Runcinerade 7-ortoplexer
| Ortogonala projektioner i B 6 Coxeter-plan | ||
|---|---|---|
 7-ortoplex    
|
 Runcinerad 7-ortoplex
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 Biruncinerad 7-ortoplex
|
 Runcitruncated 7-ortoplex
|
 Biruncitruncated 7-ortoplex
|
 Runcikantellerad 7-ortoplex
|
 Biruncikantellerad 7-ortoplex
|
 Runcicantitruncated 7-ortoplex
|
 Biruncicantitruncated 7-ortoplex
|
I sjudimensionell geometri är en runcinerad 7-ortoplex en konvex enhetlig 7-polytop med 3:e ordningens trunkationer ( runcination ) av det vanliga 7-ortoplexet .
Det finns 16 unika runcinationer av 7-ortoplexet med permutationer av trunkationer och kantelleringar. 8 är enklare konstruerade från 7-kuben .
Dessa polytoper är bland 127 enhetliga 7-polytoper med B 7 symmetri.
Runcinerad 7-ortoplex
| Runcinerad 7-ortoplex | |
|---|---|
| Typ | enhetlig 7-polytop |
| Schläfli symbol | t 0,3 {3 5 ,4} |
| Coxeter-Dynkin diagram |
|
| 6 ansikten | |
| 5 ansikten | |
| 4 ansikten | |
| Celler | |
| ansikten | |
| Kanter | 23520 |
| Vertices | 2240 |
| Vertex figur | |
| Coxeter grupper | B 7 , [4,3 5 ] |
| Egenskaper | konvex |
Alternativa namn
- Liten prismatad hecatonicosoctaexon (akronym: spaz) (Jonathan Bowers)
Bilder
| Coxeter plan | B 7 / A 6 | B 6 / D 7 | B 5 / D 6 / A 4 |
|---|---|---|---|
| Graf |
|
|
|
| Dihedral symmetri | [14] | [12] | [10] |
| Coxeter plan | B 4 / D 5 | B 3 / D 4 / A 2 | B 2 / D 3 |
| Graf |
|
|
|
| Dihedral symmetri | [8] | [6] | [4] |
| Coxeter plan | En 5 | A 3 | |
| Graf |
|
|
|
| Dihedral symmetri | [6] | [4] |
Biruncinerad 7-ortoplex
| Biruncinerad 7-ortoplex | |
|---|---|
| Typ | enhetlig 7-polytop |
| Schläfli symbol | t 1,4 {3 5 ,4} |
| Coxeter-Dynkin diagram |
|
| 6 ansikten | |
| 5 ansikten | |
| 4 ansikten | |
| Celler | |
| ansikten | |
| Kanter | 60480 |
| Vertices | 6720 |
| Vertex figur | |
| Coxeter grupper | B 7 , [4,3 5 ] |
| Egenskaper | konvex |
Alternativa namn
- Liten biprismatad hecatonicosoctaexon (Akronym sibpaz) (Jonathan Bowers)
Bilder
| Coxeter plan | B 7 / A 6 | B 6 / D 7 | B 5 / D 6 / A 4 |
|---|---|---|---|
| Graf |
|
|
|
| Dihedral symmetri | [14] | [12] | [10] |
| Coxeter plan | B 4 / D 5 | B 3 / D 4 / A 2 | B 2 / D 3 |
| Graf |
|
|
|
| Dihedral symmetri | [8] | [6] | [4] |
| Coxeter plan | En 5 | A 3 | |
| Graf |
|
|
|
| Dihedral symmetri | [6] | [4] |
Runcitruncated 7-ortoplex
| Runcitruncated 7-ortoplex | |
|---|---|
| Typ | enhetlig 7-polytop |
| Schläfli symbol | t 0,1,3 {3 5 ,4} |
| Coxeter-Dynkin diagram |
|
| 6 ansikten | |
| 5 ansikten | |
| 4 ansikten | |
| Celler | |
| ansikten | |
| Kanter | 50400 |
| Vertices | 6720 |
| Vertex figur | |
| Coxeter grupper | B 7 , [4,3 5 ] |
| Egenskaper | konvex |
Alternativa namn
- Prismatotruncated hecatonicosoctaexon (akronym: potaz) (Jonathan Bowers)
Bilder
| Coxeter plan | B 7 / A 6 | B 6 / D 7 | B 5 / D 6 / A 4 |
|---|---|---|---|
| Graf | för komplicerat |
|
|
| Dihedral symmetri | [14] | [12] | [10] |
| Coxeter plan | B 4 / D 5 | B 3 / D 4 / A 2 | B 2 / D 3 |
| Graf |
|
|
|
| Dihedral symmetri | [8] | [6] | [4] |
| Coxeter plan | En 5 | A 3 | |
| Graf |
|
|
|
| Dihedral symmetri | [6] | [4] |
Biruncitruncated 7-ortoplex
| Biruncitruncated 7-ortoplex | |
|---|---|
| Typ | enhetlig 7-polytop |
| Schläfli symbol | t 1,2,4 {3 5 ,4} |
| Coxeter-Dynkin diagram |
|
| 6 ansikten | |
| 5 ansikten | |
| 4 ansikten | |
| Celler | |
| ansikten | |
| Kanter | 120960 |
| Vertices | 20160 |
| Vertex figur | |
| Coxeter grupper | B 7 , [4,3 5 ] |
| Egenskaper | konvex |
Alternativa namn
- Biprismatotruncated hecatonicosoctaexon (akronym: döpa) (Jonathan Bowers)
Bilder
| Coxeter plan | B 7 / A 6 | B 6 / D 7 | B 5 / D 6 / A 4 |
|---|---|---|---|
| Graf |
|
|
|
| Dihedral symmetri | [14] | [12] | [10] |
| Coxeter plan | B 4 / D 5 | B 3 / D 4 / A 2 | B 2 / D 3 |
| Graf |
|
|
|
| Dihedral symmetri | [8] | [6] | [4] |
| Coxeter plan | En 5 | A 3 | |
| Graf |
|
|
|
| Dihedral symmetri | [6] | [4] |
Runcikantellerad 7-ortoplex
| Runcikantellerad 7-ortoplex | |
|---|---|
| Typ | enhetlig 7-polytop |
| Schläfli symbol | t 0,2,3 {3 5 ,4} |
| Coxeter-Dynkin diagram |
|
| 6 ansikten | |
| 5 ansikten | |
| 4 ansikten | |
| Celler | |
| ansikten | |
| Kanter | 33600 |
| Vertices | 6720 |
| Vertex figur | |
| Coxeter grupper | B 7 , [4,3 5 ] |
| Egenskaper | konvex |
Alternativa namn
- Prismatorhombated hecatonicosoctaexon (akronym: parz) (Jonathan Bowers)
Bilder
| Coxeter plan | B 7 / A 6 | B 6 / D 7 | B 5 / D 6 / A 4 |
|---|---|---|---|
| Graf | för komplicerat |
|
|
| Dihedral symmetri | [14] | [12] | [10] |
| Coxeter plan | B 4 / D 5 | B 3 / D 4 / A 2 | B 2 / D 3 |
| Graf |
|
|
|
| Dihedral symmetri | [8] | [6] | [4] |
| Coxeter plan | En 5 | A 3 | |
| Graf |
|
|
|
| Dihedral symmetri | [6] | [4] |
Biruncikantellerad 7-ortoplex
| biruncikantellerad 7-ortoplex | |
|---|---|
| Typ | enhetlig 7-polytop |
| Schläfli symbol | t 1,3,4 {3 5 ,4} |
| Coxeter-Dynkin diagram |
|
| 6 ansikten | |
| 5 ansikten | |
| 4 ansikten | |
| Celler | |
| ansikten | |
| Kanter | 100800 |
| Vertices | 20160 |
| Vertex figur | |
| Coxeter grupper | B 7 , [4,3 5 ] |
| Egenskaper | konvex |
Alternativa namn
- Biprismatorhombated hecatonicosoctaexon (akronym: boparz) (Jonathan Bowers)
Bilder
| Coxeter plan | B 7 / A 6 | B 6 / D 7 | B 5 / D 6 / A 4 |
|---|---|---|---|
| Graf |
|
|
|
| Dihedral symmetri | [14] | [12] | [10] |
| Coxeter plan | B 4 / D 5 | B 3 / D 4 / A 2 | B 2 / D 3 |
| Graf |
|
|
|
| Dihedral symmetri | [8] | [6] | [4] |
| Coxeter plan | En 5 | A 3 | |
| Graf |
|
|
|
| Dihedral symmetri | [6] | [4] |
Runcicantitruncated 7-ortoplex
| Runcicantitruncated 7-ortoplex | |
|---|---|
| Typ | enhetlig 7-polytop |
| Schläfli symbol | t 0,1,2,3 {3 5 ,4} |
| Coxeter-Dynkin diagram |
|
| 6 ansikten | |
| 5 ansikten | |
| 4 ansikten | |
| Celler | |
| ansikten | |
| Kanter | 60480 |
| Vertices | 13440 |
| Vertex figur | |
| Coxeter grupper | B 7 , [4,3 5 ] |
| Egenskaper | konvex |
Alternativa namn
- Great prismated hecatonicosoctaexon (akronym: gopaz) (Jonathan Bowers)
Bilder
| Coxeter plan | B 7 / A 6 | B 6 / D 7 | B 5 / D 6 / A 4 |
|---|---|---|---|
| Graf | för komplicerat |
|
|
| Dihedral symmetri | [14] | [12] | [10] |
| Coxeter plan | B 4 / D 5 | B 3 / D 4 / A 2 | B 2 / D 3 |
| Graf |
|
|
|
| Dihedral symmetri | [8] | [6] | [4] |
| Coxeter plan | En 5 | A 3 | |
| Graf |
|
|
|
| Dihedral symmetri | [6] | [4] |
Biruncicantitruncated 7-ortoplex
| biruncicantitruncated 7-ortoplex | |
|---|---|
| Typ | enhetlig 7-polytop |
| Schläfli symbol | t 1,2,3,4 {3 5 ,4} |
| Coxeter-Dynkin diagram |
|
| 6 ansikten | |
| 5 ansikten | |
| 4 ansikten | |
| Celler | |
| ansikten | |
| Kanter | 161280 |
| Vertices | 40320 |
| Vertex figur | |
| Coxeter grupper | B 7 , [4,3 5 ] |
| Egenskaper | konvex |
Alternativa namn
- Great biprismated hecatonicosoctaexon (akronym: gibpaz) (Jonathan Bowers)
Bilder
| Coxeter plan | B 7 / A 6 | B 6 / D 7 | B 5 / D 6 / A 4 |
|---|---|---|---|
| Graf |
|
|
|
| Dihedral symmetri | [14] | [12] | [10] |
| Coxeter plan | B 4 / D 5 | B 3 / D 4 / A 2 | B 2 / D 3 |
| Graf |
|
|
|
| Dihedral symmetri | [8] | [6] | [4] |
| Coxeter plan | En 5 | A 3 | |
| Graf |
|
|
|
| Dihedral symmetri | [6] | [4] |
Anteckningar
-
HSM Coxeter :
- HSM Coxeter, Regular Polytopes , 3:e upplagan, Dover New York, 1973
-
Kaleidoscopes: Selected Writings of HSM Coxeter , redigerad av F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 Wiley: Kaleidoscopes: Selected Wiley av HSM Coxeter
- (Papper 22) HSM Coxeter, Regular and Semi Regular Polytopes I , [Math. Zeit. 46 (1940) 380-407, MR 2,10]
- (Papper 23) HSM Coxeter, Regular and Semi-Regular Polytopes II , [Math. Zeit. 188 (1985) 559-591]
- (Papper 24) HSM Coxeter, Regular and Semi-Regular Polytopes III , [Math. Zeit. 200 (1988) 3-45]
-
Norman Johnson Uniform Polytopes , Manuscript (1991)
- NW Johnson: Theory of Uniform Polytopes and Honeycombs , Ph.D. (1966)
- Klitzing, Richard. "7D enhetliga polytoper (polyexa)" . o3o3o3x3o3o4x - spaz, o3x3o3o3x3o4o - sibpaz, o3o3o3x3x3o4x - potaz, o3o3x3o3x3x4o - döpa, o3o3o3x3x3o4x - parz, o3x3o3o3x -3xopa, o3x3o3o3xo -3xopa, o3x3o3o3xo -3xopa, o3x3o3o3xo z, o3o3x3x3x3x3o - gibpaz
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