uniform 6-polytopes generated from the regular 6-cube.
= Alternate names
=Pentisteriruncicantitruncated 6-cube or 6-orthoplex (omnitruncation for 6-polytopes)
Omnitruncated hexeract
Great teri-hexeractihexacontitetrapeton (Acronym: gotaxog) (Jonathan Bowers)
= Images
== Full snub 6-cube
=The full snub 6-cube or omnisnub 6-cube, defined as an alternation of the omnitruncated 6-cube is not uniform, but it can be given Coxeter diagram and symmetry [4,3,3,3,3]+, and constructed from 12 snub 5-cubes, 64 snub 5-simplexes, 60 snub tesseract antiprisms, 192 snub 5-cell antiprisms, 160 3-sr{4,3} duoantiprisms, 240 4-s{3,4} duoantiprisms, and 23040 irregular 5-simplexes filling the gaps at the deleted vertices.
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)". x4o3o3o3o3x - stoxog, x4x3o3o3o3x - tacog, x4o3x3o3o3x - topag, x4x3x3o3o3x - togrix, x4x3o3x3o3x - tocrag, x4o3x3x3o3x - tiprixog, x4x3x3o3x3x - tagpox, x4x3o3o3x3x - tactaxog, x4x3x3o3x3x - tocagrax, x4x3x3x3x3x - gotaxog
External links
Glossary for hyperspace, George Olshevsky.
Polytopes of Various Dimensions
Multi-dimensional Glossary
Kata Kunci Pencarian:
- Daftar bentuk matematika
- Pentellated 6-cubes
- Pentellated 6-orthoplexes
- Pentic 6-cubes
- Pentellated 7-cubes
- Pentellated 6-simplexes
- List of mathematical shapes
- List of polygons, polyhedra and polytopes
- Hexic 7-cubes
- Octagon
- B6 polytope
