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Pentellated 7-orthoplexes
| Orthogonal projections in B6 Coxeter plane | |
|---|---|
| [[File:7-cube t6_B6.svg | 120px]]7-orthoplex |
| [[File:7-cube t1456_B6.svg | 120px]]Penticantitruncated 7-orthoplex |
| [[File:7-cube t13456_B6.svg | 120px]]Pentiruncicantitruncated 7-orthoplex |
| [[File:7-cube t12456_B6.svg | 120px]]Pentistericantitruncated 7-orthoplex |
| [[File:7-cube t123456_B6.svg | 120px]]Pentisteriruncicantitruncated 7-orthoplex |
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.
Pentellated 7-orthoplex
| Pentellated 7-orthoplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter diagram |
| 6-faces |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter groups |
| Properties |
Alternate names
- Small terated hecatonicosoctaexon (acronym: Staz) (Jonathan Bowers)
Coordinates
Coordinates are permutations of (0,1,1,1,1,1,2)
Images
Pentitruncated 7-orthoplex
| pentitruncated 7-orthoplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter diagram |
| 6-faces |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter groups |
| Properties |
Alternate names
- Teritruncated hecatonicosoctaexon (acronym: Tetaz) (Jonathan Bowers)
Images
Coordinates
Coordinates are permutations of (0,1,1,1,1,2,3).
Penticantellated 7-orthoplex
| Penticantellated 7-orthoplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter diagram |
| 6-faces |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter groups |
| Properties |
Alternate names
- Terirhombated hecatonicosoctaexon (acronym: Teroz) (Jonathan Bowers)
Coordinates
Coordinates are permutations of (0,1,1,1,2,2,3).
Images
Penticantitruncated 7-orthoplex
| penticantitruncated 7-orthoplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter diagram |
| 6-faces |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter groups |
| Properties |
Alternate names
- Terigreatorhombated hecatonicosoctaexon (acronym: Tograz) (Jonathan Bowers)
Coordinates
Coordinates are permutations of (0,1,1,1,2,3,4).
Images
Pentiruncinated 7-orthoplex
| pentiruncinated 7-orthoplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter diagram |
| 6-faces |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter groups |
| Properties |
Alternate names
- Teriprismated hecatonicosoctaexon (acronym: Topaz) (Jonathan Bowers)
Coordinates
The coordinates are permutations of (0,1,1,2,2,2,3).
Images
Pentiruncitruncated 7-orthoplex
| pentiruncitruncated 7-orthoplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter diagram |
| 6-faces |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter groups |
| Properties |
Alternate names
- Teriprismatotruncated hecatonicosoctaexon (acronym: Toptaz) (Jonathan Bowers)
Coordinates
Coordinates are permutations of (0,1,1,2,2,3,4).
Images
Pentiruncicantellated 7-orthoplex
| pentiruncicantellated 7-orthoplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter diagram |
| 6-faces |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter groups |
| Properties |
Alternate names
- Teriprismatorhombated hecatonicosoctaexon (acronym: Toparz) (Jonathan Bowers)
Coordinates
Coordinates are permutations of (0,1,1,2,3,3,4).
Images
Pentiruncicantitruncated 7-orthoplex
| pentiruncicantitruncated 7-orthoplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter diagram |
| 6-faces |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter groups |
| Properties |
Alternate names
- Terigreatoprismated hecatonicosoctaexon (acronym: Tegopaz) (Jonathan Bowers)
Coordinates
Coordinates are permutations of (0,1,1,2,3,4,5).
Images
Pentistericated 7-orthoplex
| pentistericated 7-orthoplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter diagram |
| 6-faces |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter groups |
| Properties |
Alternate names
- Tericellated hecatonicosoctaexon (acronym: Tocaz) (Jonathan Bowers)
Images
Coordinates
Coordinates are permutations of (0,1,2,2,2,2,3).
Pentisteritruncated 7-orthoplex
| pentisteritruncated 7-orthoplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter diagram |
| 6-faces |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter groups |
| Properties |
Alternate names
- Tericellitruncated hecatonicosoctaexon (acronym: Tacotaz) (Jonathan Bowers)
Coordinates
Coordinates are permutations of (0,1,2,2,2,3,4).
Images
Pentistericantellated 7-orthoplex
| pentistericantellated 7-orthoplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter diagram |
| 6-faces |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter groups |
| Properties |
Alternate names
- Tericellirhombated hecatonicosoctaexon (acronym: Tocarz) (Jonathan Bowers)
Coordinates
Coordinates are permutations of (0,1,2,2,3,3,4).
Images
Pentistericantitruncated 7-orthoplex
| pentistericantitruncated 7-orthoplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter diagram |
| 6-faces |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter groups |
| Properties |
Alternate names
- Tericelligreatorhombated hecatonicosoctaexon (acronym: Tecagraz) (Jonathan Bowers)
Coordinates
Coordinates are permutations of (0,1,2,2,3,4,5).
Images
Pentisteriruncinated 7-orthoplex
| Pentisteriruncinated 7-orthoplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter diagram |
| 6-faces |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter groups |
| Properties |
Alternate names
- Bipenticantitruncated 7-orthoplex as t1,2,3,6{35,4}
- Tericelliprismated hecatonicosoctaexon (acronym: Tecpaz) (Jonathan Bowers)
Coordinates
Coordinates are permutations of (0,1,2,3,3,3,4).
Images
Pentisteriruncitruncated 7-orthoplex
| pentisteriruncitruncated 7-orthoplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter diagram |
| 6-faces |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter groups |
| Properties |
Alternate names
- Tericelliprismatotruncated hecatonicosoctaexon (acronym: Tecpotaz) (Jonathan Bowers)
Coordinates
Coordinates are permutations of (0,1,2,3,3,4,5).
Images
Pentisteriruncicantellated 7-orthoplex
| pentisteriruncicantellated 7-orthoplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter diagram |
| 6-faces |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter groups |
| Properties |
Alternate names
- Bipentiruncicantitruncated 7-orthoplex as t1,2,3,4,6{35,4}
- Tericelliprismatorhombated hecatonicosoctaexon (acronym: Tacparez) (Jonathan Bowers)
Coordinates
Coordinates are permutations of (0,1,2,3,4,4,5).
Images
Pentisteriruncicantitruncated 7-orthoplex
| pentisteriruncicantitruncated 7-orthoplex |
|---|
| Type |
| Schläfli symbol |
| Coxeter diagram |
| 6-faces |
| 5-faces |
| 4-faces |
| Cells |
| Faces |
| Edges |
| Vertices |
| Vertex figure |
| Coxeter groups |
| Properties |
Alternate names
- Great terated hecatonicosoctaexon (acronym: Gotaz) (Jonathan Bowers)
Coordinates
Coordinates are permutations of (0,1,2,3,4,5,6).
Images
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, 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.
References
- Klitzing, (x3o3o3o3o3x4o - staz)
- Klitzing, (x3x3o3o3o3x4o - tetaz)
- Klitzing, (x3o3x3o3o3x4o - teroz)
- Klitzing, (x3x3x3oxo3x4o - tograz)
- Klitzing, (x3o3o3x3o3x4o - topaz)
- Klitzing, (x3x3o3x3o3x4o - toptaz)
- Klitzing, (x3o3x3x3o3x4o - toparz)
- Klitzing, (x3x3x3x3o3x4o - tegopaz)
- Klitzing, (x3o3o3o3x3x4o - tocaz)
- Klitzing, (x3x3o3o3x3x4o - tacotaz)
- Klitzing, (x3o3x3o3x3x4o - tocarz)
- Klitzing, (x3x3x3o3x3x4o - tecagraz)
- Klitzing, (x3o3o3x3x3x4o - tecpaz)
- Klitzing, (x3x3o3x3x3x4o - tecpotaz)
- Klitzing, (x3o3x3x3x3x4o - tacparez)
- Klitzing, (x3x3x3x3x3x4o - gotaz)
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