9-simplex: Difference between revisions
Content deleted Content added
No edit summary |
No edit summary |
||
| Line 42: | Line 42: | ||
A '''decayotton''', or '''deca-9-tope''' is a 9-[[simplex]], a self-dual [[Regular polytope|regular]] [[9-polytope]] with 10 [[vertex (geometry)|vertices]], 45 [[Edge (geometry)|edge]]s, 120 triangle [[Face (geometry)|faces]], 210 tetrahedral [[Cell (mathematics)|cells]], 252 [[5-cell]] 4-faces, 210 [[5-simplex]] 5-faces, 120 [[6-simplex]] 6-faces, 45 [[7-simplex]] 7-faces, and 10 [[8-simplex]] 8-faces. |
A '''decayotton''', or '''deca-9-tope''' is a 9-[[simplex]], a self-dual [[Regular polytope|regular]] [[9-polytope]] with 10 [[vertex (geometry)|vertices]], 45 [[Edge (geometry)|edge]]s, 120 triangle [[Face (geometry)|faces]], 210 tetrahedral [[Cell (mathematics)|cells]], 252 [[5-cell]] 4-faces, 210 [[5-simplex]] 5-faces, 120 [[6-simplex]] 6-faces, 45 [[7-simplex]] 7-faces, and 10 [[8-simplex]] 8-faces. |
||
The [[5-polytope#A note on generality of terms for n-polytopes and elements|name]] ''decayotton'' is derived from ''deca'' for ten [[Facet (mathematics)|facets]] in [[Greek language|Greek]] and [[Yotta|-yott]] for eight, having 8-dimensional facets, and ''-on''. |
The [[5-polytope#A note on generality of terms for n-polytopes and elements|name]] ''decayotton'' is derived from ''deca'' for ten [[Facet (mathematics)|facets]] in [[Greek language|Greek]] and [[Yotta|-yott]] (variation of oct for eight), having 8-dimensional facets, and ''-on''. |
||
== See also == |
== See also == |
||
Revision as of 03:09, 4 September 2008
| Regular decayotton 9-simplex | |
|---|---|
 Orthogonal projection inside Petrie polygon | |
| Type | Regular 9-polytope |
| Family | simplex |
| 8-faces | 10 8-simplex
|
| 7-faces | 45 7-simplex
|
| 6-faces | 120 6-simplex
|
| 5-faces | 210 5-simplex
|
| 4-faces | 252 5-cell
|
| Cells | 210 tetrahedron
|
| Faces | 120 triangle
|
| Edges | 45 |
| Vertices | 10 |
| Vertex figure | 8-simplex |
| Petrie polygon | decagon |
| Schläfli symbol | {3,3,3,3,3,3,3,3} |
| Coxeter-Dynkin diagram |   
|
| Coxeter group | A9 [3,3,3,3,3,3,3,3] |
| Dual | Self-dual |
| Properties | convex |
A decayotton, or deca-9-tope is a 9-simplex, a self-dual regular 9-polytope with 10 vertices, 45 edges, 120 triangle faces, 210 tetrahedral cells, 252 5-cell 4-faces, 210 5-simplex 5-faces, 120 6-simplex 6-faces, 45 7-simplex 7-faces, and 10 8-simplex 8-faces.
The name decayotton is derived from deca for ten facets in Greek and -yott (variation of oct for eight), having 8-dimensional facets, and -on.
See also
- Other regular 9-polytopes:
- Enneract - {4,3,3,3,3,3,3,3}
- Enneacross - {3,3,3,3,3,3,3,4}
- Others in the simplex family
- Tetrahedron - {3,3}
- 5-cell - {3,3,3}
- 5-simplex - {3,3,3,3}
- 6-simplex - {3,3,3,3,3}
- 7-simplex - {3,3,3,3,3,3}
- 8-simplex - {3,3,3,3,3,3,3}
- 9-simplex - {3,3,3,3,3,3,3,3}
- 10-simplex - {3,3,3,3,3,3,3,3,3}
External links
 | This geometry-related article is a stub. You can help Wikipedia by expanding it. |