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Pentellated 7-orthoplexes
From Wikipedia, the free encyclopedia
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In seven-dimensional geometry, a pentellated 7-orthoplex is a convex uniform 7-polytope with 5th order truncations (pentellation) of the regular 7-orthoplex.
There are 32 unique pentellations of the 7-orthoplex with permutations of truncations, cantellations, runcinations, and sterications. 16 are more simply constructed relative to the 7-cube.
These polytopes are a part of a set of 127 uniform 7-polytopes with B7 symmetry.
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Pentellated 7-orthoplex
Pentellated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,5{35,4} |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 20160 |
Vertices | 2688 |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
- Small terated hecatonicosoctaexon (acronym: Staz) (Jonathan Bowers)[1]
Coordinates
Coordinates are permutations of (0,1,1,1,1,1,2)√2
Images
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Pentitruncated 7-orthoplex
Alternate names
- Teritruncated hecatonicosoctaexon (acronym: Tetaz) (Jonathan Bowers)[2]
Images
Coordinates
Coordinates are permutations of (0,1,1,1,1,2,3).
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Penticantellated 7-orthoplex
Alternate names
- Terirhombated hecatonicosoctaexon (acronym: Teroz) (Jonathan Bowers)[3]
Coordinates
Coordinates are permutations of (0,1,1,1,2,2,3)√2.
Images
Penticantitruncated 7-orthoplex
Alternate names
- Terigreatorhombated hecatonicosoctaexon (acronym: Tograz) (Jonathan Bowers)[4]
Coordinates
Coordinates are permutations of (0,1,1,1,2,3,4)√2.
Images
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Pentiruncinated 7-orthoplex
Alternate names
- Teriprismated hecatonicosoctaexon (acronym: Topaz) (Jonathan Bowers)[5]
Coordinates
The coordinates are permutations of (0,1,1,2,2,2,3)√2.
Images
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Pentiruncitruncated 7-orthoplex
Alternate names
- Teriprismatotruncated hecatonicosoctaexon (acronym: Toptaz) (Jonathan Bowers)[6]
Coordinates
Coordinates are permutations of (0,1,1,2,2,3,4)√2.
Images
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Pentiruncicantellated 7-orthoplex
Alternate names
- Teriprismatorhombated hecatonicosoctaexon (acronym: Toparz) (Jonathan Bowers)[7]
Coordinates
Coordinates are permutations of (0,1,1,2,3,3,4)√2.
Images
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Pentiruncicantitruncated 7-orthoplex
Alternate names
- Terigreatoprismated hecatonicosoctaexon (acronym: Tegopaz) (Jonathan Bowers)[8]
Coordinates
Coordinates are permutations of (0,1,1,2,3,4,5)√2.
Images
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Pentistericated 7-orthoplex
Alternate names
- Tericellated hecatonicosoctaexon (acronym: Tocaz) (Jonathan Bowers)[9]
Images
Coordinates
Coordinates are permutations of (0,1,2,2,2,2,3)√2.
Pentisteritruncated 7-orthoplex
Alternate names
- Tericellitruncated hecatonicosoctaexon (acronym: Tacotaz) (Jonathan Bowers)[10]
Coordinates
Coordinates are permutations of (0,1,2,2,2,3,4)√2.
Images
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Pentistericantellated 7-orthoplex
Alternate names
- Tericellirhombated hecatonicosoctaexon (acronym: Tocarz) (Jonathan Bowers)[11]
Coordinates
Coordinates are permutations of (0,1,2,2,3,3,4)√2.
Images
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Pentistericantitruncated 7-orthoplex
Alternate names
- Tericelligreatorhombated hecatonicosoctaexon (acronym: Tecagraz) (Jonathan Bowers)[12]
Coordinates
Coordinates are permutations of (0,1,2,2,3,4,5)√2.
Images
Pentisteriruncinated 7-orthoplex
Alternate names
- Bipenticantitruncated 7-orthoplex as t1,2,3,6{35,4}
- Tericelliprismated hecatonicosoctaexon (acronym: Tecpaz) (Jonathan Bowers)[13]
Coordinates
Coordinates are permutations of (0,1,2,3,3,3,4)√2.
Images
Pentisteriruncitruncated 7-orthoplex
Alternate names
- Tericelliprismatotruncated hecatonicosoctaexon (acronym: Tecpotaz) (Jonathan Bowers)[14]
Coordinates
Coordinates are permutations of (0,1,2,3,3,4,5)√2.
Images
Pentisteriruncicantellated 7-orthoplex
Alternate names
- Bipentiruncicantitruncated 7-orthoplex as t1,2,3,4,6{35,4}
- Tericelliprismatorhombated hecatonicosoctaexon (acronym: Tacparez) (Jonathan Bowers)[15]
Coordinates
Coordinates are permutations of (0,1,2,3,4,4,5)√2.
Images
Pentisteriruncicantitruncated 7-orthoplex
Alternate names
- Great terated hecatonicosoctaexon (acronym: Gotaz) (Jonathan Bowers)[16]
Coordinates
Coordinates are permutations of (0,1,2,3,4,5,6)√2.
Images
Notes
References
External links
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