9-simplex
(Redirected from Decayotton)
9-simplex | |
---|---|
Rank | 9 |
Type | Regular |
Notation | |
Bowers style acronym | Day |
Coxeter diagram | x3o3o3o3o3o3o3o3o () |
Schläfli symbol | {3,3,3,3,3,3,3,3} |
Tapertopic notation | 18 |
Elements | |
Yotta | 10 enneazetta |
Zetta | 45 octaexa |
Exa | 120 heptapeta |
Peta | 210 hexatera |
Tera | 252 pentachora |
Cells | 210 tetrahedra |
Faces | 120 triangles |
Edges | 45 |
Vertices | 10 |
Vertex figure | 8-simplex, edge length 1 |
Measures (edge length 1) | |
Circumradius | |
Inradius | |
Hypervolume | |
Diyottal angle | |
Height | |
Central density | 1 |
Number of external pieces | 10 |
Level of complexity | 1 |
Related polytopes | |
Army | Day |
Regiment | Day |
Dual | 9-simplex |
Conjugate | None |
Abstract & topological properties | |
Flag count | 3628800 |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | A9, order 3628800 |
Flag orbits | 1 |
Convex | Yes |
Nature | Tame |
The 9-simplex, also called the decayotton, or day, is the simplest possible non-degenerate 9-polytope. The full symmetry version has 10 regular 8-simplices as facets, joining 3 to a 6-simplex peak and 9 to a vertex, and is one of the 3 regular 9-polytopes. It is the 9-dimensional simplex.
Vertex coordinates[edit | edit source]
The vertices of a regular 9-simplex of edge length 1, centered at the origin, are given by:
- ,
- ,
- ,
- ,
- ,
- ,
- ,
- ,
- .
Much simpler coordinates can be given in ten dimensions, as all permutations of:
- .
External links[edit | edit source]
- Klitzing, Richard. "day".
- Wikipedia contributors. "9-simplex".